%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP125-3.005 : 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 : n008.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 07:27:39 AM UTC 2026
% Result : Unsatisfiable 19.50s 5.78s
% Output : CNFRefutation 19.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 93
% Number of leaves : 48
% Syntax : Number of formulae : 520 ( 114 unt; 0 def)
% Number of atoms : 1469 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1474 ( 525 ~; 949 |; 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 : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 245 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2),
file('theBenchmark.p',e_1_is_not_e_2) ).
cnf(c_1,plain,
~ equalish(e_1,e_2),
inference(clausify,[status(thm)],[e_1_is_not_e_2]) ).
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_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
file('theBenchmark.p',e_1_is_not_e_3) ).
cnf(c_5,plain,
~ equalish(e_1,e_3),
inference(clausify,[status(thm)],[e_1_is_not_e_3]) ).
fof(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('theBenchmark.p',e_2_is_not_e_1) ).
cnf(c_8,plain,
~ equalish(e_2,e_1),
inference(clausify,[status(thm)],[e_2_is_not_e_1]) ).
fof(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3),
file('theBenchmark.p',e_2_is_not_e_3) ).
cnf(c_9,plain,
~ equalish(e_2,e_3),
inference(clausify,[status(thm)],[e_2_is_not_e_3]) ).
fof(e_2_is_not_e_4,axiom,
~ equalish(e_2,e_4),
file('theBenchmark.p',e_2_is_not_e_4) ).
cnf(c_10,plain,
~ equalish(e_2,e_4),
inference(clausify,[status(thm)],[e_2_is_not_e_4]) ).
fof(e_2_is_not_e_5,axiom,
~ equalish(e_2,e_5),
file('theBenchmark.p',e_2_is_not_e_5) ).
cnf(c_11,plain,
~ equalish(e_2,e_5),
inference(clausify,[status(thm)],[e_2_is_not_e_5]) ).
fof(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('theBenchmark.p',e_3_is_not_e_1) ).
cnf(c_12,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_13,plain,
~ equalish(e_3,e_2),
inference(clausify,[status(thm)],[e_3_is_not_e_2]) ).
fof(e_3_is_not_e_5,axiom,
~ equalish(e_3,e_5),
file('theBenchmark.p',e_3_is_not_e_5) ).
cnf(c_15,plain,
~ equalish(e_3,e_5),
inference(clausify,[status(thm)],[e_3_is_not_e_5]) ).
fof(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1),
file('theBenchmark.p',e_4_is_not_e_1) ).
cnf(c_16,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_17,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_18,plain,
~ equalish(e_4,e_3),
inference(clausify,[status(thm)],[e_4_is_not_e_3]) ).
fof(e_5_is_not_e_1,axiom,
~ equalish(e_5,e_1),
file('theBenchmark.p',e_5_is_not_e_1) ).
cnf(c_20,plain,
~ equalish(e_5,e_1),
inference(clausify,[status(thm)],[e_5_is_not_e_1]) ).
fof(e_5_is_not_e_2,axiom,
~ equalish(e_5,e_2),
file('theBenchmark.p',e_5_is_not_e_2) ).
cnf(c_21,plain,
~ equalish(e_5,e_2),
inference(clausify,[status(thm)],[e_5_is_not_e_2]) ).
fof(e_5_is_not_e_3,axiom,
~ equalish(e_5,e_3),
file('theBenchmark.p',e_5_is_not_e_3) ).
cnf(c_22,plain,
~ equalish(e_5,e_3),
inference(clausify,[status(thm)],[e_5_is_not_e_3]) ).
fof(e_5_is_not_e_4,axiom,
~ equalish(e_5,e_4),
file('theBenchmark.p',e_5_is_not_e_4) ).
cnf(c_23,plain,
~ equalish(e_5,e_4),
inference(clausify,[status(thm)],[e_5_is_not_e_4]) ).
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_24,plain,
( equalish(C,D)
| ~ product(A,B,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_total_function2]) ).
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_25,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_26,plain,
( equalish(A,D)
| ~ product(D,B,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_left_cancellation]) ).
cnf(c_27,plain,
( ~ product(e_1,A,B)
| ~ product(e_2,A,B) ),
inference(resolve,[status(thm)],[c_26,c_8]) ).
cnf(c_28,plain,
( ~ product(e_1,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_26,c_12]) ).
cnf(c_29,plain,
( ~ product(e_2,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_26,c_13]) ).
cnf(c_30,plain,
( ~ product(e_1,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_26,c_16]) ).
cnf(c_31,plain,
( ~ product(e_2,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_26,c_17]) ).
cnf(c_32,plain,
( ~ product(e_3,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_26,c_18]) ).
cnf(c_33,plain,
( ~ product(e_1,A,B)
| ~ product(e_5,A,B) ),
inference(resolve,[status(thm)],[c_26,c_20]) ).
cnf(c_34,plain,
( ~ product(e_2,A,B)
| ~ product(e_5,A,B) ),
inference(resolve,[status(thm)],[c_26,c_21]) ).
cnf(c_35,plain,
( ~ product(e_3,A,B)
| ~ product(e_5,A,B) ),
inference(resolve,[status(thm)],[c_26,c_22]) ).
cnf(c_36,plain,
( ~ product(e_4,A,B)
| ~ product(e_5,A,B) ),
inference(resolve,[status(thm)],[c_26,c_23]) ).
cnf(c_37,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolve,[status(thm)],[c_25,c_8]) ).
cnf(c_38,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_25,c_12]) ).
cnf(c_39,plain,
( ~ product(A,e_2,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_25,c_13]) ).
cnf(c_40,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_25,c_16]) ).
cnf(c_41,plain,
( ~ product(A,e_2,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_25,c_17]) ).
cnf(c_42,plain,
( ~ product(A,e_3,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_25,c_18]) ).
cnf(c_43,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_5,B) ),
inference(resolve,[status(thm)],[c_25,c_20]) ).
cnf(c_44,plain,
( ~ product(A,e_2,B)
| ~ product(A,e_5,B) ),
inference(resolve,[status(thm)],[c_25,c_21]) ).
cnf(c_45,plain,
( ~ product(A,e_3,B)
| ~ product(A,e_5,B) ),
inference(resolve,[status(thm)],[c_25,c_22]) ).
cnf(c_46,plain,
( ~ product(A,e_4,B)
| ~ product(A,e_5,B) ),
inference(resolve,[status(thm)],[c_25,c_23]) ).
cnf(c_47,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_2) ),
inference(resolve,[status(thm)],[c_24,c_8]) ).
cnf(c_48,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_3) ),
inference(resolve,[status(thm)],[c_24,c_12]) ).
cnf(c_49,plain,
( ~ product(A,B,e_2)
| ~ product(A,B,e_3) ),
inference(resolve,[status(thm)],[c_24,c_13]) ).
cnf(c_50,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_4) ),
inference(resolve,[status(thm)],[c_24,c_16]) ).
cnf(c_52,plain,
( ~ product(A,B,e_3)
| ~ product(A,B,e_4) ),
inference(resolve,[status(thm)],[c_24,c_18]) ).
cnf(c_53,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_5) ),
inference(resolve,[status(thm)],[c_24,c_20]) ).
cnf(c_54,plain,
( ~ product(A,B,e_2)
| ~ product(A,B,e_5) ),
inference(resolve,[status(thm)],[c_24,c_21]) ).
cnf(c_68,plain,
( ~ next(C,e_3)
| ~ greater(e_4,e_0)
| ~ next(A,B)
| ~ cycle(B,C)
| ~ cycle(A,e_4) ),
inference(resolve,[status(thm)],[c_18,c_3]) ).
cnf(c_69,plain,
( ~ next(A,e_3)
| ~ greater(B,e_0)
| ~ product(A,e_1,e_4)
| ~ cycle(A,B) ),
inference(resolve,[status(thm)],[c_18,c_2]) ).
cnf(c_70,plain,
( ~ next(C,e_2)
| ~ greater(e_4,e_0)
| ~ next(A,B)
| ~ cycle(B,C)
| ~ cycle(A,e_4) ),
inference(resolve,[status(thm)],[c_17,c_3]) ).
cnf(c_72,plain,
( ~ next(C,e_1)
| ~ greater(e_4,e_0)
| ~ next(A,B)
| ~ cycle(B,C)
| ~ cycle(A,e_4) ),
inference(resolve,[status(thm)],[c_16,c_3]) ).
cnf(c_76,plain,
( ~ next(A,e_5)
| ~ greater(B,e_0)
| ~ product(A,e_1,e_3)
| ~ cycle(A,B) ),
inference(resolve,[status(thm)],[c_15,c_2]) ).
cnf(c_80,plain,
( ~ next(C,e_2)
| ~ greater(e_3,e_0)
| ~ next(A,B)
| ~ cycle(B,C)
| ~ cycle(A,e_3) ),
inference(resolve,[status(thm)],[c_13,c_3]) ).
cnf(c_82,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_12,c_3]) ).
cnf(c_86,plain,
( ~ next(A,e_5)
| ~ greater(B,e_0)
| ~ product(A,e_1,e_2)
| ~ cycle(A,B) ),
inference(resolve,[status(thm)],[c_11,c_2]) ).
cnf(c_89,plain,
( ~ next(A,e_4)
| ~ greater(B,e_0)
| ~ product(A,e_1,e_2)
| ~ cycle(A,B) ),
inference(resolve,[status(thm)],[c_10,c_2]) ).
cnf(c_91,plain,
( ~ next(C,e_3)
| ~ greater(e_2,e_0)
| ~ next(A,B)
| ~ cycle(B,C)
| ~ cycle(A,e_2) ),
inference(resolve,[status(thm)],[c_9,c_3]) ).
cnf(c_93,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_8,c_3]) ).
cnf(c_102,plain,
( ~ next(C,e_3)
| ~ greater(e_1,e_0)
| ~ next(A,B)
| ~ cycle(B,C)
| ~ cycle(A,e_1) ),
inference(resolve,[status(thm)],[c_5,c_3]) ).
cnf(c_105,plain,
( ~ next(C,e_2)
| ~ greater(e_1,e_0)
| ~ next(A,B)
| ~ cycle(B,C)
| ~ cycle(A,e_1) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
fof(qg3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( product(VAR_2,VAR_3,VAR_0)
| ~ product(VAR_1,VAR_0,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg3) ).
cnf(c_107,plain,
( product(C,D,A)
| ~ product(B,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_108,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_5)
| 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_109,plain,
( product(A,B,e_5)
| 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_5,axiom,
group_element(e_5),
file('theBenchmark.p',element_5) ).
cnf(c_110,plain,
group_element(e_5),
inference(clausify,[status(thm)],[element_5]) ).
fof(element_4,axiom,
group_element(e_4),
file('theBenchmark.p',element_4) ).
cnf(c_111,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_112,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_113,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_114,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_115,plain,
( ~ greater(B,A)
| ~ product(A,e_1,B)
| ~ cycle(A,e_0) ),
inference(clausify,[status(thm)],[cycle6]) ).
fof(cycle5,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ greater(VAR_1,VAR_4)
| ~ greater(VAR_2,VAR_0)
| ~ next(VAR_2,VAR_3)
| ~ cycle(VAR_3,VAR_4)
| ~ cycle(VAR_2,e_0)
| ~ cycle(VAR_0,VAR_1) ),
file('theBenchmark.p',cycle5) ).
cnf(c_116,plain,
( ~ greater(B,E)
| ~ greater(C,A)
| ~ next(C,D)
| ~ cycle(D,E)
| ~ cycle(C,e_0)
| ~ cycle(A,B) ),
inference(clausify,[status(thm)],[cycle5]) ).
fof(cycle3,axiom,
cycle(e_5,e_0),
file('theBenchmark.p',cycle3) ).
cnf(c_117,plain,
cycle(e_5,e_0),
inference(clausify,[status(thm)],[cycle3]) ).
fof(cycle2,axiom,
! [VAR_0] :
( cycle(VAR_0,e_4)
| 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_118,plain,
( cycle(A,e_4)
| 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_5_greater_e_4,axiom,
greater(e_5,e_4),
file('theBenchmark.p',e_5_greater_e_4) ).
cnf(c_119,plain,
greater(e_5,e_4),
inference(clausify,[status(thm)],[e_5_greater_e_4]) ).
fof(e_5_greater_e_3,axiom,
greater(e_5,e_3),
file('theBenchmark.p',e_5_greater_e_3) ).
cnf(c_120,plain,
greater(e_5,e_3),
inference(clausify,[status(thm)],[e_5_greater_e_3]) ).
fof(e_4_greater_e_3,axiom,
greater(e_4,e_3),
file('theBenchmark.p',e_4_greater_e_3) ).
cnf(c_121,plain,
greater(e_4,e_3),
inference(clausify,[status(thm)],[e_4_greater_e_3]) ).
fof(e_4_greater_e_2,axiom,
greater(e_4,e_2),
file('theBenchmark.p',e_4_greater_e_2) ).
cnf(c_123,plain,
greater(e_4,e_2),
inference(clausify,[status(thm)],[e_4_greater_e_2]) ).
fof(e_3_greater_e_2,axiom,
greater(e_3,e_2),
file('theBenchmark.p',e_3_greater_e_2) ).
cnf(c_124,plain,
greater(e_3,e_2),
inference(clausify,[status(thm)],[e_3_greater_e_2]) ).
fof(e_3_greater_e_1,axiom,
greater(e_3,e_1),
file('theBenchmark.p',e_3_greater_e_1) ).
cnf(c_127,plain,
greater(e_3,e_1),
inference(clausify,[status(thm)],[e_3_greater_e_1]) ).
fof(e_4_greater_e_0,axiom,
greater(e_4,e_0),
file('theBenchmark.p',e_4_greater_e_0) ).
cnf(c_130,plain,
greater(e_4,e_0),
inference(clausify,[status(thm)],[e_4_greater_e_0]) ).
fof(e_3_greater_e_0,axiom,
greater(e_3,e_0),
file('theBenchmark.p',e_3_greater_e_0) ).
cnf(c_131,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_132,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_133,plain,
greater(e_1,e_0),
inference(clausify,[status(thm)],[e_1_greater_e_0]) ).
fof(e_4_then_e_5,axiom,
next(e_4,e_5),
file('theBenchmark.p',e_4_then_e_5) ).
cnf(c_134,plain,
next(e_4,e_5),
inference(clausify,[status(thm)],[e_4_then_e_5]) ).
fof(e_3_then_e_4,axiom,
next(e_3,e_4),
file('theBenchmark.p',e_3_then_e_4) ).
cnf(c_135,plain,
next(e_3,e_4),
inference(clausify,[status(thm)],[e_3_then_e_4]) ).
fof(e_2_then_e_3,axiom,
next(e_2,e_3),
file('theBenchmark.p',e_2_then_e_3) ).
cnf(c_136,plain,
next(e_2,e_3),
inference(clausify,[status(thm)],[e_2_then_e_3]) ).
fof(e_1_then_e_2,axiom,
next(e_1,e_2),
file('theBenchmark.p',e_1_then_e_2) ).
cnf(c_137,plain,
next(e_1,e_2),
inference(clausify,[status(thm)],[e_1_then_e_2]) ).
fof(e_0_then_e_1,axiom,
next(e_0,e_1),
file('theBenchmark.p',e_0_then_e_1) ).
cnf(c_138,plain,
next(e_0,e_1),
inference(clausify,[status(thm)],[e_0_then_e_1]) ).
cnf(c_12851,plain,
( ~ greater(e_4,e_0)
| ~ next(A,e_3)
| ~ cycle(e_3,A)
| ~ cycle(A,e_4) ),
inference(factor,[status(thm)],[c_68]) ).
cnf(c_149,plain,
( ~ next(A,e_3)
| ~ cycle(e_3,A)
| ~ cycle(A,e_4) ),
inference(resolve,[status(thm)],[c_130,c_12851]) ).
cnf(c_12852,plain,
( ~ greater(e_2,e_0)
| ~ next(A,e_3)
| ~ cycle(e_3,A)
| ~ cycle(A,e_2) ),
inference(factor,[status(thm)],[c_91]) ).
cnf(c_163,plain,
( ~ next(A,e_3)
| ~ cycle(e_3,A)
| ~ cycle(A,e_2) ),
inference(resolve,[status(thm)],[c_132,c_12852]) ).
cnf(c_12853,plain,
( ~ greater(e_1,e_0)
| ~ next(A,e_3)
| ~ cycle(e_3,A)
| ~ cycle(A,e_1) ),
inference(factor,[status(thm)],[c_102]) ).
cnf(c_170,plain,
( ~ next(A,e_3)
| ~ cycle(e_3,A)
| ~ cycle(A,e_1) ),
inference(resolve,[status(thm)],[c_133,c_12853]) ).
cnf(c_183,plain,
( ~ next(C,e_1)
| ~ next(A,B)
| ~ cycle(B,C)
| ~ cycle(A,e_4) ),
inference(resolve,[status(thm)],[c_130,c_72]) ).
cnf(c_184,plain,
( ~ next(C,e_2)
| ~ next(A,B)
| ~ cycle(B,C)
| ~ cycle(A,e_4) ),
inference(resolve,[status(thm)],[c_130,c_70]) ).
cnf(c_187,plain,
( ~ next(C,e_1)
| ~ next(A,B)
| ~ cycle(B,C)
| ~ cycle(A,e_3) ),
inference(resolve,[status(thm)],[c_131,c_82]) ).
cnf(c_188,plain,
( ~ next(C,e_2)
| ~ next(A,B)
| ~ cycle(B,C)
| ~ cycle(A,e_3) ),
inference(resolve,[status(thm)],[c_131,c_80]) ).
cnf(c_191,plain,
( ~ next(C,e_1)
| ~ next(A,B)
| ~ cycle(B,C)
| ~ cycle(A,e_2) ),
inference(resolve,[status(thm)],[c_132,c_93]) ).
cnf(c_195,plain,
( ~ next(C,e_2)
| ~ next(A,B)
| ~ cycle(B,C)
| ~ cycle(A,e_1) ),
inference(resolve,[status(thm)],[c_133,c_105]) ).
cnf(c_210,plain,
~ product(e_5,e_5,e_1),
inference(resolve,[status(thm)],[c_108,c_53]) ).
cnf(c_211,plain,
~ product(e_4,e_4,e_3),
inference(resolve,[status(thm)],[c_108,c_52]) ).
cnf(c_213,plain,
~ product(e_4,e_4,e_1),
inference(resolve,[status(thm)],[c_108,c_50]) ).
cnf(c_215,plain,
~ product(e_3,e_3,e_1),
inference(resolve,[status(thm)],[c_108,c_48]) ).
cnf(c_216,plain,
~ product(e_2,e_2,e_1),
inference(resolve,[status(thm)],[c_108,c_47]) ).
cnf(c_217,plain,
~ product(e_5,e_4,e_5),
inference(resolve,[status(thm)],[c_108,c_46]) ).
cnf(c_220,plain,
~ product(e_5,e_1,e_5),
inference(resolve,[status(thm)],[c_108,c_43]) ).
cnf(c_223,plain,
~ product(e_4,e_1,e_4),
inference(resolve,[status(thm)],[c_108,c_40]) ).
cnf(c_225,plain,
~ product(e_3,e_1,e_3),
inference(resolve,[status(thm)],[c_108,c_38]) ).
cnf(c_226,plain,
~ product(e_2,e_1,e_2),
inference(resolve,[status(thm)],[c_108,c_37]) ).
cnf(c_227,plain,
~ product(e_4,e_5,e_5),
inference(resolve,[status(thm)],[c_108,c_36]) ).
cnf(c_228,plain,
~ product(e_3,e_5,e_5),
inference(resolve,[status(thm)],[c_108,c_35]) ).
cnf(c_230,plain,
~ product(e_1,e_5,e_5),
inference(resolve,[status(thm)],[c_108,c_33]) ).
cnf(c_232,plain,
~ product(e_2,e_4,e_4),
inference(resolve,[status(thm)],[c_108,c_31]) ).
cnf(c_233,plain,
~ product(e_1,e_4,e_4),
inference(resolve,[status(thm)],[c_108,c_30]) ).
cnf(c_234,plain,
~ product(e_2,e_3,e_3),
inference(resolve,[status(thm)],[c_108,c_29]) ).
cnf(c_235,plain,
~ product(e_1,e_3,e_3),
inference(resolve,[status(thm)],[c_108,c_28]) ).
cnf(c_236,plain,
~ product(e_1,e_2,e_2),
inference(resolve,[status(thm)],[c_108,c_27]) ).
cnf(c_237,plain,
( product(A,e_5,e_5)
| product(A,e_5,e_4)
| product(A,e_5,e_3)
| product(A,e_5,e_2)
| product(A,e_5,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_110,c_109]) ).
cnf(c_238,plain,
( product(e_5,A,e_5)
| product(e_5,A,e_4)
| product(e_5,A,e_3)
| product(e_5,A,e_2)
| product(e_5,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_110,c_109]) ).
cnf(c_239,plain,
( product(A,e_4,e_5)
| 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_111,c_109]) ).
cnf(c_240,plain,
( product(e_4,A,e_5)
| 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_111,c_109]) ).
cnf(c_241,plain,
( product(A,e_3,e_5)
| 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_112,c_109]) ).
cnf(c_242,plain,
( product(e_3,A,e_5)
| 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_112,c_109]) ).
cnf(c_243,plain,
( product(A,e_2,e_5)
| 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_113,c_109]) ).
cnf(c_244,plain,
( product(e_2,A,e_5)
| product(e_2,A,e_4)
| product(e_2,A,e_3)
| product(e_2,A,e_2)
| product(e_2,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_113,c_109]) ).
cnf(c_249,plain,
( cycle(e_2,e_4)
| cycle(e_2,e_3)
| cycle(e_2,e_2)
| cycle(e_2,e_1)
| cycle(e_2,e_0) ),
inference(resolve,[status(thm)],[c_118,c_113]) ).
cnf(c_250,plain,
( cycle(e_3,e_4)
| 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_118,c_112]) ).
cnf(c_251,plain,
( cycle(e_4,e_4)
| cycle(e_4,e_3)
| cycle(e_4,e_2)
| cycle(e_4,e_1)
| cycle(e_4,e_0) ),
inference(resolve,[status(thm)],[c_118,c_111]) ).
cnf(c_252,plain,
( ~ greater(B,C)
| ~ greater(e_4,A)
| ~ cycle(e_5,C)
| ~ cycle(e_4,e_0)
| ~ cycle(A,B) ),
inference(resolve,[status(thm)],[c_134,c_116]) ).
cnf(c_256,plain,
( ~ greater(B,C)
| ~ greater(e_3,A)
| ~ cycle(e_4,C)
| ~ cycle(e_3,e_0)
| ~ cycle(A,B) ),
inference(resolve,[status(thm)],[c_135,c_116]) ).
cnf(c_276,plain,
( ~ cycle(e_3,e_2)
| ~ cycle(e_2,e_4) ),
inference(resolve,[status(thm)],[c_149,c_136]) ).
cnf(c_285,plain,
( ~ cycle(e_3,e_2)
| ~ cycle(e_2,e_2) ),
inference(resolve,[status(thm)],[c_163,c_136]) ).
cnf(c_289,plain,
( ~ cycle(e_3,e_2)
| ~ cycle(e_2,e_1) ),
inference(resolve,[status(thm)],[c_170,c_136]) ).
cnf(c_317,plain,
( ~ next(A,e_1)
| ~ cycle(e_3,A)
| ~ cycle(e_2,e_4) ),
inference(resolve,[status(thm)],[c_183,c_136]) ).
cnf(c_318,plain,
( ~ next(A,e_1)
| ~ cycle(e_4,A)
| ~ cycle(e_3,e_4) ),
inference(resolve,[status(thm)],[c_183,c_135]) ).
cnf(c_319,plain,
( ~ next(A,e_1)
| ~ cycle(e_5,A)
| ~ cycle(e_4,e_4) ),
inference(resolve,[status(thm)],[c_183,c_134]) ).
cnf(c_324,plain,
( ~ next(A,e_2)
| ~ cycle(e_4,A)
| ~ cycle(e_3,e_4) ),
inference(resolve,[status(thm)],[c_184,c_135]) ).
cnf(c_341,plain,
( ~ next(A,e_1)
| ~ cycle(e_3,A)
| ~ cycle(e_2,e_3) ),
inference(resolve,[status(thm)],[c_187,c_136]) ).
cnf(c_342,plain,
( ~ next(A,e_1)
| ~ cycle(e_4,A)
| ~ cycle(e_3,e_3) ),
inference(resolve,[status(thm)],[c_187,c_135]) ).
cnf(c_343,plain,
( ~ next(A,e_1)
| ~ cycle(e_5,A)
| ~ cycle(e_4,e_3) ),
inference(resolve,[status(thm)],[c_187,c_134]) ).
cnf(c_348,plain,
( ~ next(A,e_2)
| ~ cycle(e_4,A)
| ~ cycle(e_3,e_3) ),
inference(resolve,[status(thm)],[c_188,c_135]) ).
cnf(c_365,plain,
( ~ next(A,e_1)
| ~ cycle(e_3,A)
| ~ cycle(e_2,e_2) ),
inference(resolve,[status(thm)],[c_191,c_136]) ).
cnf(c_366,plain,
( ~ next(A,e_1)
| ~ cycle(e_4,A)
| ~ cycle(e_3,e_2) ),
inference(resolve,[status(thm)],[c_191,c_135]) ).
cnf(c_367,plain,
( ~ next(A,e_1)
| ~ cycle(e_5,A)
| ~ cycle(e_4,e_2) ),
inference(resolve,[status(thm)],[c_191,c_134]) ).
cnf(c_390,plain,
( ~ next(A,e_2)
| ~ cycle(e_4,A)
| ~ cycle(e_3,e_1) ),
inference(resolve,[status(thm)],[c_195,c_135]) ).
cnf(c_12854,plain,
( product(e_1,e_5,e_5)
| product(e_1,e_5,e_4)
| product(e_1,e_5,e_3)
| product(e_1,e_5,e_2)
| product(e_1,e_5,e_1) ),
inference(resolve,[status(thm)],[c_237,c_114]) ).
cnf(c_434,plain,
( product(e_1,e_5,e_4)
| product(e_1,e_5,e_3)
| product(e_1,e_5,e_2)
| product(e_1,e_5,e_1) ),
inference(resolve,[status(thm)],[c_230,c_12854]) ).
cnf(c_12855,plain,
( product(e_3,e_5,e_5)
| product(e_3,e_5,e_4)
| product(e_3,e_5,e_3)
| product(e_3,e_5,e_2)
| product(e_3,e_5,e_1) ),
inference(resolve,[status(thm)],[c_237,c_112]) ).
cnf(c_436,plain,
( product(e_3,e_5,e_4)
| product(e_3,e_5,e_3)
| product(e_3,e_5,e_2)
| product(e_3,e_5,e_1) ),
inference(resolve,[status(thm)],[c_228,c_12855]) ).
cnf(c_12856,plain,
( product(e_4,e_5,e_5)
| product(e_4,e_5,e_4)
| product(e_4,e_5,e_3)
| product(e_4,e_5,e_2)
| product(e_4,e_5,e_1) ),
inference(resolve,[status(thm)],[c_237,c_111]) ).
cnf(c_437,plain,
( product(e_4,e_5,e_4)
| product(e_4,e_5,e_3)
| product(e_4,e_5,e_2)
| product(e_4,e_5,e_1) ),
inference(resolve,[status(thm)],[c_227,c_12856]) ).
cnf(c_12857,plain,
( ~ product(e_1,e_1,e_1)
| product(e_1,e_5,e_4)
| product(e_1,e_5,e_3)
| product(e_1,e_5,e_2) ),
inference(resolve,[status(thm)],[c_434,c_43]) ).
cnf(c_443,plain,
( product(e_1,e_5,e_4)
| product(e_1,e_5,e_3)
| product(e_1,e_5,e_2) ),
inference(resolve,[status(thm)],[c_108,c_12857]) ).
cnf(c_460,plain,
( product(e_2,A,e_1)
| ~ product(e_5,e_1,A)
| product(e_1,e_5,e_4)
| product(e_1,e_5,e_3) ),
inference(resolve,[status(thm)],[c_443,c_107]) ).
cnf(c_472,plain,
( product(e_4,A,e_1)
| ~ product(e_5,e_1,A)
| product(e_1,e_5,e_3)
| product(e_1,e_5,e_2) ),
inference(resolve,[status(thm)],[c_443,c_107]) ).
cnf(c_12858,plain,
( product(e_5,e_1,e_5)
| product(e_5,e_1,e_4)
| product(e_5,e_1,e_3)
| product(e_5,e_1,e_2)
| product(e_5,e_1,e_1) ),
inference(resolve,[status(thm)],[c_238,c_114]) ).
cnf(c_478,plain,
( product(e_5,e_1,e_4)
| product(e_5,e_1,e_3)
| product(e_5,e_1,e_2)
| product(e_5,e_1,e_1) ),
inference(resolve,[status(thm)],[c_220,c_12858]) ).
cnf(c_12859,plain,
( product(e_5,e_4,e_5)
| product(e_5,e_4,e_4)
| product(e_5,e_4,e_3)
| product(e_5,e_4,e_2)
| product(e_5,e_4,e_1) ),
inference(resolve,[status(thm)],[c_238,c_111]) ).
cnf(c_481,plain,
( product(e_5,e_4,e_4)
| product(e_5,e_4,e_3)
| product(e_5,e_4,e_2)
| product(e_5,e_4,e_1) ),
inference(resolve,[status(thm)],[c_217,c_12859]) ).
cnf(c_12860,plain,
( product(e_1,e_4,e_5)
| 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_239,c_114]) ).
cnf(c_482,plain,
( product(e_1,e_4,e_5)
| 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_233,c_12860]) ).
cnf(c_12861,plain,
( product(e_2,e_4,e_5)
| 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_239,c_113]) ).
cnf(c_483,plain,
( product(e_2,e_4,e_5)
| 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_232,c_12861]) ).
cnf(c_12862,plain,
( product(e_4,e_1,e_5)
| 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_240,c_114]) ).
cnf(c_489,plain,
( product(e_4,e_1,e_5)
| 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_223,c_12862]) ).
cnf(c_12863,plain,
( product(e_1,e_3,e_5)
| 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_241,c_114]) ).
cnf(c_492,plain,
( product(e_1,e_3,e_5)
| product(e_1,e_3,e_4)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_235,c_12863]) ).
cnf(c_12864,plain,
( product(e_2,e_3,e_5)
| product(e_2,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_241,c_113]) ).
cnf(c_493,plain,
( product(e_2,e_3,e_5)
| product(e_2,e_3,e_4)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_234,c_12864]) ).
cnf(c_12865,plain,
( product(e_3,e_1,e_5)
| 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_242,c_114]) ).
cnf(c_499,plain,
( product(e_3,e_1,e_5)
| product(e_3,e_1,e_4)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolve,[status(thm)],[c_225,c_12865]) ).
cnf(c_12866,plain,
( product(e_1,e_2,e_5)
| 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_243,c_114]) ).
cnf(c_501,plain,
( product(e_1,e_2,e_5)
| product(e_1,e_2,e_4)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_236,c_12866]) ).
cnf(c_12867,plain,
( product(e_2,e_1,e_5)
| product(e_2,e_1,e_4)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_244,c_114]) ).
cnf(c_511,plain,
( product(e_2,e_1,e_5)
| product(e_2,e_1,e_4)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_226,c_12867]) ).
cnf(c_527,plain,
( ~ greater(B,e_0)
| ~ greater(e_4,A)
| ~ cycle(e_4,e_0)
| ~ cycle(A,B) ),
inference(resolve,[status(thm)],[c_252,c_117]) ).
cnf(c_12868,plain,
( cycle(e_2,e_4)
| cycle(e_2,e_2)
| cycle(e_2,e_1)
| cycle(e_2,e_0)
| ~ greater(e_3,A)
| ~ greater(e_3,e_2)
| ~ cycle(e_4,A)
| ~ cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_256,c_249]) ).
cnf(c_587,plain,
( cycle(e_2,e_4)
| cycle(e_2,e_2)
| cycle(e_2,e_1)
| cycle(e_2,e_0)
| ~ greater(e_3,A)
| ~ cycle(e_4,A)
| ~ cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_124,c_12868]) ).
cnf(c_632,plain,
( ~ cycle(e_3,e_0)
| ~ cycle(e_2,e_4) ),
inference(resolve,[status(thm)],[c_317,c_138]) ).
cnf(c_635,plain,
( ~ cycle(e_4,e_0)
| ~ cycle(e_3,e_4) ),
inference(resolve,[status(thm)],[c_318,c_138]) ).
cnf(c_12869,plain,
( ~ cycle(e_5,e_0)
| ~ cycle(e_4,e_4) ),
inference(resolve,[status(thm)],[c_319,c_138]) ).
cnf(c_640,plain,
~ cycle(e_4,e_4),
inference(resolve,[status(thm)],[c_117,c_12869]) ).
cnf(c_670,plain,
( cycle(e_4,e_3)
| cycle(e_4,e_2)
| cycle(e_4,e_1)
| cycle(e_4,e_0) ),
inference(resolve,[status(thm)],[c_640,c_251]) ).
cnf(c_692,plain,
( ~ cycle(e_4,e_1)
| ~ cycle(e_3,e_4) ),
inference(resolve,[status(thm)],[c_324,c_137]) ).
cnf(c_700,plain,
( ~ cycle(e_3,e_4)
| cycle(e_4,e_3)
| cycle(e_4,e_2)
| cycle(e_4,e_0) ),
inference(resolve,[status(thm)],[c_670,c_692]) ).
cnf(c_709,plain,
( ~ cycle(e_3,e_0)
| ~ cycle(e_2,e_3) ),
inference(resolve,[status(thm)],[c_341,c_138]) ).
cnf(c_713,plain,
( ~ cycle(e_4,e_0)
| ~ cycle(e_3,e_3) ),
inference(resolve,[status(thm)],[c_342,c_138]) ).
cnf(c_12870,plain,
( ~ cycle(e_5,e_0)
| ~ cycle(e_4,e_3) ),
inference(resolve,[status(thm)],[c_343,c_138]) ).
cnf(c_715,plain,
~ cycle(e_4,e_3),
inference(resolve,[status(thm)],[c_117,c_12870]) ).
cnf(c_722,plain,
( ~ cycle(e_3,e_4)
| cycle(e_4,e_2)
| cycle(e_4,e_0) ),
inference(resolve,[status(thm)],[c_715,c_700]) ).
cnf(c_726,plain,
( cycle(e_4,e_2)
| cycle(e_4,e_1)
| cycle(e_4,e_0) ),
inference(resolve,[status(thm)],[c_715,c_670]) ).
cnf(c_745,plain,
( ~ cycle(e_4,e_1)
| ~ cycle(e_3,e_3) ),
inference(resolve,[status(thm)],[c_348,c_137]) ).
cnf(c_746,plain,
( cycle(e_4,e_2)
| cycle(e_4,e_0)
| ~ cycle(e_3,e_3) ),
inference(resolve,[status(thm)],[c_745,c_726]) ).
cnf(c_756,plain,
( cycle(e_3,e_4)
| cycle(e_3,e_2)
| cycle(e_3,e_1)
| cycle(e_3,e_0)
| cycle(e_4,e_2)
| cycle(e_4,e_0) ),
inference(resolve,[status(thm)],[c_746,c_250]) ).
cnf(c_759,plain,
( ~ cycle(e_3,e_0)
| ~ cycle(e_2,e_2) ),
inference(resolve,[status(thm)],[c_365,c_138]) ).
cnf(c_760,plain,
( ~ cycle(e_4,e_0)
| ~ cycle(e_3,e_2) ),
inference(resolve,[status(thm)],[c_366,c_138]) ).
cnf(c_12871,plain,
( ~ cycle(e_5,e_0)
| ~ cycle(e_4,e_2) ),
inference(resolve,[status(thm)],[c_367,c_138]) ).
cnf(c_761,plain,
~ cycle(e_4,e_2),
inference(resolve,[status(thm)],[c_117,c_12871]) ).
cnf(c_763,plain,
( cycle(e_3,e_4)
| cycle(e_3,e_2)
| cycle(e_3,e_1)
| cycle(e_3,e_0)
| cycle(e_4,e_0) ),
inference(resolve,[status(thm)],[c_761,c_756]) ).
cnf(c_775,plain,
( cycle(e_4,e_1)
| cycle(e_4,e_0) ),
inference(resolve,[status(thm)],[c_761,c_726]) ).
cnf(c_779,plain,
( ~ cycle(e_3,e_4)
| cycle(e_4,e_0) ),
inference(resolve,[status(thm)],[c_761,c_722]) ).
cnf(c_784,plain,
( ~ cycle(e_3,e_2)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_775,c_760]) ).
cnf(c_804,plain,
( ~ cycle(e_4,e_1)
| ~ cycle(e_3,e_1) ),
inference(resolve,[status(thm)],[c_390,c_137]) ).
cnf(c_805,plain,
( cycle(e_4,e_0)
| ~ cycle(e_3,e_1) ),
inference(resolve,[status(thm)],[c_804,c_775]) ).
cnf(c_12872,plain,
( cycle(e_4,e_0)
| cycle(e_3,e_4)
| cycle(e_3,e_2)
| cycle(e_3,e_0)
| cycle(e_4,e_0) ),
inference(resolve,[status(thm)],[c_763,c_805]) ).
cnf(c_828,plain,
( cycle(e_3,e_4)
| cycle(e_3,e_2)
| cycle(e_3,e_0)
| cycle(e_4,e_0) ),
inference(copy,[status(thm)],[c_12872]) ).
cnf(c_12873,plain,
( cycle(e_4,e_0)
| cycle(e_3,e_2)
| cycle(e_3,e_0)
| cycle(e_4,e_0) ),
inference(resolve,[status(thm)],[c_828,c_779]) ).
cnf(c_866,plain,
( cycle(e_3,e_2)
| cycle(e_3,e_0)
| cycle(e_4,e_0) ),
inference(copy,[status(thm)],[c_12873]) ).
cnf(c_868,plain,
( ~ cycle(e_3,e_3)
| cycle(e_3,e_2)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_866,c_713]) ).
cnf(c_869,plain,
( ~ cycle(e_3,e_4)
| cycle(e_3,e_2)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_866,c_635]) ).
cnf(c_12874,plain,
( cycle(e_3,e_4)
| cycle(e_3,e_2)
| cycle(e_3,e_1)
| cycle(e_3,e_0)
| cycle(e_3,e_2)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_868,c_250]) ).
cnf(c_12875,plain,
( cycle(e_3,e_4)
| cycle(e_3,e_2)
| cycle(e_3,e_1)
| cycle(e_3,e_2)
| cycle(e_3,e_0) ),
inference(copy,[status(thm)],[c_12874]) ).
cnf(c_890,plain,
( cycle(e_3,e_4)
| cycle(e_3,e_1)
| cycle(e_3,e_2)
| cycle(e_3,e_0) ),
inference(copy,[status(thm)],[c_12875]) ).
cnf(c_12876,plain,
( ~ product(e_3,e_3,e_3)
| product(e_3,e_5,e_4)
| product(e_3,e_5,e_2)
| product(e_3,e_5,e_1) ),
inference(resolve,[status(thm)],[c_436,c_45]) ).
cnf(c_943,plain,
( product(e_3,e_5,e_4)
| product(e_3,e_5,e_2)
| product(e_3,e_5,e_1) ),
inference(resolve,[status(thm)],[c_108,c_12876]) ).
cnf(c_12877,plain,
( ~ product(e_4,e_4,e_4)
| product(e_4,e_5,e_3)
| product(e_4,e_5,e_2)
| product(e_4,e_5,e_1) ),
inference(resolve,[status(thm)],[c_437,c_46]) ).
cnf(c_977,plain,
( product(e_4,e_5,e_3)
| product(e_4,e_5,e_2)
| product(e_4,e_5,e_1) ),
inference(resolve,[status(thm)],[c_108,c_12877]) ).
cnf(c_12878,plain,
( cycle(e_3,e_2)
| cycle(e_3,e_0)
| cycle(e_3,e_1)
| cycle(e_3,e_2)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_890,c_869]) ).
cnf(c_12879,plain,
( cycle(e_3,e_2)
| cycle(e_3,e_1)
| cycle(e_3,e_2)
| cycle(e_3,e_0) ),
inference(copy,[status(thm)],[c_12878]) ).
cnf(c_1028,plain,
( cycle(e_3,e_1)
| cycle(e_3,e_2)
| cycle(e_3,e_0) ),
inference(copy,[status(thm)],[c_12879]) ).
cnf(c_12880,plain,
( ~ greater(e_1,e_0)
| ~ greater(e_4,e_3)
| ~ cycle(e_4,e_0)
| cycle(e_3,e_2)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_1028,c_527]) ).
cnf(c_12881,plain,
( ~ greater(e_1,e_0)
| ~ cycle(e_4,e_0)
| cycle(e_3,e_2)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_121,c_12880]) ).
cnf(c_1056,plain,
( ~ cycle(e_4,e_0)
| cycle(e_3,e_2)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_133,c_12881]) ).
cnf(c_12882,plain,
( cycle(e_3,e_2)
| cycle(e_3,e_0)
| cycle(e_3,e_2)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_1056,c_866]) ).
cnf(c_12883,plain,
( cycle(e_3,e_2)
| cycle(e_3,e_2)
| cycle(e_3,e_0) ),
inference(copy,[status(thm)],[c_12882]) ).
cnf(c_1093,plain,
( cycle(e_3,e_2)
| cycle(e_3,e_0) ),
inference(copy,[status(thm)],[c_12883]) ).
cnf(c_1094,plain,
( ~ cycle(e_2,e_2)
| cycle(e_3,e_2) ),
inference(resolve,[status(thm)],[c_1093,c_759]) ).
cnf(c_1095,plain,
( ~ cycle(e_2,e_3)
| cycle(e_3,e_2) ),
inference(resolve,[status(thm)],[c_1093,c_709]) ).
cnf(c_1096,plain,
( ~ cycle(e_2,e_4)
| cycle(e_3,e_2) ),
inference(resolve,[status(thm)],[c_1093,c_632]) ).
cnf(c_1102,plain,
( cycle(e_4,e_1)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_1093,c_784]) ).
cnf(c_12884,plain,
( ~ product(e_1,e_1,e_1)
| product(e_5,e_1,e_4)
| product(e_5,e_1,e_3)
| product(e_5,e_1,e_2) ),
inference(resolve,[status(thm)],[c_478,c_33]) ).
cnf(c_1132,plain,
( product(e_5,e_1,e_4)
| product(e_5,e_1,e_3)
| product(e_5,e_1,e_2) ),
inference(resolve,[status(thm)],[c_108,c_12884]) ).
cnf(c_1202,plain,
( cycle(e_2,e_4)
| cycle(e_2,e_3)
| cycle(e_2,e_1)
| cycle(e_2,e_0)
| cycle(e_3,e_2) ),
inference(resolve,[status(thm)],[c_1094,c_249]) ).
cnf(c_12885,plain,
( ~ product(e_4,e_4,e_4)
| product(e_5,e_4,e_3)
| product(e_5,e_4,e_2)
| product(e_5,e_4,e_1) ),
inference(resolve,[status(thm)],[c_481,c_36]) ).
cnf(c_1275,plain,
( product(e_5,e_4,e_3)
| product(e_5,e_4,e_2)
| product(e_5,e_4,e_1) ),
inference(resolve,[status(thm)],[c_108,c_12885]) ).
cnf(c_12886,plain,
( ~ product(e_1,e_1,e_1)
| product(e_1,e_4,e_5)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_482,c_40]) ).
cnf(c_1284,plain,
( product(e_1,e_4,e_5)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_108,c_12886]) ).
cnf(c_12887,plain,
( ~ product(e_2,e_2,e_2)
| product(e_2,e_4,e_5)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_483,c_41]) ).
cnf(c_1309,plain,
( product(e_2,e_4,e_5)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_108,c_12887]) ).
cnf(c_12888,plain,
( ~ product(e_1,e_1,e_1)
| product(e_4,e_1,e_5)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_489,c_30]) ).
cnf(c_1355,plain,
( product(e_4,e_1,e_5)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_108,c_12888]) ).
cnf(c_1400,plain,
( ~ product(e_3,e_1,e_2)
| product(e_3,e_5,e_4)
| product(e_3,e_5,e_1) ),
inference(resolve,[status(thm)],[c_943,c_43]) ).
cnf(c_1476,plain,
( ~ product(e_4,e_1,e_3)
| product(e_4,e_5,e_2)
| product(e_4,e_5,e_1) ),
inference(resolve,[status(thm)],[c_977,c_43]) ).
cnf(c_12889,plain,
( ~ product(e_1,e_1,e_1)
| product(e_1,e_3,e_5)
| product(e_1,e_3,e_4)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_492,c_38]) ).
cnf(c_1488,plain,
( product(e_1,e_3,e_5)
| product(e_1,e_3,e_4)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_108,c_12889]) ).
cnf(c_12890,plain,
( ~ product(e_2,e_2,e_2)
| product(e_2,e_3,e_5)
| product(e_2,e_3,e_4)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_493,c_39]) ).
cnf(c_1509,plain,
( product(e_2,e_3,e_5)
| product(e_2,e_3,e_4)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_108,c_12890]) ).
cnf(c_1535,plain,
( ~ product(e_3,e_1,e_2)
| product(e_5,e_1,e_4)
| product(e_5,e_1,e_3) ),
inference(resolve,[status(thm)],[c_1132,c_35]) ).
cnf(c_1550,plain,
( ~ product(e_4,e_1,e_3)
| product(e_5,e_1,e_4)
| product(e_5,e_1,e_2) ),
inference(resolve,[status(thm)],[c_1132,c_36]) ).
cnf(c_1566,plain,
( ~ product(e_3,e_1,e_4)
| product(e_5,e_1,e_3)
| product(e_5,e_1,e_2) ),
inference(resolve,[status(thm)],[c_1132,c_35]) ).
cnf(c_12891,plain,
( ~ product(e_1,e_1,e_1)
| product(e_3,e_1,e_5)
| product(e_3,e_1,e_4)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_499,c_28]) ).
cnf(c_1596,plain,
( product(e_3,e_1,e_5)
| product(e_3,e_1,e_4)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_108,c_12891]) ).
cnf(c_1676,plain,
( ~ product(e_5,e_1,e_2)
| product(e_5,e_4,e_3)
| product(e_5,e_4,e_1) ),
inference(resolve,[status(thm)],[c_1275,c_40]) ).
cnf(c_1701,plain,
( product(e_5,A,e_1)
| ~ product(e_4,e_1,A)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_1284,c_107]) ).
cnf(c_1717,plain,
( ~ product(e_2,e_1,e_3)
| product(e_2,e_4,e_5)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_1309,c_40]) ).
cnf(c_12892,plain,
( ~ product(e_1,e_1,e_1)
| product(e_1,e_2,e_5)
| product(e_1,e_2,e_4)
| product(e_1,e_2,e_3) ),
inference(resolve,[status(thm)],[c_501,c_37]) ).
cnf(c_1728,plain,
( product(e_1,e_2,e_5)
| product(e_1,e_2,e_4)
| product(e_1,e_2,e_3) ),
inference(resolve,[status(thm)],[c_108,c_12892]) ).
cnf(c_12893,plain,
( ~ product(e_1,e_1,e_1)
| product(e_2,e_1,e_5)
| product(e_2,e_1,e_4)
| product(e_2,e_1,e_3) ),
inference(resolve,[status(thm)],[c_511,c_27]) ).
cnf(c_1746,plain,
( product(e_2,e_1,e_5)
| product(e_2,e_1,e_4)
| product(e_2,e_1,e_3) ),
inference(resolve,[status(thm)],[c_108,c_12893]) ).
cnf(c_12894,plain,
( ~ next(e_4,e_5)
| ~ greater(A,e_0)
| ~ cycle(e_4,A)
| product(e_4,e_1,e_5)
| product(e_4,e_1,e_3) ),
inference(resolve,[status(thm)],[c_1355,c_86]) ).
cnf(c_1797,plain,
( ~ greater(A,e_0)
| ~ cycle(e_4,A)
| product(e_4,e_1,e_5)
| product(e_4,e_1,e_3) ),
inference(resolve,[status(thm)],[c_134,c_12894]) ).
cnf(c_12895,plain,
( ~ greater(e_5,e_4)
| ~ cycle(e_4,e_0)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_1355,c_115]) ).
cnf(c_1811,plain,
( ~ cycle(e_4,e_0)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_119,c_12895]) ).
cnf(c_1822,plain,
( cycle(e_4,e_1)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_1811,c_775]) ).
cnf(c_1831,plain,
( ~ product(e_3,e_1,e_2)
| cycle(e_4,e_1)
| product(e_4,e_1,e_3) ),
inference(resolve,[status(thm)],[c_1822,c_32]) ).
cnf(c_2006,plain,
( product(A,e_4,e_3)
| ~ product(e_3,e_1,A)
| product(e_1,e_3,e_5)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_1488,c_107]) ).
cnf(c_12896,plain,
( ~ greater(e_4,e_3)
| ~ cycle(e_3,e_0)
| product(e_3,e_1,e_5)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_1596,c_115]) ).
cnf(c_2056,plain,
( ~ cycle(e_3,e_0)
| product(e_3,e_1,e_5)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_121,c_12896]) ).
cnf(c_2076,plain,
( cycle(e_4,e_1)
| product(e_3,e_1,e_5)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_2056,c_1102]) ).
cnf(c_2077,plain,
( cycle(e_3,e_2)
| product(e_3,e_1,e_5)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_2056,c_1093]) ).
cnf(c_12897,plain,
( ~ greater(e_5,e_3)
| ~ cycle(e_3,e_0)
| cycle(e_4,e_1)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_2076,c_115]) ).
cnf(c_2091,plain,
( ~ cycle(e_3,e_0)
| cycle(e_4,e_1)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_120,c_12897]) ).
cnf(c_12898,plain,
( cycle(e_4,e_1)
| cycle(e_4,e_1)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_2091,c_1102]) ).
cnf(c_2112,plain,
( cycle(e_4,e_1)
| product(e_3,e_1,e_2) ),
inference(copy,[status(thm)],[c_12898]) ).
cnf(c_12899,plain,
( cycle(e_4,e_1)
| product(e_4,e_1,e_3)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2112,c_1831]) ).
cnf(c_2113,plain,
( product(e_4,e_1,e_3)
| cycle(e_4,e_1) ),
inference(copy,[status(thm)],[c_12899]) ).
cnf(c_2114,plain,
( product(e_5,e_1,e_4)
| product(e_5,e_1,e_3)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2112,c_1535]) ).
cnf(c_2115,plain,
( product(e_3,e_5,e_4)
| product(e_3,e_5,e_1)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2112,c_1400]) ).
cnf(c_2117,plain,
( product(A,e_2,e_1)
| ~ product(e_1,e_3,A)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2112,c_107]) ).
cnf(c_2158,plain,
( product(e_5,e_1,e_4)
| product(e_5,e_1,e_2)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2113,c_1550]) ).
cnf(c_2159,plain,
( product(e_4,e_5,e_2)
| product(e_4,e_5,e_1)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2113,c_1476]) ).
cnf(c_2161,plain,
( product(A,e_3,e_1)
| ~ product(e_1,e_4,A)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2113,c_107]) ).
cnf(c_2162,plain,
( product(e_3,A,e_4)
| ~ product(e_1,e_4,A)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2113,c_107]) ).
cnf(c_12900,plain,
( ~ greater(e_5,e_3)
| ~ cycle(e_3,e_0)
| cycle(e_3,e_2)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_2077,c_115]) ).
cnf(c_2191,plain,
( ~ cycle(e_3,e_0)
| cycle(e_3,e_2)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_120,c_12900]) ).
cnf(c_12901,plain,
( cycle(e_3,e_2)
| cycle(e_3,e_2)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_2191,c_1093]) ).
cnf(c_2221,plain,
( cycle(e_3,e_2)
| product(e_3,e_1,e_2) ),
inference(copy,[status(thm)],[c_12901]) ).
cnf(c_2225,plain,
( product(A,e_2,e_1)
| ~ product(e_1,e_3,A)
| cycle(e_3,e_2) ),
inference(resolve,[status(thm)],[c_2221,c_107]) ).
cnf(c_2226,plain,
( product(e_2,A,e_3)
| ~ product(e_1,e_3,A)
| cycle(e_3,e_2) ),
inference(resolve,[status(thm)],[c_2221,c_107]) ).
cnf(c_2289,plain,
( ~ product(e_5,e_1,e_2)
| product(e_5,e_1,e_4)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2114,c_49]) ).
cnf(c_2333,plain,
( ~ product(e_3,e_4,e_1)
| product(e_3,e_5,e_4)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2115,c_46]) ).
cnf(c_2342,plain,
( ~ product(e_3,e_2,e_4)
| product(e_3,e_5,e_1)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2115,c_44]) ).
cnf(c_12902,plain,
( product(e_1,e_3,e_5)
| product(e_1,e_3,e_4)
| product(e_2,e_2,e_1)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2117,c_1488]) ).
cnf(c_2348,plain,
( product(e_1,e_3,e_5)
| product(e_1,e_3,e_4)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_216,c_12902]) ).
cnf(c_2421,plain,
( ~ product(e_3,e_5,e_1)
| product(e_4,e_5,e_2)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2159,c_32]) ).
cnf(c_2430,plain,
( ~ product(e_1,e_5,e_2)
| product(e_4,e_5,e_1)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2159,c_30]) ).
cnf(c_12903,plain,
( product(e_1,e_4,e_5)
| product(e_1,e_4,e_2)
| product(e_3,e_3,e_1)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2161,c_1284]) ).
cnf(c_2432,plain,
( product(e_1,e_4,e_5)
| product(e_1,e_4,e_2)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_215,c_12903]) ).
cnf(c_12904,plain,
( product(e_1,e_3,e_5)
| product(e_1,e_3,e_4)
| product(e_2,e_2,e_1)
| cycle(e_3,e_2) ),
inference(resolve,[status(thm)],[c_2225,c_1488]) ).
cnf(c_2528,plain,
( product(e_1,e_3,e_5)
| product(e_1,e_3,e_4)
| cycle(e_3,e_2) ),
inference(resolve,[status(thm)],[c_216,c_12904]) ).
cnf(c_12905,plain,
( product(e_5,e_1,e_4)
| cycle(e_4,e_1)
| product(e_5,e_1,e_4)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2289,c_2158]) ).
cnf(c_12906,plain,
( product(e_5,e_1,e_4)
| product(e_5,e_1,e_4)
| cycle(e_4,e_1) ),
inference(copy,[status(thm)],[c_12905]) ).
cnf(c_2531,plain,
( product(e_5,e_1,e_4)
| cycle(e_4,e_1) ),
inference(copy,[status(thm)],[c_12906]) ).
cnf(c_12907,plain,
( product(e_4,e_4,e_1)
| product(e_1,e_5,e_3)
| product(e_1,e_5,e_2)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2531,c_472]) ).
cnf(c_2553,plain,
( product(e_1,e_5,e_3)
| product(e_1,e_5,e_2)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_213,c_12907]) ).
cnf(c_2559,plain,
( product(A,e_4,e_1)
| ~ product(e_1,e_5,A)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2531,c_107]) ).
cnf(c_2560,plain,
( product(e_4,A,e_5)
| ~ product(e_1,e_5,A)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2531,c_107]) ).
cnf(c_12908,plain,
( cycle(e_3,e_2)
| cycle(e_2,e_4)
| cycle(e_2,e_1)
| cycle(e_2,e_0)
| cycle(e_3,e_2) ),
inference(resolve,[status(thm)],[c_1202,c_1095]) ).
cnf(c_2616,plain,
( cycle(e_2,e_4)
| cycle(e_2,e_1)
| cycle(e_2,e_0)
| cycle(e_3,e_2) ),
inference(copy,[status(thm)],[c_12908]) ).
cnf(c_12909,plain,
( product(e_4,e_2,e_1)
| cycle(e_4,e_1)
| product(e_1,e_3,e_5)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2348,c_2117]) ).
cnf(c_2693,plain,
( product(e_4,e_2,e_1)
| product(e_1,e_3,e_5)
| cycle(e_4,e_1) ),
inference(copy,[status(thm)],[c_12909]) ).
cnf(c_12910,plain,
( product(e_3,e_5,e_4)
| cycle(e_4,e_1)
| product(e_4,e_5,e_2)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2421,c_2115]) ).
cnf(c_2734,plain,
( product(e_3,e_5,e_4)
| product(e_4,e_5,e_2)
| cycle(e_4,e_1) ),
inference(copy,[status(thm)],[c_12910]) ).
cnf(c_12911,plain,
( product(e_3,e_2,e_4)
| cycle(e_4,e_1)
| product(e_1,e_4,e_5)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2432,c_2162]) ).
cnf(c_2769,plain,
( product(e_3,e_2,e_4)
| product(e_1,e_4,e_5)
| cycle(e_4,e_1) ),
inference(copy,[status(thm)],[c_12911]) ).
cnf(c_2782,plain,
( ~ product(e_1,e_3,e_5)
| product(e_1,e_4,e_2)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2432,c_42]) ).
cnf(c_12912,plain,
( product(e_2,e_4,e_3)
| cycle(e_3,e_2)
| product(e_1,e_3,e_5)
| cycle(e_3,e_2) ),
inference(resolve,[status(thm)],[c_2528,c_2226]) ).
cnf(c_2883,plain,
( product(e_2,e_4,e_3)
| product(e_1,e_3,e_5)
| cycle(e_3,e_2) ),
inference(copy,[status(thm)],[c_12912]) ).
cnf(c_12913,plain,
( product(e_4,e_5,e_1)
| cycle(e_4,e_1)
| product(e_1,e_5,e_3)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2553,c_2430]) ).
cnf(c_2959,plain,
( product(e_4,e_5,e_1)
| product(e_1,e_5,e_3)
| cycle(e_4,e_1) ),
inference(copy,[status(thm)],[c_12913]) ).
cnf(c_12914,plain,
( product(e_1,e_5,e_2)
| cycle(e_4,e_1)
| product(e_3,e_4,e_1)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2559,c_2553]) ).
cnf(c_3048,plain,
( product(e_1,e_5,e_2)
| product(e_3,e_4,e_1)
| cycle(e_4,e_1) ),
inference(copy,[status(thm)],[c_12914]) ).
cnf(c_3298,plain,
( ~ product(e_1,e_5,e_2)
| product(e_3,e_5,e_4)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2734,c_30]) ).
cnf(c_12915,plain,
( product(e_5,e_3,e_1)
| cycle(e_4,e_1)
| product(e_3,e_2,e_4)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2769,c_2161]) ).
cnf(c_3327,plain,
( product(e_5,e_3,e_1)
| product(e_3,e_2,e_4)
| cycle(e_4,e_1) ),
inference(copy,[status(thm)],[c_12915]) ).
cnf(c_12916,plain,
( product(e_3,e_5,e_1)
| cycle(e_4,e_1)
| product(e_1,e_4,e_5)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2769,c_2342]) ).
cnf(c_3336,plain,
( product(e_3,e_5,e_1)
| product(e_1,e_4,e_5)
| cycle(e_4,e_1) ),
inference(copy,[status(thm)],[c_12916]) ).
cnf(c_12917,plain,
( product(e_4,e_2,e_1)
| cycle(e_4,e_1)
| product(e_1,e_4,e_2)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2782,c_2693]) ).
cnf(c_3512,plain,
( product(e_4,e_2,e_1)
| product(e_1,e_4,e_2)
| cycle(e_4,e_1) ),
inference(copy,[status(thm)],[c_12917]) ).
cnf(c_12918,plain,
( product(e_1,e_3,e_4)
| cycle(e_4,e_1)
| product(e_1,e_4,e_2)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2782,c_2348]) ).
cnf(c_3515,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_4,e_2)
| cycle(e_4,e_1) ),
inference(copy,[status(thm)],[c_12918]) ).
cnf(c_12919,plain,
( product(e_2,e_5,e_3)
| cycle(e_3,e_2)
| product(e_2,e_4,e_3)
| cycle(e_3,e_2) ),
inference(resolve,[status(thm)],[c_2883,c_2226]) ).
cnf(c_3584,plain,
( product(e_2,e_5,e_3)
| product(e_2,e_4,e_3)
| cycle(e_3,e_2) ),
inference(copy,[status(thm)],[c_12919]) ).
cnf(c_3779,plain,
( ~ product(e_4,e_2,e_1)
| product(e_1,e_5,e_3)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_2959,c_44]) ).
cnf(c_12920,plain,
( product(e_3,e_5,e_4)
| cycle(e_4,e_1)
| product(e_1,e_5,e_2)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_3048,c_2333]) ).
cnf(c_3805,plain,
( product(e_3,e_5,e_4)
| product(e_1,e_5,e_2)
| cycle(e_4,e_1) ),
inference(copy,[status(thm)],[c_12920]) ).
cnf(c_4514,plain,
( ~ product(e_2,e_1,e_3)
| product(e_2,e_4,e_3)
| cycle(e_3,e_2) ),
inference(resolve,[status(thm)],[c_3584,c_43]) ).
cnf(c_12921,plain,
( product(e_3,e_5,e_4)
| cycle(e_4,e_1)
| product(e_3,e_5,e_4)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_3805,c_3298]) ).
cnf(c_12922,plain,
( product(e_3,e_5,e_4)
| product(e_3,e_5,e_4)
| cycle(e_4,e_1) ),
inference(copy,[status(thm)],[c_12921]) ).
cnf(c_5013,plain,
( product(e_3,e_5,e_4)
| cycle(e_4,e_1) ),
inference(copy,[status(thm)],[c_12922]) ).
cnf(c_5050,plain,
( ~ product(e_3,e_5,e_1)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_5013,c_50]) ).
cnf(c_5052,plain,
( ~ product(e_3,e_2,e_4)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_5013,c_44]) ).
cnf(c_12923,plain,
( product(e_1,e_4,e_5)
| cycle(e_4,e_1)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_5050,c_3336]) ).
cnf(c_5058,plain,
( product(e_1,e_4,e_5)
| cycle(e_4,e_1) ),
inference(copy,[status(thm)],[c_12923]) ).
cnf(c_12924,plain,
( product(e_5,e_3,e_1)
| cycle(e_4,e_1)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_5052,c_3327]) ).
cnf(c_5059,plain,
( product(e_5,e_3,e_1)
| cycle(e_4,e_1) ),
inference(copy,[status(thm)],[c_12924]) ).
cnf(c_5087,plain,
( ~ product(e_1,e_4,e_2)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_5058,c_54]) ).
cnf(c_5116,plain,
( ~ product(e_2,e_3,e_1)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_5059,c_34]) ).
cnf(c_12925,plain,
( product(e_1,e_3,e_4)
| cycle(e_4,e_1)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_5087,c_3515]) ).
cnf(c_5122,plain,
( product(e_1,e_3,e_4)
| cycle(e_4,e_1) ),
inference(copy,[status(thm)],[c_12925]) ).
cnf(c_12926,plain,
( product(e_4,e_2,e_1)
| cycle(e_4,e_1)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_5087,c_3512]) ).
cnf(c_5124,plain,
( product(e_4,e_2,e_1)
| cycle(e_4,e_1) ),
inference(copy,[status(thm)],[c_12926]) ).
cnf(c_5179,plain,
( product(e_2,e_3,e_5)
| product(e_2,e_3,e_4)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_5116,c_1509]) ).
cnf(c_12927,plain,
( product(e_1,e_5,e_3)
| cycle(e_4,e_1)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_5124,c_3779]) ).
cnf(c_5248,plain,
( product(e_1,e_5,e_3)
| cycle(e_4,e_1) ),
inference(copy,[status(thm)],[c_12927]) ).
cnf(c_12928,plain,
( product(e_4,e_3,e_5)
| cycle(e_4,e_1)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_5248,c_2560]) ).
cnf(c_5379,plain,
( product(e_4,e_3,e_5)
| cycle(e_4,e_1) ),
inference(copy,[status(thm)],[c_12928]) ).
cnf(c_5418,plain,
( ~ product(e_2,e_3,e_5)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_5379,c_31]) ).
cnf(c_12929,plain,
( ~ greater(e_4,e_2)
| ~ cycle(e_2,e_0)
| product(e_2,e_1,e_5)
| product(e_2,e_1,e_3) ),
inference(resolve,[status(thm)],[c_1746,c_115]) ).
cnf(c_5491,plain,
( ~ cycle(e_2,e_0)
| product(e_2,e_1,e_5)
| product(e_2,e_1,e_3) ),
inference(resolve,[status(thm)],[c_123,c_12929]) ).
cnf(c_12930,plain,
( ~ next(e_2,e_3)
| ~ greater(A,e_0)
| ~ cycle(e_2,A)
| product(e_2,e_1,e_5)
| product(e_2,e_1,e_3) ),
inference(resolve,[status(thm)],[c_1746,c_69]) ).
cnf(c_5496,plain,
( ~ greater(A,e_0)
| ~ cycle(e_2,A)
| product(e_2,e_1,e_5)
| product(e_2,e_1,e_3) ),
inference(resolve,[status(thm)],[c_136,c_12930]) ).
cnf(c_12931,plain,
( product(e_4,e_1,e_3)
| ~ greater(e_1,e_0)
| product(e_4,e_1,e_5)
| product(e_4,e_1,e_3) ),
inference(resolve,[status(thm)],[c_1797,c_2113]) ).
cnf(c_12932,plain,
( ~ greater(e_1,e_0)
| product(e_4,e_1,e_5)
| product(e_4,e_1,e_3) ),
inference(copy,[status(thm)],[c_12931]) ).
cnf(c_5581,plain,
( product(e_4,e_1,e_5)
| product(e_4,e_1,e_3) ),
inference(resolve,[status(thm)],[c_133,c_12932]) ).
cnf(c_12933,plain,
( ~ next(e_4,e_5)
| ~ greater(A,e_0)
| ~ cycle(e_4,A)
| product(e_4,e_1,e_5) ),
inference(resolve,[status(thm)],[c_5581,c_76]) ).
cnf(c_5596,plain,
( ~ greater(A,e_0)
| ~ cycle(e_4,A)
| product(e_4,e_1,e_5) ),
inference(resolve,[status(thm)],[c_134,c_12933]) ).
cnf(c_12934,plain,
( product(e_3,e_1,e_2)
| ~ greater(e_1,e_0)
| product(e_4,e_1,e_5) ),
inference(resolve,[status(thm)],[c_5596,c_2112]) ).
cnf(c_5879,plain,
( product(e_3,e_1,e_2)
| product(e_4,e_1,e_5) ),
inference(resolve,[status(thm)],[c_133,c_12934]) ).
cnf(c_6705,plain,
( ~ product(e_3,e_1,e_5)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_5879,c_32]) ).
cnf(c_12935,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_6705,c_1596]) ).
cnf(c_7106,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_2) ),
inference(copy,[status(thm)],[c_12935]) ).
cnf(c_12936,plain,
( ~ next(e_3,e_4)
| ~ greater(A,e_0)
| ~ cycle(e_3,A)
| product(e_3,e_1,e_4) ),
inference(resolve,[status(thm)],[c_7106,c_89]) ).
cnf(c_7147,plain,
( ~ greater(A,e_0)
| ~ cycle(e_3,A)
| product(e_3,e_1,e_4) ),
inference(resolve,[status(thm)],[c_135,c_12936]) ).
cnf(c_12937,plain,
( ~ greater(e_4,e_3)
| ~ cycle(e_3,e_0)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_7106,c_115]) ).
cnf(c_7152,plain,
( ~ cycle(e_3,e_0)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_121,c_12937]) ).
cnf(c_7160,plain,
( ~ product(e_2,e_1,e_4)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_7106,c_29]) ).
cnf(c_7166,plain,
( product(e_2,e_1,e_5)
| product(e_2,e_1,e_3)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_7160,c_1746]) ).
cnf(c_12938,plain,
( cycle(e_3,e_0)
| ~ greater(e_2,e_0)
| product(e_3,e_1,e_4) ),
inference(resolve,[status(thm)],[c_7147,c_1093]) ).
cnf(c_7234,plain,
( cycle(e_3,e_0)
| product(e_3,e_1,e_4) ),
inference(resolve,[status(thm)],[c_132,c_12938]) ).
cnf(c_7235,plain,
( product(e_5,e_1,e_3)
| product(e_5,e_1,e_2)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_7234,c_1566]) ).
cnf(c_7237,plain,
( product(A,e_4,e_1)
| ~ product(e_1,e_3,A)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_7234,c_107]) ).
cnf(c_7245,plain,
( ~ product(e_2,e_1,e_4)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_7234,c_29]) ).
cnf(c_7293,plain,
( product(e_2,e_1,e_5)
| product(e_2,e_1,e_3)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_7245,c_1746]) ).
cnf(c_7309,plain,
( product(e_2,e_1,e_5)
| product(e_2,e_1,e_4)
| product(e_2,e_4,e_3)
| cycle(e_3,e_2) ),
inference(resolve,[status(thm)],[c_4514,c_1746]) ).
cnf(c_12939,plain,
( cycle(e_4,e_1)
| product(e_2,e_3,e_4)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_5179,c_5418]) ).
cnf(c_7633,plain,
( product(e_2,e_3,e_4)
| cycle(e_4,e_1) ),
inference(copy,[status(thm)],[c_12939]) ).
cnf(c_7658,plain,
( ~ product(e_1,e_3,e_4)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_7633,c_27]) ).
cnf(c_12940,plain,
( cycle(e_4,e_1)
| cycle(e_4,e_1) ),
inference(resolve,[status(thm)],[c_7658,c_5122]) ).
cnf(c_7661,plain,
cycle(e_4,e_1),
inference(copy,[status(thm)],[c_12940]) ).
cnf(c_12941,plain,
( ~ greater(e_1,e_0)
| product(e_4,e_1,e_5) ),
inference(resolve,[status(thm)],[c_7661,c_5596]) ).
cnf(c_7675,plain,
product(e_4,e_1,e_5),
inference(resolve,[status(thm)],[c_133,c_12941]) ).
cnf(c_12942,plain,
( cycle(e_2,e_4)
| cycle(e_2,e_2)
| cycle(e_2,e_1)
| cycle(e_2,e_0)
| ~ greater(e_3,e_1)
| ~ cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_7661,c_587]) ).
cnf(c_7680,plain,
( cycle(e_2,e_4)
| cycle(e_2,e_2)
| cycle(e_2,e_1)
| cycle(e_2,e_0)
| ~ cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_127,c_12942]) ).
cnf(c_12943,plain,
( product(e_5,e_5,e_1)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_7675,c_1701]) ).
cnf(c_7748,plain,
( product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(resolve,[status(thm)],[c_210,c_12943]) ).
cnf(c_7760,plain,
~ product(e_2,e_1,e_5),
inference(resolve,[status(thm)],[c_7675,c_31]) ).
cnf(c_7852,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_4,e_3)
| cycle(e_3,e_2) ),
inference(resolve,[status(thm)],[c_7760,c_7309]) ).
cnf(c_7854,plain,
( product(e_2,e_1,e_3)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_7760,c_7293]) ).
cnf(c_7856,plain,
( product(e_2,e_1,e_3)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_7760,c_7166]) ).
cnf(c_7865,plain,
( ~ greater(A,e_0)
| ~ cycle(e_2,A)
| product(e_2,e_1,e_3) ),
inference(resolve,[status(thm)],[c_7760,c_5496]) ).
cnf(c_7868,plain,
( ~ cycle(e_2,e_0)
| product(e_2,e_1,e_3) ),
inference(resolve,[status(thm)],[c_7760,c_5491]) ).
cnf(c_8036,plain,
( product(e_2,e_4,e_5)
| product(e_2,e_4,e_1)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_7854,c_1717]) ).
cnf(c_8040,plain,
( product(A,e_3,e_1)
| ~ product(e_1,e_2,A)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_7854,c_107]) ).
cnf(c_8364,plain,
( ~ product(e_1,e_3,e_2)
| product(e_1,e_4,e_3) ),
inference(resolve,[status(thm)],[c_7748,c_42]) ).
cnf(c_12944,plain,
( ~ next(e_3,e_4)
| ~ greater(A,e_0)
| ~ cycle(e_3,A)
| product(e_2,e_1,e_3) ),
inference(resolve,[status(thm)],[c_7856,c_89]) ).
cnf(c_8390,plain,
( ~ greater(A,e_0)
| ~ cycle(e_3,A)
| product(e_2,e_1,e_3) ),
inference(resolve,[status(thm)],[c_135,c_12944]) ).
cnf(c_12945,plain,
( cycle(e_3,e_0)
| product(e_4,e_4,e_3)
| product(e_1,e_3,e_5)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_2006,c_7234]) ).
cnf(c_8650,plain,
( cycle(e_3,e_0)
| product(e_1,e_3,e_5)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_211,c_12945]) ).
cnf(c_9200,plain,
( ~ product(e_2,e_1,e_3)
| product(e_5,e_1,e_2)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_7235,c_34]) ).
cnf(c_9400,plain,
( ~ product(e_2,e_1,e_3)
| product(e_2,e_1,e_4)
| cycle(e_3,e_2) ),
inference(resolve,[status(thm)],[c_7852,c_40]) ).
cnf(c_9737,plain,
( ~ product(e_2,e_3,e_5)
| product(e_2,e_4,e_1)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_8036,c_42]) ).
cnf(c_12946,plain,
( product(e_1,e_2,e_5)
| product(e_1,e_2,e_4)
| product(e_3,e_3,e_1)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_8040,c_1728]) ).
cnf(c_9819,plain,
( product(e_1,e_2,e_5)
| product(e_1,e_2,e_4)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_215,c_12946]) ).
cnf(c_12947,plain,
( product(e_5,e_4,e_1)
| cycle(e_3,e_0)
| cycle(e_3,e_0)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_8650,c_7237]) ).
cnf(c_10391,plain,
( product(e_5,e_4,e_1)
| cycle(e_3,e_0)
| product(e_1,e_3,e_2) ),
inference(copy,[status(thm)],[c_12947]) ).
cnf(c_12948,plain,
( cycle(e_3,e_0)
| product(e_5,e_1,e_2)
| cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_9200,c_7854]) ).
cnf(c_11099,plain,
( product(e_5,e_1,e_2)
| cycle(e_3,e_0) ),
inference(copy,[status(thm)],[c_12948]) ).
cnf(c_11104,plain,
( product(e_3,e_1,e_2)
| product(e_5,e_1,e_2) ),
inference(resolve,[status(thm)],[c_11099,c_7152]) ).
cnf(c_12949,plain,
( ~ next(e_3,e_4)
| ~ greater(A,e_0)
| ~ cycle(e_3,A)
| product(e_5,e_1,e_2) ),
inference(resolve,[status(thm)],[c_11104,c_89]) ).
cnf(c_11161,plain,
( ~ greater(A,e_0)
| ~ cycle(e_3,A)
| product(e_5,e_1,e_2) ),
inference(resolve,[status(thm)],[c_135,c_12949]) ).
cnf(c_12950,plain,
( cycle(e_3,e_2)
| cycle(e_2,e_1)
| cycle(e_2,e_0)
| cycle(e_3,e_2) ),
inference(resolve,[status(thm)],[c_2616,c_1096]) ).
cnf(c_11264,plain,
( cycle(e_2,e_1)
| cycle(e_2,e_0)
| cycle(e_3,e_2) ),
inference(copy,[status(thm)],[c_12950]) ).
cnf(c_12951,plain,
( ~ greater(e_2,e_0)
| product(e_5,e_1,e_2)
| cycle(e_2,e_1)
| cycle(e_2,e_0) ),
inference(resolve,[status(thm)],[c_11264,c_11161]) ).
cnf(c_11265,plain,
( product(e_5,e_1,e_2)
| cycle(e_2,e_1)
| cycle(e_2,e_0) ),
inference(resolve,[status(thm)],[c_132,c_12951]) ).
cnf(c_12952,plain,
( ~ greater(e_2,e_0)
| product(e_2,e_1,e_3)
| cycle(e_2,e_1)
| cycle(e_2,e_0) ),
inference(resolve,[status(thm)],[c_11264,c_8390]) ).
cnf(c_11266,plain,
( product(e_2,e_1,e_3)
| cycle(e_2,e_1)
| cycle(e_2,e_0) ),
inference(resolve,[status(thm)],[c_132,c_12952]) ).
cnf(c_11329,plain,
( product(e_5,e_4,e_3)
| product(e_5,e_4,e_1)
| cycle(e_2,e_1)
| cycle(e_2,e_0) ),
inference(resolve,[status(thm)],[c_11265,c_1676]) ).
cnf(c_12953,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_5,e_4)
| product(e_1,e_5,e_3)
| cycle(e_2,e_1)
| cycle(e_2,e_0) ),
inference(resolve,[status(thm)],[c_11265,c_460]) ).
cnf(c_11335,plain,
( product(e_1,e_5,e_4)
| product(e_1,e_5,e_3)
| cycle(e_2,e_1)
| cycle(e_2,e_0) ),
inference(resolve,[status(thm)],[c_216,c_12953]) ).
cnf(c_11338,plain,
( product(e_2,A,e_5)
| ~ product(e_1,e_5,A)
| cycle(e_2,e_1)
| cycle(e_2,e_0) ),
inference(resolve,[status(thm)],[c_11265,c_107]) ).
cnf(c_12954,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_3)
| cycle(e_2,e_1) ),
inference(resolve,[status(thm)],[c_11266,c_7868]) ).
cnf(c_11346,plain,
( product(e_2,e_1,e_3)
| cycle(e_2,e_1) ),
inference(copy,[status(thm)],[c_12954]) ).
cnf(c_12955,plain,
( ~ greater(e_1,e_0)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_3) ),
inference(resolve,[status(thm)],[c_11346,c_7865]) ).
cnf(c_12956,plain,
( ~ greater(e_1,e_0)
| product(e_2,e_1,e_3) ),
inference(copy,[status(thm)],[c_12955]) ).
cnf(c_11359,plain,
product(e_2,e_1,e_3),
inference(resolve,[status(thm)],[c_133,c_12956]) ).
cnf(c_11381,plain,
( product(e_2,e_1,e_4)
| cycle(e_3,e_2) ),
inference(resolve,[status(thm)],[c_11359,c_9400]) ).
cnf(c_12957,plain,
( ~ greater(e_3,e_2)
| ~ cycle(e_2,e_0) ),
inference(resolve,[status(thm)],[c_11359,c_115]) ).
cnf(c_11409,plain,
~ cycle(e_2,e_0),
inference(resolve,[status(thm)],[c_124,c_12957]) ).
cnf(c_11410,plain,
( product(A,e_3,e_1)
| ~ product(e_1,e_2,A) ),
inference(resolve,[status(thm)],[c_11359,c_107]) ).
cnf(c_11425,plain,
( product(e_2,A,e_5)
| ~ product(e_1,e_5,A)
| cycle(e_2,e_1) ),
inference(resolve,[status(thm)],[c_11409,c_11338]) ).
cnf(c_11428,plain,
( product(e_1,e_5,e_4)
| product(e_1,e_5,e_3)
| cycle(e_2,e_1) ),
inference(resolve,[status(thm)],[c_11409,c_11335]) ).
cnf(c_11434,plain,
( product(e_5,e_4,e_3)
| product(e_5,e_4,e_1)
| cycle(e_2,e_1) ),
inference(resolve,[status(thm)],[c_11409,c_11329]) ).
cnf(c_11541,plain,
( cycle(e_2,e_4)
| cycle(e_2,e_2)
| cycle(e_2,e_1)
| ~ cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_11409,c_7680]) ).
cnf(c_12958,plain,
( ~ product(e_2,e_1,e_3)
| cycle(e_3,e_2) ),
inference(resolve,[status(thm)],[c_11381,c_52]) ).
cnf(c_11921,plain,
cycle(e_3,e_2),
inference(resolve,[status(thm)],[c_11359,c_12958]) ).
cnf(c_11926,plain,
~ cycle(e_2,e_1),
inference(resolve,[status(thm)],[c_11921,c_289]) ).
cnf(c_11927,plain,
~ cycle(e_2,e_2),
inference(resolve,[status(thm)],[c_11921,c_285]) ).
cnf(c_11928,plain,
~ cycle(e_2,e_4),
inference(resolve,[status(thm)],[c_11921,c_276]) ).
cnf(c_12959,plain,
( cycle(e_2,e_4)
| cycle(e_2,e_2)
| ~ cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_11926,c_11541]) ).
cnf(c_12960,plain,
( cycle(e_2,e_4)
| ~ cycle(e_3,e_0) ),
inference(resolve,[status(thm)],[c_11927,c_12959]) ).
cnf(c_11958,plain,
~ cycle(e_3,e_0),
inference(resolve,[status(thm)],[c_11928,c_12960]) ).
cnf(c_11972,plain,
( product(e_5,e_4,e_3)
| product(e_5,e_4,e_1) ),
inference(resolve,[status(thm)],[c_11926,c_11434]) ).
cnf(c_11978,plain,
( product(e_1,e_5,e_4)
| product(e_1,e_5,e_3) ),
inference(resolve,[status(thm)],[c_11926,c_11428]) ).
cnf(c_11981,plain,
( product(e_2,A,e_5)
| ~ product(e_1,e_5,A) ),
inference(resolve,[status(thm)],[c_11926,c_11425]) ).
cnf(c_12002,plain,
( product(e_5,e_4,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_11958,c_10391]) ).
cnf(c_12015,plain,
( product(e_1,e_2,e_5)
| product(e_1,e_2,e_4) ),
inference(resolve,[status(thm)],[c_11958,c_9819]) ).
cnf(c_12034,plain,
( ~ product(e_2,e_3,e_5)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_11958,c_9737]) ).
cnf(c_12196,plain,
( ~ product(e_1,e_4,e_3)
| product(e_5,e_4,e_1) ),
inference(resolve,[status(thm)],[c_11972,c_33]) ).
cnf(c_12227,plain,
( product(e_1,e_5,e_4)
| product(e_2,e_3,e_5) ),
inference(resolve,[status(thm)],[c_11981,c_11978]) ).
cnf(c_12313,plain,
( product(e_1,e_4,e_3)
| product(e_5,e_4,e_1) ),
inference(resolve,[status(thm)],[c_12002,c_8364]) ).
cnf(c_12467,plain,
( product(e_5,e_3,e_1)
| product(e_1,e_2,e_4) ),
inference(resolve,[status(thm)],[c_12015,c_11410]) ).
cnf(c_12701,plain,
( ~ product(e_1,e_2,e_4)
| product(e_2,e_3,e_5) ),
inference(resolve,[status(thm)],[c_12227,c_44]) ).
cnf(c_12961,plain,
( product(e_5,e_4,e_1)
| product(e_5,e_4,e_1) ),
inference(resolve,[status(thm)],[c_12313,c_12196]) ).
cnf(c_12768,plain,
product(e_5,e_4,e_1),
inference(copy,[status(thm)],[c_12961]) ).
cnf(c_12773,plain,
~ product(e_5,e_3,e_1),
inference(resolve,[status(thm)],[c_12768,c_42]) ).
cnf(c_12776,plain,
~ product(e_2,e_4,e_1),
inference(resolve,[status(thm)],[c_12768,c_34]) ).
cnf(c_12797,plain,
product(e_1,e_2,e_4),
inference(resolve,[status(thm)],[c_12773,c_12467]) ).
cnf(c_12845,plain,
~ product(e_2,e_3,e_5),
inference(resolve,[status(thm)],[c_12776,c_12034]) ).
cnf(c_12962,plain,
~ product(e_1,e_2,e_4),
inference(resolve,[status(thm)],[c_12845,c_12701]) ).
cnf(c_12850,plain,
$false,
inference(resolve,[status(thm)],[c_12797,c_12962]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP125-3.005 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.42 % Computer : n008.cluster.edu
% 0.09/0.42 % Model : x86_64 x86_64
% 0.09/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.42 % Memory : 8046.5625MB
% 0.09/0.42 % OS : Linux 6.8.0-71-generic
% 0.09/0.42 % CPULimit : 300
% 0.09/0.42 % WCLimit : 300
% 0.09/0.42 % DateTime : Fri Sep 25 14:26:56 UTC 2026
% 0.09/0.43 % CPUTime :
% 0.09/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.43 % Process 1261442 was started by sandbox on n008,
% 0.09/0.43 % Fri Sep 25 14:26:56 2026
% 0.09/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.43
% 0.09/0.43 % From the command line: assign(max_seconds, 300).
% 19.50/5.78
% 19.50/5.78 % given #500 (A,wt=21): 436 product(e_3,e_5,e_1) | product(e_3,e_5,e_2) | product(e_3,e_5,e_3) | product(e_3,e_5,e_4). [resolve(237,a,112,a),unit_del(e,228)].
% 19.50/5.78
% 19.50/5.78 % given #1000 (A,wt=22): 1561 product(e_5,e_1,e_2) | product(e_5,e_1,e_3) | -cycle(e_5,A) | -greater(A,e_0) | -next(e_5,e_1). [resolve(1132,c,73,b)].
% 19.50/5.78
% 19.50/5.78 % given #1500 (T,wt=13): 5597 product(e_4,e_1,e_5) | -product(e_4,e_1,e_2). [resolve(5581,a,49,a)].
% 19.50/5.78
% 19.50/5.78 % given #2000 (A,wt=21): 2002 product(e_1,e_3,e_4) | product(e_1,e_3,e_5) | -product(e_3,e_1,A) | product(e_2,A,e_1). [resolve(1488,a,107,a)].
% 19.50/5.78
% 19.50/5.78 % given #2500 (A,wt=25): 2998 product(e_5,e_1,e_3) | product(e_5,e_1,e_4) | product(e_1,e_5,e_2) | product(e_2,e_4,e_5) | -product(e_1,e_5,e_1). [resolve(1522,d,48,a)].
% 19.50/5.78
% 19.50/5.78 % SZS status Unsatisfiable for theBenchmark
% 19.50/5.78
% 19.50/5.78 % Proof 1 at 2.07 (+ 0.39) seconds.
% 19.50/5.78 % Length of proof is 360.
% 19.50/5.78 % Level of proof is 54.
% 19.50/5.78 % Maximum clause weight is 29.000.
% 19.50/5.78 % Given clauses 2627.
% 19.50/5.78
% 19.50/5.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
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