%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP128-2.006 : 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 : n018.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 4.75s 1.14s
% Output : CNFRefutation 4.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 71
% Number of leaves : 40
% Syntax : Number of formulae : 320 ( 116 unt; 0 def)
% Number of atoms : 780 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 662 ( 202 ~; 460 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 123 ( 1 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(no_redundancy,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ greater(VAR_1,VAR_2)
| ~ next(VAR_0,VAR_2)
| ~ product(VAR_0,e_1,VAR_1) ),
file('theBenchmark.p',no_redundancy) ).
cnf(c_1,plain,
( ~ greater(B,C)
| ~ next(A,C)
| ~ product(A,e_1,B) ),
inference(clausify,[status(thm)],[no_redundancy]) ).
fof(e_4_then_e_5,axiom,
next(e_4,e_5),
file('theBenchmark.p',e_4_then_e_5) ).
cnf(c_3,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_4,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_5,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_6,plain,
next(e_1,e_2),
inference(clausify,[status(thm)],[e_1_then_e_2]) ).
fof(e_6_greater_e_5,axiom,
greater(e_6,e_5),
file('theBenchmark.p',e_6_greater_e_5) ).
cnf(c_7,plain,
greater(e_6,e_5),
inference(clausify,[status(thm)],[e_6_greater_e_5]) ).
cnf(c_9,plain,
( ~ greater(A,e_5)
| ~ product(e_4,e_1,A) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_10,plain,
( ~ greater(A,e_4)
| ~ product(e_3,e_1,A) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_11,plain,
( ~ greater(A,e_3)
| ~ product(e_2,e_1,A) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_12,plain,
( ~ greater(A,e_2)
| ~ product(e_1,e_1,A) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
fof(e_6_greater_e_4,axiom,
greater(e_6,e_4),
file('theBenchmark.p',e_6_greater_e_4) ).
cnf(c_13,plain,
greater(e_6,e_4),
inference(clausify,[status(thm)],[e_6_greater_e_4]) ).
fof(e_5_greater_e_4,axiom,
greater(e_5,e_4),
file('theBenchmark.p',e_5_greater_e_4) ).
cnf(c_14,plain,
greater(e_5,e_4),
inference(clausify,[status(thm)],[e_5_greater_e_4]) ).
fof(e_6_greater_e_3,axiom,
greater(e_6,e_3),
file('theBenchmark.p',e_6_greater_e_3) ).
cnf(c_15,plain,
greater(e_6,e_3),
inference(clausify,[status(thm)],[e_6_greater_e_3]) ).
fof(e_5_greater_e_3,axiom,
greater(e_5,e_3),
file('theBenchmark.p',e_5_greater_e_3) ).
cnf(c_16,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_17,plain,
greater(e_4,e_3),
inference(clausify,[status(thm)],[e_4_greater_e_3]) ).
fof(e_6_greater_e_2,axiom,
greater(e_6,e_2),
file('theBenchmark.p',e_6_greater_e_2) ).
cnf(c_18,plain,
greater(e_6,e_2),
inference(clausify,[status(thm)],[e_6_greater_e_2]) ).
fof(e_5_greater_e_2,axiom,
greater(e_5,e_2),
file('theBenchmark.p',e_5_greater_e_2) ).
cnf(c_19,plain,
greater(e_5,e_2),
inference(clausify,[status(thm)],[e_5_greater_e_2]) ).
fof(e_4_greater_e_2,axiom,
greater(e_4,e_2),
file('theBenchmark.p',e_4_greater_e_2) ).
cnf(c_20,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_21,plain,
greater(e_3,e_2),
inference(clausify,[status(thm)],[e_3_greater_e_2]) ).
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_27,plain,
( equalish(C,D)
| ~ product(A,B,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_total_function2]) ).
fof(e_6_is_not_e_5,axiom,
~ equalish(e_6,e_5),
file('theBenchmark.p',e_6_is_not_e_5) ).
cnf(c_28,plain,
~ equalish(e_6,e_5),
inference(clausify,[status(thm)],[e_6_is_not_e_5]) ).
fof(e_6_is_not_e_4,axiom,
~ equalish(e_6,e_4),
file('theBenchmark.p',e_6_is_not_e_4) ).
cnf(c_29,plain,
~ equalish(e_6,e_4),
inference(clausify,[status(thm)],[e_6_is_not_e_4]) ).
fof(e_6_is_not_e_3,axiom,
~ equalish(e_6,e_3),
file('theBenchmark.p',e_6_is_not_e_3) ).
cnf(c_30,plain,
~ equalish(e_6,e_3),
inference(clausify,[status(thm)],[e_6_is_not_e_3]) ).
fof(e_6_is_not_e_2,axiom,
~ equalish(e_6,e_2),
file('theBenchmark.p',e_6_is_not_e_2) ).
cnf(c_31,plain,
~ equalish(e_6,e_2),
inference(clausify,[status(thm)],[e_6_is_not_e_2]) ).
fof(e_6_is_not_e_1,axiom,
~ equalish(e_6,e_1),
file('theBenchmark.p',e_6_is_not_e_1) ).
cnf(c_32,plain,
~ equalish(e_6,e_1),
inference(clausify,[status(thm)],[e_6_is_not_e_1]) ).
fof(e_5_is_not_e_4,axiom,
~ equalish(e_5,e_4),
file('theBenchmark.p',e_5_is_not_e_4) ).
cnf(c_34,plain,
~ equalish(e_5,e_4),
inference(clausify,[status(thm)],[e_5_is_not_e_4]) ).
fof(e_5_is_not_e_3,axiom,
~ equalish(e_5,e_3),
file('theBenchmark.p',e_5_is_not_e_3) ).
cnf(c_35,plain,
~ equalish(e_5,e_3),
inference(clausify,[status(thm)],[e_5_is_not_e_3]) ).
fof(e_5_is_not_e_2,axiom,
~ equalish(e_5,e_2),
file('theBenchmark.p',e_5_is_not_e_2) ).
cnf(c_36,plain,
~ equalish(e_5,e_2),
inference(clausify,[status(thm)],[e_5_is_not_e_2]) ).
fof(e_5_is_not_e_1,axiom,
~ equalish(e_5,e_1),
file('theBenchmark.p',e_5_is_not_e_1) ).
cnf(c_37,plain,
~ equalish(e_5,e_1),
inference(clausify,[status(thm)],[e_5_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_41,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_42,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_46,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_47,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_52,plain,
~ equalish(e_2,e_1),
inference(clausify,[status(thm)],[e_2_is_not_e_1]) ).
fof(product_right_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_1,VAR_3)
| ~ product(VAR_0,VAR_3,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product_right_cancellation) ).
cnf(c_58,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_59,plain,
( equalish(A,D)
| ~ product(D,B,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_left_cancellation]) ).
cnf(c_60,plain,
( ~ product(e_1,A,B)
| ~ product(e_2,A,B) ),
inference(resolve,[status(thm)],[c_59,c_52]) ).
cnf(c_61,plain,
( ~ product(e_1,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_59,c_47]) ).
cnf(c_62,plain,
( ~ product(e_2,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_59,c_46]) ).
cnf(c_63,plain,
( ~ product(e_1,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_59,c_42]) ).
cnf(c_64,plain,
( ~ product(e_2,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_59,c_41]) ).
cnf(c_66,plain,
( ~ product(e_1,A,B)
| ~ product(e_5,A,B) ),
inference(resolve,[status(thm)],[c_59,c_37]) ).
cnf(c_67,plain,
( ~ product(e_2,A,B)
| ~ product(e_5,A,B) ),
inference(resolve,[status(thm)],[c_59,c_36]) ).
cnf(c_68,plain,
( ~ product(e_3,A,B)
| ~ product(e_5,A,B) ),
inference(resolve,[status(thm)],[c_59,c_35]) ).
cnf(c_69,plain,
( ~ product(e_4,A,B)
| ~ product(e_5,A,B) ),
inference(resolve,[status(thm)],[c_59,c_34]) ).
cnf(c_70,plain,
( ~ product(e_1,A,B)
| ~ product(e_6,A,B) ),
inference(resolve,[status(thm)],[c_59,c_32]) ).
cnf(c_71,plain,
( ~ product(e_2,A,B)
| ~ product(e_6,A,B) ),
inference(resolve,[status(thm)],[c_59,c_31]) ).
cnf(c_72,plain,
( ~ product(e_3,A,B)
| ~ product(e_6,A,B) ),
inference(resolve,[status(thm)],[c_59,c_30]) ).
cnf(c_73,plain,
( ~ product(e_4,A,B)
| ~ product(e_6,A,B) ),
inference(resolve,[status(thm)],[c_59,c_29]) ).
cnf(c_74,plain,
( ~ product(e_5,A,B)
| ~ product(e_6,A,B) ),
inference(resolve,[status(thm)],[c_59,c_28]) ).
cnf(c_75,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolve,[status(thm)],[c_58,c_52]) ).
cnf(c_76,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_58,c_47]) ).
cnf(c_77,plain,
( ~ product(A,e_2,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_58,c_46]) ).
cnf(c_78,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_58,c_42]) ).
cnf(c_79,plain,
( ~ product(A,e_2,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_58,c_41]) ).
cnf(c_81,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_5,B) ),
inference(resolve,[status(thm)],[c_58,c_37]) ).
cnf(c_83,plain,
( ~ product(A,e_3,B)
| ~ product(A,e_5,B) ),
inference(resolve,[status(thm)],[c_58,c_35]) ).
cnf(c_85,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_6,B) ),
inference(resolve,[status(thm)],[c_58,c_32]) ).
cnf(c_88,plain,
( ~ product(A,e_4,B)
| ~ product(A,e_6,B) ),
inference(resolve,[status(thm)],[c_58,c_29]) ).
cnf(c_89,plain,
( ~ product(A,e_5,B)
| ~ product(A,e_6,B) ),
inference(resolve,[status(thm)],[c_58,c_28]) ).
cnf(c_94,plain,
( ~ product(A,B,e_2)
| ~ product(A,B,e_4) ),
inference(resolve,[status(thm)],[c_27,c_41]) ).
cnf(c_97,plain,
( ~ product(A,B,e_2)
| ~ product(A,B,e_5) ),
inference(resolve,[status(thm)],[c_27,c_36]) ).
fof(qg3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( product(VAR_0,VAR_2,VAR_3)
| ~ product(VAR_2,VAR_1,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg3) ).
cnf(c_105,plain,
( product(A,C,D)
| ~ product(C,B,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[qg3]) ).
fof(product_total_function1,axiom,
! [VAR_0,VAR_1] :
( product(VAR_0,VAR_1,e_6)
| 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_106,plain,
( product(A,B,e_6)
| 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_6,axiom,
group_element(e_6),
file('theBenchmark.p',element_6) ).
cnf(c_107,plain,
group_element(e_6),
inference(clausify,[status(thm)],[element_6]) ).
fof(element_5,axiom,
group_element(e_5),
file('theBenchmark.p',element_5) ).
cnf(c_108,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_109,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_110,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_111,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_112,plain,
group_element(e_1),
inference(clausify,[status(thm)],[element_1]) ).
cnf(c_113,plain,
~ product(e_4,e_1,e_6),
inference(resolve,[status(thm)],[c_7,c_9]) ).
cnf(c_114,plain,
~ product(e_3,e_1,e_6),
inference(resolve,[status(thm)],[c_13,c_10]) ).
cnf(c_115,plain,
~ product(e_3,e_1,e_5),
inference(resolve,[status(thm)],[c_14,c_10]) ).
cnf(c_116,plain,
~ product(e_2,e_1,e_6),
inference(resolve,[status(thm)],[c_15,c_11]) ).
cnf(c_117,plain,
~ product(e_2,e_1,e_5),
inference(resolve,[status(thm)],[c_16,c_11]) ).
cnf(c_118,plain,
~ product(e_2,e_1,e_4),
inference(resolve,[status(thm)],[c_17,c_11]) ).
cnf(c_119,plain,
~ product(e_1,e_1,e_6),
inference(resolve,[status(thm)],[c_18,c_12]) ).
cnf(c_120,plain,
~ product(e_1,e_1,e_5),
inference(resolve,[status(thm)],[c_19,c_12]) ).
cnf(c_121,plain,
~ product(e_1,e_1,e_4),
inference(resolve,[status(thm)],[c_20,c_12]) ).
cnf(c_122,plain,
~ product(e_1,e_1,e_3),
inference(resolve,[status(thm)],[c_21,c_12]) ).
cnf(c_123,plain,
( product(A,A,A)
| ~ product(A,B,A) ),
inference(factor,[status(thm)],[c_105]) ).
cnf(c_124,plain,
( product(A,A,e_6)
| product(A,A,e_5)
| product(A,A,e_4)
| product(A,A,e_3)
| product(A,A,e_2)
| product(A,A,e_1)
| ~ group_element(A) ),
inference(factor,[status(thm)],[c_106]) ).
cnf(c_126,plain,
( product(e_6,A,e_6)
| product(e_6,A,e_5)
| product(e_6,A,e_4)
| product(e_6,A,e_3)
| product(e_6,A,e_2)
| product(e_6,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_107,c_106]) ).
cnf(c_128,plain,
( product(e_5,A,e_6)
| 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_108,c_106]) ).
cnf(c_130,plain,
( product(e_4,A,e_6)
| 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_109,c_106]) ).
cnf(c_131,plain,
( product(A,e_3,e_6)
| 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_110,c_106]) ).
cnf(c_132,plain,
( product(e_3,A,e_6)
| 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_110,c_106]) ).
cnf(c_134,plain,
( product(e_2,A,e_6)
| 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_111,c_106]) ).
cnf(c_4709,plain,
( product(e_1,e_1,e_6)
| product(e_1,e_1,e_5)
| product(e_1,e_1,e_4)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_124,c_112]) ).
cnf(c_4710,plain,
( product(e_1,e_1,e_6)
| product(e_1,e_1,e_5)
| product(e_1,e_1,e_4)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_122,c_4709]) ).
cnf(c_4711,plain,
( product(e_1,e_1,e_6)
| product(e_1,e_1,e_5)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_121,c_4710]) ).
cnf(c_4712,plain,
( product(e_1,e_1,e_6)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_120,c_4711]) ).
cnf(c_137,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_119,c_4712]) ).
cnf(c_148,plain,
( product(e_6,e_1,e_6)
| product(e_6,e_1,e_5)
| product(e_6,e_1,e_4)
| product(e_6,e_1,e_3)
| product(e_6,e_1,e_2)
| product(e_6,e_1,e_1) ),
inference(resolve,[status(thm)],[c_126,c_112]) ).
cnf(c_153,plain,
( product(A,e_1,e_2)
| ~ product(A,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_137,c_105]) ).
cnf(c_255,plain,
( product(e_5,e_1,e_6)
| 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_128,c_112]) ).
cnf(c_258,plain,
( product(e_5,e_4,e_6)
| 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_128,c_109]) ).
cnf(c_4713,plain,
( product(e_4,e_1,e_6)
| 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_130,c_112]) ).
cnf(c_608,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_113,c_4713]) ).
cnf(c_610,plain,
( product(e_4,e_3,e_6)
| product(e_4,e_3,e_5)
| 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_130,c_110]) ).
cnf(c_4714,plain,
( product(e_4,e_1,e_2)
| product(e_1,e_1,e_1)
| 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) ),
inference(resolve,[status(thm)],[c_608,c_153]) ).
cnf(c_611,plain,
( product(e_1,e_1,e_1)
| 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) ),
inference(copy,[status(thm)],[c_4714]) ).
cnf(c_616,plain,
( ~ product(e_1,e_1,e_1)
| 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) ),
inference(resolve,[status(thm)],[c_608,c_63]) ).
cnf(c_4715,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_5)
| 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_616,c_611]) ).
cnf(c_4716,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_5)
| product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2) ),
inference(copy,[status(thm)],[c_4715]) ).
cnf(c_4717,plain,
( product(e_4,e_1,e_5)
| product(e_4,e_1,e_4)
| 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) ),
inference(copy,[status(thm)],[c_4716]) ).
cnf(c_4718,plain,
( product(e_4,e_1,e_5)
| 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) ),
inference(copy,[status(thm)],[c_4717]) ).
cnf(c_649,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) ),
inference(copy,[status(thm)],[c_4718]) ).
cnf(c_655,plain,
( ~ product(e_1,e_1,e_2)
| product(e_4,e_1,e_5)
| product(e_4,e_1,e_4)
| product(e_4,e_1,e_3) ),
inference(resolve,[status(thm)],[c_649,c_63]) ).
cnf(c_660,plain,
( ~ product(e_2,e_1,e_3)
| product(e_4,e_1,e_5)
| product(e_4,e_1,e_4)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_649,c_64]) ).
cnf(c_661,plain,
( product(e_4,e_4,e_4)
| 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_649,c_123]) ).
cnf(c_669,plain,
( product(e_1,e_3,e_6)
| 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_131,c_112]) ).
cnf(c_4719,plain,
( product(e_3,e_1,e_6)
| 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_132,c_112]) ).
cnf(c_4720,plain,
( product(e_3,e_1,e_6)
| 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_115,c_4719]) ).
cnf(c_671,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_114,c_4720]) ).
cnf(c_673,plain,
( product(e_1,e_1,e_1)
| product(e_4,e_1,e_5)
| product(e_4,e_1,e_4)
| product(e_4,e_1,e_3) ),
inference(resolve,[status(thm)],[c_655,c_137]) ).
cnf(c_4721,plain,
( product(e_2,e_1,e_6)
| 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_134,c_112]) ).
cnf(c_4722,plain,
( product(e_2,e_1,e_6)
| product(e_2,e_1,e_5)
| 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_118,c_4721]) ).
cnf(c_4723,plain,
( product(e_2,e_1,e_6)
| 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_117,c_4722]) ).
cnf(c_675,plain,
( 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_116,c_4723]) ).
cnf(c_4724,plain,
( product(e_2,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(resolve,[status(thm)],[c_675,c_153]) ).
cnf(c_677,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(copy,[status(thm)],[c_4724]) ).
cnf(c_680,plain,
( ~ product(e_1,e_1,e_1)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(resolve,[status(thm)],[c_675,c_60]) ).
cnf(c_4725,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(resolve,[status(thm)],[c_680,c_677]) ).
cnf(c_4726,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(copy,[status(thm)],[c_4725]) ).
cnf(c_700,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(copy,[status(thm)],[c_4726]) ).
cnf(c_702,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_1,e_3) ),
inference(resolve,[status(thm)],[c_700,c_123]) ).
cnf(c_715,plain,
( ~ product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(resolve,[status(thm)],[c_702,c_75]) ).
cnf(c_4727,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_3) ),
inference(resolve,[status(thm)],[c_715,c_700]) ).
cnf(c_718,plain,
product(e_2,e_1,e_3),
inference(copy,[status(thm)],[c_4727]) ).
cnf(c_719,plain,
( product(e_4,e_1,e_5)
| product(e_4,e_1,e_4)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_718,c_660]) ).
cnf(c_724,plain,
( product(e_2,e_3,A)
| ~ product(e_3,e_1,A) ),
inference(resolve,[status(thm)],[c_718,c_105]) ).
cnf(c_729,plain,
~ product(e_2,e_4,e_3),
inference(resolve,[status(thm)],[c_78,c_718]) ).
cnf(c_732,plain,
~ product(e_6,e_1,e_3),
inference(resolve,[status(thm)],[c_71,c_718]) ).
cnf(c_733,plain,
~ product(e_5,e_1,e_3),
inference(resolve,[status(thm)],[c_67,c_718]) ).
cnf(c_734,plain,
~ product(e_4,e_1,e_3),
inference(resolve,[status(thm)],[c_64,c_718]) ).
cnf(c_735,plain,
~ product(e_3,e_1,e_3),
inference(resolve,[status(thm)],[c_62,c_718]) ).
cnf(c_793,plain,
( product(e_6,e_1,e_6)
| product(e_6,e_1,e_5)
| product(e_6,e_1,e_4)
| product(e_6,e_1,e_2)
| product(e_6,e_1,e_1) ),
inference(resolve,[status(thm)],[c_732,c_148]) ).
cnf(c_794,plain,
( product(e_5,e_1,e_6)
| product(e_5,e_1,e_5)
| product(e_5,e_1,e_4)
| product(e_5,e_1,e_2)
| product(e_5,e_1,e_1) ),
inference(resolve,[status(thm)],[c_733,c_255]) ).
cnf(c_795,plain,
( product(e_1,e_1,e_1)
| product(e_4,e_1,e_5)
| product(e_4,e_1,e_4) ),
inference(resolve,[status(thm)],[c_734,c_673]) ).
cnf(c_803,plain,
( product(e_4,e_4,e_4)
| product(e_4,e_1,e_5)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_734,c_661]) ).
cnf(c_809,plain,
( 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_735,c_671]) ).
cnf(c_1059,plain,
( ~ product(e_4,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_4,e_1,e_5) ),
inference(resolve,[status(thm)],[c_795,c_94]) ).
cnf(c_1151,plain,
( ~ product(e_4,e_1,e_4)
| product(e_4,e_1,e_5)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_803,c_78]) ).
cnf(c_4728,plain,
( product(e_3,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_3,e_1,e_4)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_809,c_153]) ).
cnf(c_1156,plain,
( product(e_1,e_1,e_1)
| product(e_3,e_1,e_4)
| product(e_3,e_1,e_2) ),
inference(copy,[status(thm)],[c_4728]) ).
cnf(c_1159,plain,
( ~ product(e_1,e_1,e_1)
| product(e_3,e_1,e_4)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_809,c_61]) ).
cnf(c_4729,plain,
( product(e_4,e_1,e_5)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_5)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_1151,c_719]) ).
cnf(c_4730,plain,
( product(e_4,e_1,e_5)
| product(e_4,e_1,e_5)
| product(e_4,e_1,e_2) ),
inference(copy,[status(thm)],[c_4729]) ).
cnf(c_1222,plain,
( product(e_4,e_1,e_5)
| product(e_4,e_1,e_2) ),
inference(copy,[status(thm)],[c_4730]) ).
cnf(c_4731,plain,
( product(e_1,e_1,e_1)
| product(e_4,e_1,e_5)
| product(e_4,e_1,e_5) ),
inference(resolve,[status(thm)],[c_1222,c_1059]) ).
cnf(c_1223,plain,
( product(e_1,e_1,e_1)
| product(e_4,e_1,e_5) ),
inference(copy,[status(thm)],[c_4731]) ).
cnf(c_1231,plain,
( product(e_4,e_5,A)
| ~ product(e_5,e_1,A)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_1222,c_105]) ).
cnf(c_4732,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_4)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_1159,c_1156]) ).
cnf(c_4733,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_4)
| product(e_3,e_1,e_2) ),
inference(copy,[status(thm)],[c_4732]) ).
cnf(c_1278,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_2) ),
inference(copy,[status(thm)],[c_4733]) ).
cnf(c_1280,plain,
( product(e_2,e_3,e_2)
| product(e_3,e_1,e_4) ),
inference(resolve,[status(thm)],[c_1278,c_724]) ).
cnf(c_1287,plain,
( product(e_2,e_3,e_4)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_1278,c_724]) ).
cnf(c_1304,plain,
( product(e_2,e_2,e_2)
| product(e_3,e_1,e_4) ),
inference(resolve,[status(thm)],[c_1280,c_123]) ).
cnf(c_1308,plain,
( ~ product(e_2,e_2,e_2)
| product(e_3,e_1,e_4) ),
inference(resolve,[status(thm)],[c_1280,c_77]) ).
cnf(c_1330,plain,
( product(e_2,e_4,A)
| ~ product(e_4,e_3,A)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_1287,c_105]) ).
cnf(c_1334,plain,
( ~ product(e_1,e_3,e_4)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_1287,c_60]) ).
cnf(c_4734,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_4) ),
inference(resolve,[status(thm)],[c_1308,c_1304]) ).
cnf(c_1371,plain,
product(e_3,e_1,e_4),
inference(copy,[status(thm)],[c_4734]) ).
cnf(c_1374,plain,
product(e_2,e_3,e_4),
inference(resolve,[status(thm)],[c_1371,c_724]) ).
cnf(c_1376,plain,
( product(e_3,e_4,A)
| ~ product(e_4,e_1,A) ),
inference(resolve,[status(thm)],[c_1371,c_105]) ).
cnf(c_1377,plain,
~ product(e_3,e_1,e_2),
inference(resolve,[status(thm)],[c_1371,c_94]) ).
cnf(c_1380,plain,
~ product(e_3,e_5,e_4),
inference(resolve,[status(thm)],[c_81,c_1371]) ).
cnf(c_1384,plain,
~ product(e_6,e_1,e_4),
inference(resolve,[status(thm)],[c_72,c_1371]) ).
cnf(c_1385,plain,
~ product(e_5,e_1,e_4),
inference(resolve,[status(thm)],[c_68,c_1371]) ).
cnf(c_1389,plain,
~ product(e_1,e_3,e_4),
inference(resolve,[status(thm)],[c_1377,c_1334]) ).
cnf(c_1393,plain,
( product(e_2,e_4,A)
| ~ product(e_4,e_3,A) ),
inference(resolve,[status(thm)],[c_1377,c_1330]) ).
cnf(c_1462,plain,
( product(e_6,e_1,e_6)
| product(e_6,e_1,e_5)
| product(e_6,e_1,e_2)
| product(e_6,e_1,e_1) ),
inference(resolve,[status(thm)],[c_1384,c_793]) ).
cnf(c_1463,plain,
( product(e_5,e_1,e_6)
| product(e_5,e_1,e_5)
| product(e_5,e_1,e_2)
| product(e_5,e_1,e_1) ),
inference(resolve,[status(thm)],[c_1385,c_794]) ).
cnf(c_1464,plain,
( product(e_1,e_3,e_6)
| product(e_1,e_3,e_5)
| 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_1389,c_669]) ).
cnf(c_4735,plain,
( product(e_2,e_4,A)
| ~ product(e_4,e_3,A) ),
inference(resolve,[status(thm)],[c_105,c_1374]) ).
cnf(c_1476,plain,
~ product(e_4,e_3,e_3),
inference(resolve,[status(thm)],[c_4735,c_729]) ).
cnf(c_1484,plain,
~ product(e_4,e_3,e_4),
inference(resolve,[status(thm)],[c_64,c_1374]) ).
cnf(c_4736,plain,
( product(e_4,e_3,e_6)
| product(e_4,e_3,e_5)
| 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_1476,c_610]) ).
cnf(c_1485,plain,
( product(e_4,e_3,e_6)
| product(e_4,e_3,e_5)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_1484,c_4736]) ).
cnf(c_1567,plain,
( product(e_4,e_1,e_2)
| product(e_3,e_4,e_5) ),
inference(resolve,[status(thm)],[c_1376,c_1222]) ).
cnf(c_1610,plain,
( product(A,e_3,e_5)
| ~ product(A,e_4,e_3)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_1567,c_105]) ).
cnf(c_4737,plain,
( product(e_6,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_6,e_1,e_6)
| product(e_6,e_1,e_5)
| product(e_6,e_1,e_2) ),
inference(resolve,[status(thm)],[c_1462,c_153]) ).
cnf(c_1676,plain,
( product(e_1,e_1,e_1)
| product(e_6,e_1,e_6)
| product(e_6,e_1,e_5)
| product(e_6,e_1,e_2) ),
inference(copy,[status(thm)],[c_4737]) ).
cnf(c_1681,plain,
( ~ product(e_1,e_1,e_1)
| product(e_6,e_1,e_6)
| product(e_6,e_1,e_5)
| product(e_6,e_1,e_2) ),
inference(resolve,[status(thm)],[c_1462,c_70]) ).
cnf(c_1722,plain,
( ~ product(e_4,e_1,e_5)
| product(e_5,e_1,e_6)
| product(e_5,e_1,e_2)
| product(e_5,e_1,e_1) ),
inference(resolve,[status(thm)],[c_1463,c_69]) ).
cnf(c_1740,plain,
( product(e_2,e_4,e_2)
| product(e_4,e_3,e_6)
| product(e_4,e_3,e_5)
| product(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_1485,c_1393]) ).
cnf(c_1986,plain,
( product(e_5,e_3,e_5)
| product(e_4,e_1,e_2)
| product(e_5,e_4,e_6)
| product(e_5,e_4,e_5)
| product(e_5,e_4,e_4)
| product(e_5,e_4,e_2)
| product(e_5,e_4,e_1) ),
inference(resolve,[status(thm)],[c_258,c_1610]) ).
cnf(c_4738,plain,
( product(e_6,e_1,e_6)
| product(e_6,e_1,e_5)
| product(e_6,e_1,e_2)
| product(e_6,e_1,e_6)
| product(e_6,e_1,e_5)
| product(e_6,e_1,e_2) ),
inference(resolve,[status(thm)],[c_1681,c_1676]) ).
cnf(c_4739,plain,
( product(e_6,e_1,e_6)
| product(e_6,e_1,e_5)
| product(e_6,e_1,e_6)
| product(e_6,e_1,e_5)
| product(e_6,e_1,e_2) ),
inference(copy,[status(thm)],[c_4738]) ).
cnf(c_4740,plain,
( product(e_6,e_1,e_6)
| product(e_6,e_1,e_6)
| product(e_6,e_1,e_5)
| product(e_6,e_1,e_2) ),
inference(copy,[status(thm)],[c_4739]) ).
cnf(c_2201,plain,
( product(e_6,e_1,e_6)
| product(e_6,e_1,e_5)
| product(e_6,e_1,e_2) ),
inference(copy,[status(thm)],[c_4740]) ).
cnf(c_2214,plain,
( product(e_6,e_6,e_6)
| product(e_6,e_1,e_5)
| product(e_6,e_1,e_2) ),
inference(resolve,[status(thm)],[c_2201,c_123]) ).
cnf(c_2270,plain,
( ~ product(e_6,e_1,e_6)
| product(e_6,e_1,e_5)
| product(e_6,e_1,e_2) ),
inference(resolve,[status(thm)],[c_2214,c_85]) ).
cnf(c_4741,plain,
( product(e_6,e_1,e_5)
| product(e_6,e_1,e_2)
| product(e_6,e_1,e_5)
| product(e_6,e_1,e_2) ),
inference(resolve,[status(thm)],[c_2270,c_2201]) ).
cnf(c_4742,plain,
( product(e_6,e_1,e_5)
| product(e_6,e_1,e_5)
| product(e_6,e_1,e_2) ),
inference(copy,[status(thm)],[c_4741]) ).
cnf(c_2451,plain,
( product(e_6,e_1,e_5)
| product(e_6,e_1,e_2) ),
inference(copy,[status(thm)],[c_4742]) ).
cnf(c_2453,plain,
( product(A,e_6,e_2)
| ~ product(A,e_1,e_6)
| product(e_6,e_1,e_5) ),
inference(resolve,[status(thm)],[c_2451,c_105]) ).
cnf(c_2456,plain,
( ~ product(e_5,e_1,e_2)
| product(e_6,e_1,e_5) ),
inference(resolve,[status(thm)],[c_2451,c_74]) ).
cnf(c_2457,plain,
( ~ product(e_4,e_1,e_2)
| product(e_6,e_1,e_5) ),
inference(resolve,[status(thm)],[c_2451,c_73]) ).
cnf(c_2458,plain,
( ~ product(e_1,e_1,e_2)
| product(e_6,e_1,e_5) ),
inference(resolve,[status(thm)],[c_2451,c_70]) ).
cnf(c_2463,plain,
( ~ product(e_4,e_1,e_5)
| product(e_6,e_1,e_2) ),
inference(resolve,[status(thm)],[c_2451,c_73]) ).
cnf(c_2480,plain,
( product(e_3,e_4,e_5)
| product(e_6,e_1,e_5) ),
inference(resolve,[status(thm)],[c_2457,c_1567]) ).
cnf(c_2481,plain,
( product(e_4,e_1,e_5)
| product(e_6,e_1,e_5) ),
inference(resolve,[status(thm)],[c_2457,c_1222]) ).
cnf(c_2482,plain,
( product(e_1,e_1,e_1)
| product(e_6,e_1,e_5) ),
inference(resolve,[status(thm)],[c_2458,c_137]) ).
cnf(c_2486,plain,
( product(e_1,e_1,e_1)
| product(e_6,e_1,e_2) ),
inference(resolve,[status(thm)],[c_2463,c_1223]) ).
cnf(c_2487,plain,
( product(e_4,e_1,e_2)
| product(e_6,e_1,e_2) ),
inference(resolve,[status(thm)],[c_2463,c_1222]) ).
cnf(c_2497,plain,
( product(A,e_6,e_5)
| ~ product(A,e_1,e_6)
| product(e_3,e_4,e_5) ),
inference(resolve,[status(thm)],[c_2480,c_105]) ).
cnf(c_2513,plain,
( product(A,e_6,e_5)
| ~ product(A,e_1,e_6)
| product(e_4,e_1,e_5) ),
inference(resolve,[status(thm)],[c_2481,c_105]) ).
cnf(c_2517,plain,
( ~ product(e_5,e_1,e_5)
| product(e_4,e_1,e_5) ),
inference(resolve,[status(thm)],[c_2481,c_74]) ).
cnf(c_2523,plain,
( ~ product(e_6,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_2482,c_97]) ).
cnf(c_2565,plain,
( product(A,e_6,e_2)
| ~ product(A,e_1,e_6)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_2487,c_105]) ).
cnf(c_2568,plain,
( ~ product(e_5,e_1,e_2)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_2487,c_74]) ).
cnf(c_2631,plain,
( product(e_5,e_1,e_6)
| product(e_5,e_1,e_2)
| product(e_5,e_1,e_1)
| product(e_4,e_1,e_5) ),
inference(resolve,[status(thm)],[c_2517,c_1463]) ).
cnf(c_4743,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_2523,c_2486]) ).
cnf(c_2633,plain,
product(e_1,e_1,e_1),
inference(copy,[status(thm)],[c_4743]) ).
cnf(c_2641,plain,
~ product(e_1,e_3,e_1),
inference(resolve,[status(thm)],[c_76,c_2633]) ).
cnf(c_2644,plain,
~ product(e_5,e_1,e_1),
inference(resolve,[status(thm)],[c_66,c_2633]) ).
cnf(c_2723,plain,
( product(e_1,e_3,e_6)
| product(e_1,e_3,e_5)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_2641,c_1464]) ).
cnf(c_2725,plain,
( product(e_5,e_1,e_6)
| product(e_5,e_1,e_2)
| product(e_4,e_1,e_5) ),
inference(resolve,[status(thm)],[c_2644,c_2631]) ).
cnf(c_2736,plain,
( ~ product(e_4,e_1,e_5)
| product(e_5,e_1,e_6)
| product(e_5,e_1,e_2) ),
inference(resolve,[status(thm)],[c_2644,c_1722]) ).
cnf(c_4744,plain,
( product(e_5,e_1,e_6)
| product(e_5,e_1,e_2)
| product(e_5,e_1,e_6)
| product(e_5,e_1,e_2) ),
inference(resolve,[status(thm)],[c_2736,c_2725]) ).
cnf(c_4745,plain,
( product(e_5,e_1,e_6)
| product(e_5,e_1,e_6)
| product(e_5,e_1,e_2) ),
inference(copy,[status(thm)],[c_4744]) ).
cnf(c_2925,plain,
( product(e_5,e_1,e_6)
| product(e_5,e_1,e_2) ),
inference(copy,[status(thm)],[c_4745]) ).
cnf(c_2926,plain,
( product(e_4,e_1,e_2)
| product(e_5,e_1,e_6) ),
inference(resolve,[status(thm)],[c_2925,c_2568]) ).
cnf(c_2930,plain,
( product(e_6,e_1,e_5)
| product(e_5,e_1,e_6) ),
inference(resolve,[status(thm)],[c_2925,c_2456]) ).
cnf(c_2935,plain,
( ~ product(e_4,e_1,e_2)
| product(e_5,e_1,e_6) ),
inference(resolve,[status(thm)],[c_2925,c_69]) ).
cnf(c_4746,plain,
( product(e_5,e_6,e_2)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_2926,c_2565]) ).
cnf(c_2948,plain,
( product(e_5,e_6,e_2)
| product(e_4,e_1,e_2) ),
inference(copy,[status(thm)],[c_4746]) ).
cnf(c_4747,plain,
( product(e_4,e_5,e_6)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_2926,c_1231]) ).
cnf(c_2952,plain,
( product(e_4,e_5,e_6)
| product(e_4,e_1,e_2) ),
inference(copy,[status(thm)],[c_4747]) ).
cnf(c_4748,plain,
( product(e_5,e_6,e_2)
| product(e_6,e_1,e_5)
| product(e_6,e_1,e_5) ),
inference(resolve,[status(thm)],[c_2930,c_2453]) ).
cnf(c_2989,plain,
( product(e_5,e_6,e_2)
| product(e_6,e_1,e_5) ),
inference(copy,[status(thm)],[c_4748]) ).
cnf(c_4749,plain,
( product(e_5,e_1,e_6)
| product(e_5,e_1,e_6) ),
inference(resolve,[status(thm)],[c_2935,c_2926]) ).
cnf(c_3018,plain,
product(e_5,e_1,e_6),
inference(copy,[status(thm)],[c_4749]) ).
cnf(c_3024,plain,
( product(e_5,e_6,e_5)
| product(e_4,e_1,e_5) ),
inference(resolve,[status(thm)],[c_3018,c_2513]) ).
cnf(c_3026,plain,
( product(e_5,e_6,e_5)
| product(e_3,e_4,e_5) ),
inference(resolve,[status(thm)],[c_3018,c_2497]) ).
cnf(c_3037,plain,
~ product(e_5,e_4,e_6),
inference(resolve,[status(thm)],[c_78,c_3018]) ).
cnf(c_3221,plain,
( product(e_5,e_3,e_5)
| product(e_4,e_1,e_2)
| product(e_5,e_4,e_5)
| product(e_5,e_4,e_4)
| product(e_5,e_4,e_2)
| product(e_5,e_4,e_1) ),
inference(resolve,[status(thm)],[c_3037,c_1986]) ).
cnf(c_3296,plain,
( ~ product(e_5,e_4,e_2)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_2948,c_88]) ).
cnf(c_3318,plain,
( ~ product(e_4,e_3,e_6)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_2952,c_83]) ).
cnf(c_3416,plain,
( ~ product(e_4,e_1,e_5)
| product(e_5,e_6,e_2) ),
inference(resolve,[status(thm)],[c_2989,c_73]) ).
cnf(c_3451,plain,
( product(e_5,e_5,e_5)
| product(e_4,e_1,e_5) ),
inference(resolve,[status(thm)],[c_3024,c_123]) ).
cnf(c_3458,plain,
( ~ product(e_5,e_5,e_5)
| product(e_4,e_1,e_5) ),
inference(resolve,[status(thm)],[c_3024,c_89]) ).
cnf(c_3506,plain,
( ~ product(e_5,e_6,e_2)
| product(e_3,e_4,e_5) ),
inference(resolve,[status(thm)],[c_3026,c_97]) ).
cnf(c_4750,plain,
( product(e_4,e_1,e_5)
| product(e_4,e_1,e_5) ),
inference(resolve,[status(thm)],[c_3458,c_3451]) ).
cnf(c_3697,plain,
product(e_4,e_1,e_5),
inference(copy,[status(thm)],[c_4750]) ).
cnf(c_3698,plain,
product(e_5,e_6,e_2),
inference(resolve,[status(thm)],[c_3697,c_3416]) ).
cnf(c_3704,plain,
product(e_3,e_4,e_5),
inference(resolve,[status(thm)],[c_3698,c_3506]) ).
cnf(c_3721,plain,
~ product(e_4,e_1,e_2),
inference(resolve,[status(thm)],[c_3697,c_97]) ).
cnf(c_3725,plain,
~ product(e_4,e_3,e_5),
inference(resolve,[status(thm)],[c_76,c_3697]) ).
cnf(c_3737,plain,
~ product(e_4,e_3,e_6),
inference(resolve,[status(thm)],[c_3721,c_3318]) ).
cnf(c_3751,plain,
~ product(e_5,e_4,e_2),
inference(resolve,[status(thm)],[c_3721,c_3296]) ).
cnf(c_4751,plain,
( product(e_5,e_3,e_5)
| product(e_4,e_1,e_2)
| product(e_5,e_4,e_5)
| product(e_5,e_4,e_4)
| product(e_5,e_4,e_1) ),
inference(resolve,[status(thm)],[c_3751,c_3221]) ).
cnf(c_3760,plain,
( product(e_5,e_3,e_5)
| product(e_5,e_4,e_5)
| product(e_5,e_4,e_4)
| product(e_5,e_4,e_1) ),
inference(resolve,[status(thm)],[c_3721,c_4751]) ).
cnf(c_4752,plain,
( product(e_2,e_4,e_2)
| product(e_4,e_3,e_6)
| product(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_3725,c_1740]) ).
cnf(c_3842,plain,
( product(e_2,e_4,e_2)
| product(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_3737,c_4752]) ).
cnf(c_4753,plain,
( product(e_3,e_5,A)
| ~ product(e_5,e_4,A) ),
inference(resolve,[status(thm)],[c_105,c_3704]) ).
cnf(c_4282,plain,
~ product(e_5,e_4,e_4),
inference(resolve,[status(thm)],[c_4753,c_1380]) ).
cnf(c_4287,plain,
~ product(e_5,e_4,e_5),
inference(resolve,[status(thm)],[c_68,c_3704]) ).
cnf(c_4754,plain,
( product(e_5,e_3,e_5)
| product(e_5,e_4,e_5)
| product(e_5,e_4,e_1) ),
inference(resolve,[status(thm)],[c_4282,c_3760]) ).
cnf(c_4302,plain,
( product(e_5,e_3,e_5)
| product(e_5,e_4,e_1) ),
inference(resolve,[status(thm)],[c_4287,c_4754]) ).
cnf(c_4484,plain,
( product(e_2,e_2,e_2)
| product(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_3842,c_123]) ).
cnf(c_4488,plain,
( ~ product(e_2,e_2,e_2)
| product(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_3842,c_79]) ).
cnf(c_4563,plain,
( ~ product(e_1,e_3,e_5)
| product(e_5,e_4,e_1) ),
inference(resolve,[status(thm)],[c_4302,c_66]) ).
cnf(c_4755,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_4488,c_4484]) ).
cnf(c_4612,plain,
product(e_4,e_3,e_1),
inference(copy,[status(thm)],[c_4755]) ).
cnf(c_4616,plain,
product(e_2,e_4,e_1),
inference(resolve,[status(thm)],[c_4612,c_1393]) ).
cnf(c_4756,plain,
( product(e_4,e_1,A)
| ~ product(e_1,e_3,A) ),
inference(resolve,[status(thm)],[c_105,c_4612]) ).
cnf(c_4621,plain,
~ product(e_1,e_3,e_2),
inference(resolve,[status(thm)],[c_4756,c_3721]) ).
cnf(c_4757,plain,
( product(e_4,e_1,A)
| ~ product(e_1,e_3,A) ),
inference(resolve,[status(thm)],[c_105,c_4612]) ).
cnf(c_4622,plain,
~ product(e_1,e_3,e_3),
inference(resolve,[status(thm)],[c_4757,c_734]) ).
cnf(c_4758,plain,
( product(e_4,e_1,A)
| ~ product(e_1,e_3,A) ),
inference(resolve,[status(thm)],[c_105,c_4612]) ).
cnf(c_4623,plain,
~ product(e_1,e_3,e_6),
inference(resolve,[status(thm)],[c_4758,c_113]) ).
cnf(c_4759,plain,
( product(e_1,e_3,e_6)
| product(e_1,e_3,e_5)
| product(e_1,e_3,e_3) ),
inference(resolve,[status(thm)],[c_4621,c_2723]) ).
cnf(c_4760,plain,
( product(e_1,e_3,e_6)
| product(e_1,e_3,e_5) ),
inference(resolve,[status(thm)],[c_4622,c_4759]) ).
cnf(c_4652,plain,
product(e_1,e_3,e_5),
inference(resolve,[status(thm)],[c_4623,c_4760]) ).
cnf(c_4688,plain,
product(e_5,e_4,e_1),
inference(resolve,[status(thm)],[c_4652,c_4563]) ).
cnf(c_4761,plain,
~ product(e_5,e_4,e_1),
inference(resolve,[status(thm)],[c_67,c_4616]) ).
cnf(c_4708,plain,
$false,
inference(resolve,[status(thm)],[c_4688,c_4761]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP128-2.006 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n018.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 14:29:53 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 2161407 was started by sandbox on n018,
% 0.12/0.38 % Fri Sep 25 14:29:53 2026
% 0.12/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 4.75/1.14
% 4.75/1.14 % given #500 (T,wt=13): 2456 product(e_6,e_1,e_5) | -product(e_5,e_1,e_2). [resolve(2451,a,74,a)].
% 4.75/1.14
% 4.75/1.14 % given #1000 (T,wt=13): 4445 product(e_6,e_5,e_4) | -product(e_6,e_3,e_1). [back_unit_del(4424),unit_del(b,4441)].
% 4.75/1.14
% 4.75/1.14 % SZS status Unsatisfiable for theBenchmark
% 4.75/1.14
% 4.75/1.14 % Proof 1 at 0.42 (+ 0.09) seconds.
% 4.75/1.14 % Length of proof is 227.
% 4.75/1.14 % Level of proof is 44.
% 4.75/1.14 % Maximum clause weight is 33.000.
% 4.75/1.14 % Given clauses 1023.
% 4.75/1.14
% 4.75/1.14 % SZS output start CNFRefutation for theBenchmark
% See solution above
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