%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP127-4.004 : TPTP v9.2.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:24:04 PM UTC 2026
% Result : Unsatisfiable 0.45s 1.60s
% Output : CNFRefutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 26
% Syntax : Number of clauses : 249 ( 121 unt; 45 nHn; 211 RR)
% Number of literals : 537 ( 0 equ; 261 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 356 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(row_surjectivity,axiom,
( product(e_1,X1,X2)
| product(e_2,X1,X2)
| product(e_3,X1,X2)
| product(e_4,X1,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',row_surjectivity) ).
cnf(column_surjectivity,axiom,
( product(X1,e_1,X2)
| product(X1,e_2,X2)
| product(X1,e_3,X2)
| product(X1,e_4,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',column_surjectivity) ).
cnf(product_total_function1,axiom,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| product(X1,X2,e_3)
| product(X1,X2,e_4)
| ~ group_element(X1)
| ~ group_element(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
cnf(qg3_2,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X3,X2,X4)
| ~ product(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3_2) ).
cnf(qg3_1,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X4,X1,X2)
| ~ product(X3,X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3_1) ).
cnf(qg3,negated_conjecture,
( product(X4,X1,X2)
| ~ product(X1,X2,X3)
| ~ product(X3,X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
cnf(product_left_cancellation,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(product_right_cancellation,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(product_total_function2,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
cnf(product_idempotence,axiom,
product(X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
cnf(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
cnf(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
cnf(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
cnf(e_3_is_not_e_4,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
cnf(e_2_is_not_e_4,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
cnf(e_1_is_not_e_4,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
cnf(element_4,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
cnf(i_0_26,axiom,
( product(e_1,X1,X2)
| product(e_2,X1,X2)
| product(e_3,X1,X2)
| product(e_4,X1,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
row_surjectivity,
[final] ).
cnf(i_0_27,axiom,
( product(X1,e_1,X2)
| product(X1,e_2,X2)
| product(X1,e_3,X2)
| product(X1,e_4,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
column_surjectivity,
[final] ).
cnf(i_0_28,axiom,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| product(X1,X2,e_3)
| product(X1,X2,e_4)
| ~ group_element(X1)
| ~ group_element(X2) ),
product_total_function1,
[final] ).
cnf(i_0_29,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X3,X2,X4)
| ~ product(X2,X4,X1) ),
qg3_2,
[final] ).
cnf(i_0_30,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X4,X1,X2)
| ~ product(X3,X1,X4) ),
qg3_1,
[final] ).
cnf(i_0_31,negated_conjecture,
( product(X4,X1,X2)
| ~ product(X1,X2,X3)
| ~ product(X3,X1,X4) ),
qg3,
[final] ).
cnf(i_0_32,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
product_left_cancellation,
[final] ).
cnf(i_0_33,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_right_cancellation,
[final] ).
cnf(i_0_34,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
product_total_function2,
[final] ).
cnf(i_0_35,axiom,
product(X1,X1,X1),
product_idempotence,
[final] ).
cnf(i_0_36,axiom,
~ equalish(e_4,e_3),
e_4_is_not_e_3,
[final] ).
cnf(i_0_37,axiom,
~ equalish(e_4,e_2),
e_4_is_not_e_2,
[final] ).
cnf(i_0_38,axiom,
~ equalish(e_4,e_1),
e_4_is_not_e_1,
[final] ).
cnf(i_0_39,axiom,
~ equalish(e_3,e_4),
e_3_is_not_e_4,
[final] ).
cnf(i_0_40,axiom,
~ equalish(e_3,e_2),
e_3_is_not_e_2,
[final] ).
cnf(i_0_41,axiom,
~ equalish(e_3,e_1),
e_3_is_not_e_1,
[final] ).
cnf(i_0_42,axiom,
~ equalish(e_2,e_4),
e_2_is_not_e_4,
[final] ).
cnf(i_0_43,axiom,
~ equalish(e_2,e_3),
e_2_is_not_e_3,
[final] ).
cnf(i_0_44,axiom,
~ equalish(e_2,e_1),
e_2_is_not_e_1,
[final] ).
cnf(i_0_45,axiom,
~ equalish(e_1,e_4),
e_1_is_not_e_4,
[final] ).
cnf(i_0_46,axiom,
~ equalish(e_1,e_3),
e_1_is_not_e_3,
[final] ).
cnf(i_0_47,axiom,
~ equalish(e_1,e_2),
e_1_is_not_e_2,
[final] ).
cnf(i_0_48,axiom,
group_element(e_4),
element_4,
[final] ).
cnf(i_0_49,axiom,
group_element(e_3),
element_3,
[final] ).
cnf(i_0_50,axiom,
group_element(e_2),
element_2,
[final] ).
cnf(i_0_51,axiom,
group_element(e_1),
element_1,
[final] ).
cnf(i_0_52,plain,
~ product(e_4,e_3,e_3),
inference(scs_inference,[],[i_0_35,i_0_36,i_0_32]) ).
cnf(i_0_53,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_54,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X1)
| ~ product(X4,X2,X3) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_55,plain,
~ product(e_3,e_4,e_3),
inference(scs_inference,[],[i_0_35,i_0_53,i_0_36,i_0_32,i_0_33]) ).
cnf(i_0_56,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_57,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X2)
| ~ product(X1,X4,X3) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_58,plain,
~ product(e_3,e_3,e_4),
inference(scs_inference,[],[i_0_35,i_0_53,i_0_56,i_0_36,i_0_32,i_0_33,i_0_34]) ).
cnf(i_0_59,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_60,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X3)
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_61,plain,
~ product(e_4,e_2,e_2),
inference(scs_inference,[],[i_0_35,i_0_37,i_0_32]) ).
cnf(i_0_62,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_63,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X1)
| ~ product(X4,X2,X3) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_64,plain,
~ product(e_2,e_4,e_2),
inference(scs_inference,[],[i_0_35,i_0_62,i_0_37,i_0_32,i_0_33]) ).
cnf(i_0_65,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_66,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X2)
| ~ product(X1,X4,X3) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_67,plain,
~ product(e_2,e_2,e_4),
inference(scs_inference,[],[i_0_35,i_0_62,i_0_65,i_0_37,i_0_32,i_0_33,i_0_34]) ).
cnf(i_0_68,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_69,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X3)
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_70,plain,
( product(e_4,e_2,e_3)
| product(e_4,e_2,e_4)
| product(e_4,e_2,e_1) ),
inference(scs_inference,[],[i_0_35,i_0_62,i_0_65,i_0_37,i_0_48,i_0_50,i_0_32,i_0_33,i_0_34,i_0_28]) ).
cnf(i_0_71,plain,
~ product(e_4,e_1,e_1),
inference(scs_inference,[],[i_0_35,i_0_38,i_0_32]) ).
cnf(i_0_72,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_73,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X1)
| ~ product(X4,X2,X3) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_74,plain,
~ product(e_1,e_4,e_1),
inference(scs_inference,[],[i_0_35,i_0_72,i_0_38,i_0_32,i_0_33]) ).
cnf(i_0_75,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_76,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X2)
| ~ product(X1,X4,X3) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_77,plain,
~ product(e_1,e_1,e_4),
inference(scs_inference,[],[i_0_35,i_0_72,i_0_75,i_0_38,i_0_32,i_0_33,i_0_34]) ).
cnf(i_0_78,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_79,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X3)
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_81,plain,
~ product(e_3,e_4,e_4),
inference(scs_inference,[],[i_0_35,i_0_39,i_0_32]) ).
cnf(i_0_82,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_83,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X1)
| ~ product(X4,X2,X3) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_84,plain,
~ product(e_4,e_3,e_4),
inference(scs_inference,[],[i_0_35,i_0_82,i_0_39,i_0_32,i_0_33]) ).
cnf(i_0_85,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_86,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X2)
| ~ product(X1,X4,X3) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_87,plain,
~ product(e_4,e_4,e_3),
inference(scs_inference,[],[i_0_35,i_0_82,i_0_85,i_0_39,i_0_32,i_0_33,i_0_34]) ).
cnf(i_0_88,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_89,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X3)
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_90,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_4,e_4)
| product(e_2,e_4,e_1) ),
inference(scs_inference,[],[i_0_35,i_0_82,i_0_85,i_0_67,i_0_64,i_0_39,i_0_48,i_0_50,i_0_32,i_0_33,i_0_34,i_0_28]) ).
cnf(i_0_91,plain,
~ product(e_3,e_2,e_2),
inference(scs_inference,[],[i_0_35,i_0_40,i_0_32]) ).
cnf(i_0_92,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_93,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X1)
| ~ product(X4,X2,X3) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_94,plain,
~ product(e_2,e_3,e_2),
inference(scs_inference,[],[i_0_35,i_0_92,i_0_40,i_0_32,i_0_33]) ).
cnf(i_0_95,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_96,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X2)
| ~ product(X1,X4,X3) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_97,plain,
~ product(e_2,e_2,e_3),
inference(scs_inference,[],[i_0_35,i_0_92,i_0_95,i_0_40,i_0_32,i_0_33,i_0_34]) ).
cnf(i_0_98,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_99,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X3)
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_101,plain,
~ product(e_3,e_1,e_1),
inference(scs_inference,[],[i_0_35,i_0_41,i_0_32]) ).
cnf(i_0_102,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_103,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X1)
| ~ product(X4,X2,X3) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_104,plain,
~ product(e_1,e_3,e_1),
inference(scs_inference,[],[i_0_35,i_0_102,i_0_41,i_0_32,i_0_33]) ).
cnf(i_0_105,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_106,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X2)
| ~ product(X1,X4,X3) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_107,plain,
~ product(e_1,e_1,e_3),
inference(scs_inference,[],[i_0_35,i_0_102,i_0_105,i_0_41,i_0_32,i_0_33,i_0_34]) ).
cnf(i_0_108,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_109,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X3)
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_110,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_4)
| product(e_3,e_2,e_1) ),
inference(scs_inference,[],[i_0_35,i_0_102,i_0_105,i_0_91,i_0_94,i_0_41,i_0_49,i_0_50,i_0_32,i_0_33,i_0_34,i_0_28]) ).
cnf(i_0_111,plain,
~ product(e_2,e_4,e_4),
inference(scs_inference,[],[i_0_35,i_0_42,i_0_32]) ).
cnf(i_0_112,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_113,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X1)
| ~ product(X4,X2,X3) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_114,plain,
~ product(e_4,e_2,e_4),
inference(scs_inference,[],[i_0_35,i_0_112,i_0_42,i_0_32,i_0_33]) ).
cnf(i_0_115,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_116,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X2)
| ~ product(X1,X4,X3) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_117,plain,
~ product(e_4,e_4,e_2),
inference(scs_inference,[],[i_0_35,i_0_112,i_0_115,i_0_42,i_0_32,i_0_33,i_0_34]) ).
cnf(i_0_118,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_119,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X3)
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_120,plain,
( product(e_3,e_2,e_4)
| product(e_1,e_2,e_4) ),
inference(scs_inference,[],[i_0_35,i_0_112,i_0_115,i_0_67,i_0_42,i_0_48,i_0_50,i_0_32,i_0_33,i_0_34,i_0_26]) ).
cnf(i_0_121,plain,
( product(e_2,X1,X2)
| product(e_3,X1,X2)
| product(e_4,X1,X2)
| product(e_1,X1,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_122,plain,
( ~ product(e_3,e_3,e_2)
| product(e_1,e_2,e_4) ),
inference(scs_inference,[],[i_0_35,i_0_112,i_0_115,i_0_52,i_0_67,i_0_42,i_0_48,i_0_50,i_0_32,i_0_33,i_0_34,i_0_26,i_0_29]) ).
cnf(i_0_123,plain,
( ~ product(X1,X2,X3)
| product(X3,X1,X4)
| ~ product(X4,X1,X2) ),
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_124,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_4)
| product(e_1,e_2,e_4)
| product(e_2,e_3,e_1) ),
inference(scs_inference,[],[i_0_35,i_0_112,i_0_115,i_0_52,i_0_97,i_0_94,i_0_67,i_0_42,i_0_49,i_0_48,i_0_50,i_0_32,i_0_33,i_0_34,i_0_26,i_0_29,i_0_28]) ).
cnf(i_0_125,plain,
( product(e_4,e_2,e_3)
| product(e_4,e_2,e_1) ),
inference(scs_inference,[],[i_0_114,i_0_70]) ).
cnf(i_0_126,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_4,e_1) ),
inference(scs_inference,[],[i_0_111,i_0_90]) ).
cnf(i_0_127,plain,
~ product(e_2,e_3,e_3),
inference(scs_inference,[],[i_0_35,i_0_43,i_0_32]) ).
cnf(i_0_128,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_129,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X1)
| ~ product(X4,X2,X3) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_130,plain,
~ product(e_3,e_2,e_3),
inference(scs_inference,[],[i_0_35,i_0_128,i_0_43,i_0_32,i_0_33]) ).
cnf(i_0_131,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_132,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X2)
| ~ product(X1,X4,X3) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_133,plain,
~ product(e_3,e_3,e_2),
inference(scs_inference,[],[i_0_35,i_0_128,i_0_131,i_0_43,i_0_32,i_0_33,i_0_34]) ).
cnf(i_0_134,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_135,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X3)
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_136,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_1) ),
inference(scs_inference,[],[i_0_35,i_0_128,i_0_131,i_0_43,i_0_32,i_0_33,i_0_34,i_0_110]) ).
cnf(i_0_137,plain,
( ~ product(e_1,e_2,e_2)
| product(e_3,e_2,e_4) ),
inference(scs_inference,[],[i_0_35,i_0_128,i_0_131,i_0_97,i_0_43,i_0_32,i_0_33,i_0_34,i_0_110,i_0_30]) ).
cnf(i_0_138,plain,
( ~ product(X1,X2,X3)
| product(X2,X4,X1)
| ~ product(X3,X2,X4) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_139,plain,
( ~ product(e_1,e_3,e_2)
| product(e_3,e_2,e_4) ),
inference(scs_inference,[],[i_0_35,i_0_128,i_0_131,i_0_104,i_0_97,i_0_43,i_0_32,i_0_33,i_0_34,i_0_110,i_0_30,i_0_29]) ).
cnf(i_0_140,plain,
( ~ product(X1,X2,X3)
| product(X3,X1,X4)
| ~ product(X4,X1,X2) ),
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_141,plain,
( product(e_4,e_3,e_2)
| product(e_3,e_2,e_4) ),
inference(scs_inference,[],[i_0_35,i_0_128,i_0_131,i_0_104,i_0_97,i_0_94,i_0_43,i_0_49,i_0_50,i_0_32,i_0_33,i_0_34,i_0_110,i_0_30,i_0_29,i_0_26]) ).
cnf(i_0_142,plain,
( product(e_2,X1,X2)
| product(e_3,X1,X2)
| product(e_4,X1,X2)
| product(e_1,X1,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_143,plain,
( ~ product(e_3,e_2,e_4)
| product(e_3,e_2,e_4) ),
inference(scs_inference,[],[i_0_35,i_0_128,i_0_131,i_0_104,i_0_97,i_0_94,i_0_43,i_0_49,i_0_50,i_0_32,i_0_33,i_0_34,i_0_110,i_0_30,i_0_29,i_0_26,i_0_31]) ).
cnf(i_0_144,plain,
( ~ product(X1,X2,X3)
| product(X3,X2,X4)
| ~ product(X2,X4,X1) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_146,plain,
( product(e_1,e_2,e_4)
| product(e_2,e_3,e_4)
| product(e_2,e_3,e_1) ),
inference(scs_inference,[],[i_0_127,i_0_124]) ).
cnf(i_0_147,plain,
~ product(e_2,e_1,e_1),
inference(scs_inference,[],[i_0_35,i_0_44,i_0_32]) ).
cnf(i_0_148,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_149,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X1)
| ~ product(X4,X2,X3) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_150,plain,
~ product(e_1,e_2,e_1),
inference(scs_inference,[],[i_0_35,i_0_148,i_0_44,i_0_32,i_0_33]) ).
cnf(i_0_151,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_152,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X2)
| ~ product(X1,X4,X3) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_153,plain,
~ product(e_1,e_1,e_2),
inference(scs_inference,[],[i_0_35,i_0_148,i_0_151,i_0_44,i_0_32,i_0_33,i_0_34]) ).
cnf(i_0_154,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_155,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X3)
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_156,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_1,e_3) ),
inference(scs_inference,[],[i_0_35,i_0_148,i_0_151,i_0_127,i_0_97,i_0_44,i_0_49,i_0_50,i_0_32,i_0_33,i_0_34,i_0_27]) ).
cnf(i_0_157,plain,
( product(X1,e_2,X2)
| product(X1,e_3,X2)
| product(X1,e_4,X2)
| product(X1,e_1,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_158,plain,
( ~ product(e_4,e_3,e_2)
| product(e_2,e_1,e_3) ),
inference(scs_inference,[],[i_0_35,i_0_148,i_0_151,i_0_55,i_0_127,i_0_97,i_0_44,i_0_49,i_0_50,i_0_32,i_0_33,i_0_34,i_0_27,i_0_31]) ).
cnf(i_0_159,plain,
( ~ product(X1,X2,X3)
| product(X3,X2,X4)
| ~ product(X2,X4,X1) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_160,plain,
( ~ product(e_3,e_2,e_4)
| product(e_2,e_1,e_3) ),
inference(scs_inference,[],[i_0_35,i_0_148,i_0_151,i_0_55,i_0_127,i_0_130,i_0_97,i_0_44,i_0_49,i_0_50,i_0_32,i_0_33,i_0_34,i_0_27,i_0_31,i_0_29]) ).
cnf(i_0_161,plain,
( ~ product(X1,X2,X3)
| product(X3,X1,X4)
| ~ product(X4,X1,X2) ),
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_163,plain,
~ product(e_1,e_4,e_4),
inference(scs_inference,[],[i_0_35,i_0_45,i_0_32]) ).
cnf(i_0_164,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_165,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X1)
| ~ product(X4,X2,X3) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_166,plain,
~ product(e_4,e_1,e_4),
inference(scs_inference,[],[i_0_35,i_0_164,i_0_45,i_0_32,i_0_33]) ).
cnf(i_0_167,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_168,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X2)
| ~ product(X1,X4,X3) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_169,plain,
~ product(e_4,e_4,e_1),
inference(scs_inference,[],[i_0_35,i_0_164,i_0_167,i_0_45,i_0_32,i_0_33,i_0_34]) ).
cnf(i_0_170,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_171,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X3)
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_172,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_1) ),
inference(scs_inference,[],[i_0_35,i_0_164,i_0_167,i_0_127,i_0_94,i_0_45,i_0_49,i_0_50,i_0_32,i_0_33,i_0_34,i_0_28]) ).
cnf(i_0_173,plain,
( product(X1,X2,e_2)
| product(X1,X2,e_3)
| product(X1,X2,e_4)
| product(X1,X2,e_1)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_174,plain,
( ~ product(e_4,e_2,e_3)
| product(e_2,e_3,e_1) ),
inference(scs_inference,[],[i_0_35,i_0_164,i_0_167,i_0_114,i_0_127,i_0_94,i_0_45,i_0_49,i_0_50,i_0_32,i_0_33,i_0_34,i_0_28,i_0_29]) ).
cnf(i_0_175,plain,
( ~ product(X1,X2,X3)
| product(X3,X1,X4)
| ~ product(X4,X1,X2) ),
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_177,plain,
~ product(e_1,e_3,e_3),
inference(scs_inference,[],[i_0_35,i_0_46,i_0_32]) ).
cnf(i_0_178,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_179,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X1)
| ~ product(X4,X2,X3) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_180,plain,
~ product(e_3,e_1,e_3),
inference(scs_inference,[],[i_0_35,i_0_178,i_0_46,i_0_32,i_0_33]) ).
cnf(i_0_181,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_182,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X2)
| ~ product(X1,X4,X3) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_183,plain,
~ product(e_3,e_3,e_1),
inference(scs_inference,[],[i_0_35,i_0_178,i_0_181,i_0_46,i_0_32,i_0_33,i_0_34]) ).
cnf(i_0_184,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_185,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X3)
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_186,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_1,e_2) ),
inference(scs_inference,[],[i_0_35,i_0_178,i_0_181,i_0_133,i_0_91,i_0_46,i_0_49,i_0_50,i_0_32,i_0_33,i_0_34,i_0_27]) ).
cnf(i_0_187,plain,
( product(X1,e_2,X2)
| product(X1,e_3,X2)
| product(X1,e_4,X2)
| product(X1,e_1,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_188,plain,
( product(e_3,e_4,e_2)
| product(e_1,e_4,e_2) ),
inference(scs_inference,[],[i_0_35,i_0_178,i_0_181,i_0_133,i_0_91,i_0_64,i_0_117,i_0_46,i_0_49,i_0_48,i_0_50,i_0_32,i_0_33,i_0_34,i_0_27,i_0_26]) ).
cnf(i_0_189,plain,
( product(e_2,X1,X2)
| product(e_3,X1,X2)
| product(e_4,X1,X2)
| product(e_1,X1,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_190,plain,
~ product(e_1,e_2,e_2),
inference(scs_inference,[],[i_0_35,i_0_47,i_0_32]) ).
cnf(i_0_191,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_192,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X1)
| ~ product(X4,X2,X3) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_193,plain,
~ product(e_2,e_1,e_2),
inference(scs_inference,[],[i_0_35,i_0_191,i_0_47,i_0_32,i_0_33]) ).
cnf(i_0_194,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_195,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X2)
| ~ product(X1,X4,X3) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_196,plain,
~ product(e_2,e_2,e_1),
inference(scs_inference,[],[i_0_35,i_0_191,i_0_194,i_0_47,i_0_32,i_0_33,i_0_34]) ).
cnf(i_0_197,plain,
product(X1,X1,X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_198,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X3)
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_199,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(scs_inference,[],[i_0_35,i_0_191,i_0_194,i_0_150,i_0_47,i_0_51,i_0_50,i_0_32,i_0_33,i_0_34,i_0_28]) ).
cnf(i_0_200,plain,
( product(X1,X2,e_2)
| product(X1,X2,e_3)
| product(X1,X2,e_4)
| product(X1,X2,e_1)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_201,plain,
( ~ product(e_3,e_2,e_1)
| product(e_1,e_2,e_4) ),
inference(scs_inference,[],[i_0_35,i_0_191,i_0_194,i_0_147,i_0_150,i_0_47,i_0_51,i_0_50,i_0_32,i_0_33,i_0_34,i_0_28,i_0_30]) ).
cnf(i_0_202,plain,
( ~ product(X1,X2,X3)
| product(X2,X4,X1)
| ~ product(X3,X2,X4) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_204,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_4) ),
inference(scs_inference,[],[i_0_193,i_0_147,i_0_51,i_0_50,i_0_28]) ).
cnf(i_0_205,plain,
( product(X1,X2,e_2)
| product(X1,X2,e_3)
| product(X1,X2,e_4)
| product(X1,X2,e_1)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_206,plain,
( ~ product(e_4,e_1,e_3)
| product(e_2,e_1,e_4) ),
inference(scs_inference,[],[i_0_193,i_0_147,i_0_51,i_0_37,i_0_50,i_0_28,i_0_32]) ).
cnf(i_0_207,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X1)
| ~ product(X4,X2,X3) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_208,plain,
( ~ product(e_2,e_4,e_3)
| product(e_2,e_1,e_4) ),
inference(scs_inference,[],[i_0_193,i_0_147,i_0_51,i_0_37,i_0_38,i_0_50,i_0_28,i_0_32,i_0_33]) ).
cnf(i_0_209,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X2)
| ~ product(X1,X4,X3) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_210,plain,
( ~ product(e_2,e_1,e_4)
| product(e_2,e_1,e_4) ),
inference(scs_inference,[],[i_0_193,i_0_147,i_0_51,i_0_36,i_0_37,i_0_38,i_0_50,i_0_28,i_0_32,i_0_33,i_0_34]) ).
cnf(i_0_211,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X3)
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_212,plain,
( product(e_2,e_1,e_4)
| product(e_4,e_3,e_2)
| product(e_4,e_1,e_2) ),
inference(scs_inference,[],[i_0_61,i_0_64,i_0_117,i_0_193,i_0_147,i_0_51,i_0_36,i_0_37,i_0_38,i_0_48,i_0_50,i_0_28,i_0_32,i_0_33,i_0_34,i_0_27]) ).
cnf(i_0_213,plain,
( product(e_4,e_3,e_2)
| product(e_1,e_3,e_2) ),
inference(scs_inference,[],[i_0_133,i_0_94,i_0_49,i_0_50,i_0_26]) ).
cnf(i_0_214,plain,
( product(e_2,X1,X2)
| product(e_3,X1,X2)
| product(e_4,X1,X2)
| product(e_1,X1,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_215,plain,
( product(e_2,e_1,e_3)
| product(e_1,e_3,e_2) ),
inference(scs_inference,[],[i_0_133,i_0_94,i_0_49,i_0_50,i_0_26,i_0_158]) ).
cnf(i_0_216,plain,
( ~ product(e_3,e_1,e_2)
| product(e_1,e_3,e_2) ),
inference(scs_inference,[],[i_0_133,i_0_94,i_0_190,i_0_49,i_0_50,i_0_26,i_0_158,i_0_30]) ).
cnf(i_0_217,plain,
( ~ product(X1,X2,X3)
| product(X2,X4,X1)
| ~ product(X3,X2,X4) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_218,plain,
( product(e_3,e_4,e_2)
| product(e_1,e_3,e_2) ),
inference(scs_inference,[],[i_0_91,i_0_130,i_0_133,i_0_94,i_0_190,i_0_49,i_0_50,i_0_26,i_0_158,i_0_30,i_0_28,i_0_27]) ).
cnf(i_0_219,plain,
( product(X1,e_2,X2)
| product(X1,e_3,X2)
| product(X1,e_4,X2)
| product(X1,e_1,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_220,plain,
( product(e_4,e_3,e_2)
| product(e_4,e_1,e_2) ),
inference(scs_inference,[],[i_0_61,i_0_117,i_0_48,i_0_50,i_0_27]) ).
cnf(i_0_221,plain,
( product(X1,e_2,X2)
| product(X1,e_3,X2)
| product(X1,e_4,X2)
| product(X1,e_1,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_222,plain,
( product(e_2,e_1,e_3)
| product(e_4,e_1,e_2) ),
inference(scs_inference,[],[i_0_61,i_0_117,i_0_48,i_0_50,i_0_27,i_0_158]) ).
cnf(i_0_223,plain,
( ~ product(e_3,e_2,e_4)
| product(e_4,e_1,e_2) ),
inference(scs_inference,[],[i_0_61,i_0_94,i_0_117,i_0_48,i_0_50,i_0_27,i_0_158,i_0_31]) ).
cnf(i_0_224,plain,
( ~ product(X1,X2,X3)
| product(X3,X2,X4)
| ~ product(X2,X4,X1) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_225,plain,
( ~ product(e_3,e_1,e_2)
| product(e_4,e_1,e_2) ),
inference(scs_inference,[],[i_0_61,i_0_94,i_0_190,i_0_117,i_0_48,i_0_50,i_0_27,i_0_158,i_0_31,i_0_30]) ).
cnf(i_0_226,plain,
( ~ product(X1,X2,X3)
| product(X2,X4,X1)
| ~ product(X3,X2,X4) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_228,plain,
( product(e_3,e_1,e_2)
| product(e_4,e_1,e_2) ),
inference(scs_inference,[],[i_0_193,i_0_153,i_0_51,i_0_50,i_0_26]) ).
cnf(i_0_229,plain,
( product(e_2,X1,X2)
| product(e_3,X1,X2)
| product(e_4,X1,X2)
| product(e_1,X1,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_230,plain,
( product(e_1,e_3,e_2)
| product(e_4,e_1,e_2) ),
inference(scs_inference,[],[i_0_193,i_0_153,i_0_51,i_0_50,i_0_26,i_0_216]) ).
cnf(i_0_231,plain,
product(e_4,e_1,e_2),
inference(scs_inference,[],[i_0_193,i_0_153,i_0_51,i_0_50,i_0_26,i_0_216,i_0_225]) ).
cnf(i_0_232,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X1)
| ~ product(X4,X2,X3) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_234,plain,
~ product(e_1,e_2,e_4),
inference(scs_inference,[],[i_0_193,i_0_231,i_0_31]) ).
cnf(i_0_235,plain,
( ~ product(X1,X2,X3)
| product(X3,X2,X4)
| ~ product(X2,X4,X1) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_236,plain,
~ product(e_4,e_3,e_2),
inference(scs_inference,[],[i_0_193,i_0_231,i_0_41,i_0_31,i_0_33]) ).
cnf(i_0_237,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X2)
| ~ product(X1,X4,X3) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_238,plain,
~ product(e_4,e_1,e_3),
inference(scs_inference,[],[i_0_193,i_0_231,i_0_40,i_0_41,i_0_31,i_0_33,i_0_34]) ).
cnf(i_0_239,plain,
( ~ product(X1,X2,X3)
| equalish(X4,X3)
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_240,plain,
product(e_1,e_2,e_3),
inference(scs_inference,[],[i_0_190,i_0_193,i_0_231,i_0_150,i_0_40,i_0_41,i_0_51,i_0_50,i_0_31,i_0_33,i_0_34,i_0_28]) ).
cnf(i_0_241,plain,
( product(X1,X2,e_2)
| product(X1,X2,e_3)
| product(X1,X2,e_4)
| product(X1,X2,e_1)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_242,plain,
product(e_1,e_3,e_4),
inference(scs_inference,[],[i_0_190,i_0_193,i_0_231,i_0_77,i_0_163,i_0_150,i_0_40,i_0_41,i_0_51,i_0_48,i_0_50,i_0_31,i_0_33,i_0_34,i_0_28,i_0_27]) ).
cnf(i_0_243,plain,
( product(X1,e_2,X2)
| product(X1,e_3,X2)
| product(X1,e_4,X2)
| product(X1,e_1,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_244,plain,
product(e_1,e_3,e_2),
inference(scs_inference,[],[i_0_94,i_0_190,i_0_193,i_0_133,i_0_231,i_0_77,i_0_163,i_0_150,i_0_40,i_0_41,i_0_51,i_0_49,i_0_48,i_0_50,i_0_31,i_0_33,i_0_34,i_0_28,i_0_27,i_0_26]) ).
cnf(i_0_245,plain,
( product(e_2,X1,X2)
| product(e_3,X1,X2)
| product(e_4,X1,X2)
| product(e_1,X1,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_246,plain,
product(e_3,e_2,e_4),
inference(scs_inference,[],[i_0_94,i_0_190,i_0_193,i_0_133,i_0_231,i_0_77,i_0_163,i_0_150,i_0_40,i_0_41,i_0_51,i_0_49,i_0_48,i_0_50,i_0_31,i_0_33,i_0_34,i_0_28,i_0_27,i_0_26,i_0_139]) ).
cnf(i_0_247,plain,
product(e_2,e_1,e_3),
inference(scs_inference,[],[i_0_94,i_0_190,i_0_193,i_0_133,i_0_231,i_0_77,i_0_163,i_0_150,i_0_40,i_0_41,i_0_51,i_0_49,i_0_48,i_0_50,i_0_31,i_0_33,i_0_34,i_0_28,i_0_27,i_0_26,i_0_139,i_0_160]) ).
cnf(i_0_248,plain,
~ product(e_3,e_1,e_2),
inference(scs_inference,[],[i_0_94,i_0_190,i_0_193,i_0_133,i_0_231,i_0_180,i_0_77,i_0_163,i_0_150,i_0_40,i_0_41,i_0_51,i_0_49,i_0_48,i_0_50,i_0_31,i_0_33,i_0_34,i_0_28,i_0_27,i_0_26,i_0_139,i_0_160,i_0_29]) ).
cnf(i_0_249,plain,
( ~ product(X1,X2,X3)
| product(X3,X1,X4)
| ~ product(X4,X1,X2) ),
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_250,plain,
~ product(e_4,e_3,e_1),
inference(scs_inference,[],[i_0_94,i_0_190,i_0_193,i_0_133,i_0_231,i_0_180,i_0_101,i_0_77,i_0_163,i_0_150,i_0_40,i_0_41,i_0_51,i_0_49,i_0_48,i_0_50,i_0_31,i_0_33,i_0_34,i_0_28,i_0_27,i_0_26,i_0_139,i_0_160,i_0_29,i_0_30]) ).
cnf(i_0_251,plain,
( ~ product(X1,X2,X3)
| product(X2,X4,X1)
| ~ product(X3,X2,X4) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_252,plain,
product(e_3,e_4,e_2),
inference(scs_inference,[],[i_0_94,i_0_190,i_0_193,i_0_133,i_0_231,i_0_180,i_0_101,i_0_77,i_0_163,i_0_150,i_0_40,i_0_41,i_0_51,i_0_49,i_0_48,i_0_50,i_0_31,i_0_33,i_0_34,i_0_28,i_0_27,i_0_26,i_0_139,i_0_160,i_0_29,i_0_30,i_0_186]) ).
cnf(i_0_253,plain,
~ product(e_3,e_2,e_1),
inference(scs_inference,[],[i_0_234,i_0_201]) ).
cnf(i_0_254,plain,
~ product(e_2,e_4,e_3),
inference(scs_inference,[],[i_0_114,i_0_246,i_0_31]) ).
cnf(i_0_255,plain,
( ~ product(X1,X2,X3)
| product(X3,X2,X4)
| ~ product(X2,X4,X1) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_256,plain,
$false,
inference(scs_inference,[],[i_0_114,i_0_193,i_0_244,i_0_247,i_0_246,i_0_31,i_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP127-4.004 : TPTP v9.2.1. Bugfixed v1.2.1.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n017.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 18:22:12 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 0.45/1.60 % Version : CSE_E---1.7
% 0.45/1.60 % Problem : theBenchmark.p
% 0.45/1.60 % SZS status Unsatisfiable for theBenchmark.p
% 0.45/1.60 % SZS output start CNFRefutation
% See solution above
% 0.76/1.94 % Total time : 1.270s
%------------------------------------------------------------------------------