%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP129-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 : Thu Sep 24 12:38:40 PM UTC 2026
% Result : Unsatisfiable 1.59s 0.77s
% Output : CNFRefutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 23
% Syntax : Number of clauses : 239 ( 59 unt; 106 nHn; 239 RR)
% Number of literals : 640 ( 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 : 156 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_total_function1,axiom,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_4)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
cnf(element_4,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
cnf(qg3_1,negated_conjecture,
( ~ product(X2,X3,X4)
| ~ product(X3,X1,X4)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3_1) ).
cnf(product_left_cancellation,axiom,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
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_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(product_total_function2,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
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(product_right_cancellation,axiom,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
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(row_surjectivity,axiom,
( ~ group_element(X2)
| ~ group_element(X1)
| product(e_4,X1,X2)
| product(e_3,X1,X2)
| product(e_2,X1,X2)
| product(e_1,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',row_surjectivity) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
cnf(column_surjectivity,axiom,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,e_4,X2)
| product(X1,e_3,X2)
| product(X1,e_2,X2)
| product(X1,e_1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',column_surjectivity) ).
cnf(qg3_2,negated_conjecture,
( ~ product(X4,X1,X2)
| ~ product(X2,X4,X3)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3_2) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
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_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(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_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(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
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_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(qg3,negated_conjecture,
( ~ product(X2,X3,X4)
| ~ product(X1,X2,X3)
| product(X3,X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
cnf(c_0_23,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_4)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
inference(fof_simplification,[status(thm)],[product_total_function1]) ).
cnf(c_0_24,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_4)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
c_0_23 ).
cnf(c_0_25,axiom,
group_element(e_4),
element_4 ).
cnf(c_0_26,negated_conjecture,
( ~ product(X2,X3,X4)
| ~ product(X3,X1,X4)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[qg3_1]) ).
cnf(c_0_27,plain,
( ~ group_element(X1)
| product(X1,e_4,e_4)
| product(X1,e_4,e_3)
| product(X1,e_4,e_2)
| product(X1,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
( ~ product(X2,X3,X4)
| ~ product(X3,X1,X4)
| product(X1,X2,X3) ),
c_0_26 ).
cnf(c_0_29,plain,
( product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_27,c_0_25]) ).
cnf(c_0_30,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
inference(fof_simplification,[status(thm)],[product_left_cancellation]) ).
cnf(c_0_31,negated_conjecture,
( ~ product(X1,e_4,e_1)
| product(e_4,X1,e_4)
| product(e_4,e_4,e_4)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,plain,
~ equalish(e_2,e_4),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_4]) ).
cnf(c_0_33,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_30 ).
cnf(c_0_34,negated_conjecture,
( product(e_4,e_4,e_2)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_31,c_0_29]) ).
cnf(c_0_35,plain,
~ equalish(e_3,e_4),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_4]) ).
cnf(c_0_36,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
inference(fof_simplification,[status(thm)],[product_total_function2]) ).
cnf(c_0_37,plain,
~ equalish(e_2,e_4),
c_0_32 ).
cnf(c_0_38,negated_conjecture,
( ~ product(X1,e_4,e_4)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,plain,
~ equalish(e_3,e_4),
c_0_35 ).
cnf(c_0_40,plain,
~ equalish(e_4,e_3),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_3]) ).
cnf(c_0_41,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
c_0_36 ).
cnf(c_0_42,negated_conjecture,
( ~ product(e_2,e_4,e_4)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,negated_conjecture,
( ~ product(e_3,e_4,e_4)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_39,c_0_38]) ).
cnf(c_0_44,plain,
~ equalish(e_4,e_3),
c_0_40 ).
cnf(c_0_45,negated_conjecture,
( ~ product(e_4,e_4,X1)
| ~ product(e_2,e_4,e_4)
| product(e_4,e_4,e_2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
( ~ product(e_4,e_4,X1)
| ~ product(e_3,e_4,e_4)
| product(e_4,e_4,e_2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_41,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
( ~ product(X1,e_4,e_3)
| ~ product(e_2,e_4,e_4)
| product(e_4,X1,e_4)
| product(e_4,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_28,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
( ~ product(e_4,e_4,e_4)
| ~ product(e_2,e_4,e_4)
| product(e_4,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,negated_conjecture,
( ~ product(X1,e_4,e_3)
| ~ product(e_3,e_4,e_4)
| product(e_4,X1,e_4)
| product(e_4,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_28,c_0_43]) ).
cnf(c_0_50,negated_conjecture,
( ~ product(e_4,e_4,e_4)
| ~ product(e_3,e_4,e_4)
| product(e_4,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_44,c_0_46]) ).
cnf(c_0_51,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
inference(fof_simplification,[status(thm)],[product_right_cancellation]) ).
cnf(c_0_52,plain,
~ equalish(e_4,e_2),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_2]) ).
cnf(c_0_53,negated_conjecture,
( ~ product(e_2,e_4,e_4)
| product(e_4,e_4,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_42]),c_0_48]) ).
cnf(c_0_54,negated_conjecture,
( ~ product(e_3,e_4,e_4)
| product(e_4,e_4,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_43]),c_0_50]) ).
cnf(c_0_55,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_51 ).
cnf(c_0_56,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(e_4,X1,X2)
| product(e_3,X1,X2)
| product(e_2,X1,X2)
| product(e_1,X1,X2) ),
inference(fof_simplification,[status(thm)],[row_surjectivity]) ).
cnf(c_0_57,plain,
~ equalish(e_4,e_2),
c_0_52 ).
cnf(c_0_58,negated_conjecture,
( ~ product(e_4,e_4,X1)
| ~ product(e_2,e_4,e_4)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_41,c_0_53]) ).
cnf(c_0_59,negated_conjecture,
( ~ product(e_4,e_4,X1)
| ~ product(e_3,e_4,e_4)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_41,c_0_54]) ).
cnf(c_0_60,negated_conjecture,
( ~ product(e_4,X1,e_4)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_55,c_0_34]) ).
cnf(c_0_61,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_62,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(e_4,X1,X2)
| product(e_3,X1,X2)
| product(e_2,X1,X2)
| product(e_1,X1,X2) ),
c_0_56 ).
cnf(c_0_63,negated_conjecture,
( ~ product(X1,e_4,e_2)
| ~ product(e_2,e_4,e_4)
| product(e_4,X1,e_4) ),
inference(spm,[status(thm)],[c_0_28,c_0_53]) ).
cnf(c_0_64,negated_conjecture,
( ~ product(e_4,e_4,e_4)
| ~ product(e_2,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_65,negated_conjecture,
( ~ product(X1,e_4,e_2)
| ~ product(e_3,e_4,e_4)
| product(e_4,X1,e_4) ),
inference(spm,[status(thm)],[c_0_28,c_0_54]) ).
cnf(c_0_66,negated_conjecture,
( ~ product(e_4,e_4,e_4)
| ~ product(e_3,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_57,c_0_59]) ).
cnf(c_0_67,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,e_4,X2)
| product(X1,e_3,X2)
| product(X1,e_2,X2)
| product(X1,e_1,X2) ),
inference(fof_simplification,[status(thm)],[column_surjectivity]) ).
cnf(c_0_68,negated_conjecture,
( ~ product(e_4,e_2,e_4)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_37,c_0_60]) ).
cnf(c_0_69,negated_conjecture,
( ~ product(e_4,e_3,e_4)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_39,c_0_60]) ).
cnf(c_0_70,plain,
( ~ group_element(X1)
| product(X1,e_3,e_4)
| product(X1,e_3,e_3)
| product(X1,e_3,e_2)
| product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_24,c_0_61]) ).
cnf(c_0_71,negated_conjecture,
( ~ product(X4,X1,X2)
| ~ product(X2,X4,X3)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[qg3_2]) ).
cnf(c_0_72,plain,
( ~ group_element(X1)
| product(e_4,X1,e_4)
| product(e_3,X1,e_4)
| product(e_2,X1,e_4)
| product(e_1,X1,e_4) ),
inference(spm,[status(thm)],[c_0_62,c_0_25]) ).
cnf(c_0_73,negated_conjecture,
~ product(e_2,e_4,e_4),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_53]),c_0_64]) ).
cnf(c_0_74,negated_conjecture,
~ product(e_3,e_4,e_4),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_54]),c_0_66]) ).
cnf(c_0_75,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,e_4,X2)
| product(X1,e_3,X2)
| product(X1,e_2,X2)
| product(X1,e_1,X2) ),
c_0_67 ).
cnf(c_0_76,negated_conjecture,
( ~ product(e_4,e_4,X1)
| ~ product(e_4,e_2,e_4)
| product(e_4,e_4,e_2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_41,c_0_68]) ).
cnf(c_0_77,negated_conjecture,
( ~ product(e_4,e_4,X1)
| ~ product(e_4,e_3,e_4)
| product(e_4,e_4,e_2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_41,c_0_69]) ).
cnf(c_0_78,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_70,c_0_61]) ).
cnf(c_0_79,negated_conjecture,
( ~ product(X4,X1,X2)
| ~ product(X2,X4,X3)
| product(X1,X2,X3) ),
c_0_71 ).
cnf(c_0_80,plain,
( product(e_1,e_4,e_4)
| product(e_4,e_4,e_4) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_25]),c_0_73]),c_0_74]) ).
cnf(c_0_81,plain,
( ~ group_element(X1)
| product(X1,e_4,e_4)
| product(X1,e_3,e_4)
| product(X1,e_2,e_4)
| product(X1,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_75,c_0_25]) ).
cnf(c_0_82,negated_conjecture,
( ~ product(X1,e_4,e_3)
| ~ product(e_4,e_2,e_4)
| product(e_4,X1,e_4)
| product(e_4,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_28,c_0_68]) ).
cnf(c_0_83,negated_conjecture,
( ~ product(e_4,e_4,e_4)
| ~ product(e_4,e_2,e_4)
| product(e_4,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_44,c_0_76]) ).
cnf(c_0_84,negated_conjecture,
( ~ product(X1,e_4,e_3)
| ~ product(e_4,e_3,e_4)
| product(e_4,X1,e_4)
| product(e_4,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_28,c_0_69]) ).
cnf(c_0_85,negated_conjecture,
( ~ product(e_4,e_4,e_4)
| ~ product(e_4,e_3,e_4)
| product(e_4,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_44,c_0_77]) ).
cnf(c_0_86,negated_conjecture,
( ~ product(X1,e_3,e_1)
| product(e_3,X1,e_3)
| product(e_3,e_3,e_4)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_28,c_0_78]) ).
cnf(c_0_87,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_88,negated_conjecture,
( ~ product(e_4,e_1,X1)
| product(e_4,e_4,X1)
| product(e_4,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_89,plain,
( product(e_4,e_1,e_4)
| product(e_4,e_2,e_4)
| product(e_4,e_3,e_4)
| product(e_4,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_81,c_0_25]) ).
cnf(c_0_90,plain,
~ equalish(e_3,e_2),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_2]) ).
cnf(c_0_91,negated_conjecture,
( ~ product(e_4,e_2,e_4)
| product(e_4,e_4,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_68]),c_0_83]) ).
cnf(c_0_92,negated_conjecture,
( ~ product(e_4,e_3,e_4)
| product(e_4,e_4,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_69]),c_0_85]) ).
cnf(c_0_93,negated_conjecture,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_86,c_0_78]) ).
cnf(c_0_94,plain,
( ~ group_element(X1)
| product(X1,e_2,e_4)
| product(X1,e_2,e_3)
| product(X1,e_2,e_2)
| product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_24,c_0_87]) ).
cnf(c_0_95,negated_conjecture,
( product(e_4,e_4,e_4)
| product(e_4,e_3,e_4)
| product(e_4,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_96,plain,
~ equalish(e_3,e_2),
c_0_90 ).
cnf(c_0_97,negated_conjecture,
( ~ product(e_4,e_4,X1)
| ~ product(e_4,e_2,e_4)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_41,c_0_91]) ).
cnf(c_0_98,negated_conjecture,
( ~ product(e_4,e_4,X1)
| ~ product(e_4,e_3,e_4)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_41,c_0_92]) ).
cnf(c_0_99,negated_conjecture,
( ~ product(X1,e_3,e_4)
| product(e_3,X1,e_3)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_28,c_0_93]) ).
cnf(c_0_100,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_94,c_0_87]) ).
cnf(c_0_101,plain,
( ~ group_element(X1)
| product(X1,e_4,e_3)
| product(X1,e_3,e_3)
| product(X1,e_2,e_3)
| product(X1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_75,c_0_61]) ).
cnf(c_0_102,negated_conjecture,
( ~ product(e_4,e_4,X1)
| product(e_4,e_2,e_4)
| product(e_4,e_3,e_4)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_41,c_0_95]) ).
cnf(c_0_103,negated_conjecture,
( ~ product(e_4,e_4,e_3)
| ~ product(e_4,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_104,negated_conjecture,
( ~ product(e_4,e_4,e_3)
| ~ product(e_4,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_96,c_0_98]) ).
cnf(c_0_105,plain,
~ equalish(e_1,e_2),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_2]) ).
cnf(c_0_106,plain,
~ equalish(e_2,e_3),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_3]) ).
cnf(c_0_107,negated_conjecture,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_99,c_0_93]) ).
cnf(c_0_108,negated_conjecture,
( ~ product(X1,e_2,e_1)
| product(e_2,X1,e_2)
| product(e_2,e_2,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_28,c_0_100]) ).
cnf(c_0_109,plain,
( product(e_4,e_1,e_3)
| product(e_4,e_2,e_3)
| product(e_4,e_3,e_3)
| product(e_4,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_101,c_0_25]) ).
cnf(c_0_110,negated_conjecture,
~ product(e_4,e_4,e_3),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_102]),c_0_103]),c_0_104]) ).
cnf(c_0_111,plain,
~ equalish(e_1,e_4),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_4]) ).
cnf(c_0_112,plain,
~ equalish(e_1,e_2),
c_0_105 ).
cnf(c_0_113,plain,
~ equalish(e_2,e_3),
c_0_106 ).
cnf(c_0_114,negated_conjecture,
( ~ product(X1,e_3,e_3)
| product(e_3,e_3,e_2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_33,c_0_107]) ).
cnf(c_0_115,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_108,c_0_100]) ).
cnf(c_0_116,plain,
( product(e_4,e_3,e_3)
| product(e_4,e_2,e_3)
| product(e_4,e_1,e_3) ),
inference(sr,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_117,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_118,plain,
~ equalish(e_1,e_4),
c_0_111 ).
cnf(c_0_119,negated_conjecture,
( ~ product(e_4,e_4,e_1)
| ~ product(e_4,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_112,c_0_97]) ).
cnf(c_0_120,negated_conjecture,
( ~ product(e_4,e_4,e_1)
| ~ product(e_4,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_112,c_0_98]) ).
cnf(c_0_121,negated_conjecture,
( ~ product(e_2,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_122,negated_conjecture,
( ~ product(X1,e_2,e_4)
| product(e_2,X1,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_28,c_0_115]) ).
cnf(c_0_123,negated_conjecture,
( ~ product(e_4,e_4,e_4)
| ~ product(e_4,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_57,c_0_97]) ).
cnf(c_0_124,negated_conjecture,
( product(e_4,e_4,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_116]),c_0_110]) ).
cnf(c_0_125,plain,
( ~ group_element(X1)
| product(X1,e_4,e_1)
| product(X1,e_3,e_1)
| product(X1,e_2,e_1)
| product(X1,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_75,c_0_117]) ).
cnf(c_0_126,negated_conjecture,
~ product(e_4,e_4,e_1),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_102]),c_0_119]),c_0_120]) ).
cnf(c_0_127,negated_conjecture,
( ~ product(e_3,e_3,X1)
| ~ product(e_2,e_3,e_3)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_41,c_0_121]) ).
cnf(c_0_128,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_122,c_0_115]) ).
cnf(c_0_129,plain,
~ equalish(e_1,e_3),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_3]) ).
cnf(c_0_130,negated_conjecture,
( ~ product(e_4,e_2,e_4)
| product(e_4,e_3,e_3)
| product(e_4,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_131,plain,
( product(e_4,e_1,e_1)
| product(e_4,e_2,e_1)
| product(e_4,e_3,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_25]),c_0_126]) ).
cnf(c_0_132,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_3,e_4)
| product(e_3,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_81,c_0_61]) ).
cnf(c_0_133,negated_conjecture,
( ~ product(X1,e_3,e_2)
| ~ product(e_2,e_3,e_3)
| product(e_3,X1,e_3) ),
inference(spm,[status(thm)],[c_0_28,c_0_121]) ).
cnf(c_0_134,negated_conjecture,
( ~ product(e_3,e_3,e_3)
| ~ product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_96,c_0_127]) ).
cnf(c_0_135,negated_conjecture,
( ~ product(X1,e_2,e_3)
| product(e_2,X1,e_2)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_28,c_0_128]) ).
cnf(c_0_136,plain,
~ equalish(e_1,e_3),
c_0_129 ).
cnf(c_0_137,negated_conjecture,
( ~ product(e_4,e_3,X1)
| ~ product(e_4,e_2,e_4)
| product(e_4,e_2,e_3)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_41,c_0_130]) ).
cnf(c_0_138,negated_conjecture,
( product(e_4,e_4,e_4)
| product(e_4,e_3,e_1)
| product(e_4,e_2,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_131]),c_0_126]) ).
cnf(c_0_139,plain,
( product(e_3,e_3,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_1,e_4) ),
inference(sr,[status(thm)],[c_0_132,c_0_74]) ).
cnf(c_0_140,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_2,e_3)
| product(e_2,e_3,e_3)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_101,c_0_87]) ).
cnf(c_0_141,negated_conjecture,
~ product(e_2,e_3,e_3),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_121]),c_0_134]) ).
cnf(c_0_142,negated_conjecture,
product(e_2,e_2,e_2),
inference(spm,[status(thm)],[c_0_135,c_0_128]) ).
cnf(c_0_143,negated_conjecture,
( ~ product(e_4,e_3,e_1)
| ~ product(e_4,e_2,e_4)
| product(e_4,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_144,negated_conjecture,
( ~ product(e_4,e_2,e_4)
| product(e_4,e_2,e_1)
| product(e_4,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_123,c_0_138]) ).
cnf(c_0_145,plain,
( ~ product(X1,e_1,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_3,e_4)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_33,c_0_139]) ).
cnf(c_0_146,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_2,e_3)
| product(e_2,e_1,e_3) ),
inference(sr,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_147,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_2,e_4)
| product(e_2,e_3,e_4)
| product(e_2,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_81,c_0_87]) ).
cnf(c_0_148,negated_conjecture,
( ~ product(e_2,e_2,X1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_41,c_0_142]) ).
cnf(c_0_149,plain,
~ equalish(e_4,e_1),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_1]) ).
cnf(c_0_150,negated_conjecture,
( ~ product(e_4,e_2,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_143,c_0_144]) ).
cnf(c_0_151,plain,
( ~ product(e_2,e_1,e_4)
| product(e_3,e_3,e_4)
| product(e_3,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_113,c_0_145]) ).
cnf(c_0_152,negated_conjecture,
( ~ product(X1,e_3,e_4)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_33,c_0_93]) ).
cnf(c_0_153,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_27,c_0_87]) ).
cnf(c_0_154,negated_conjecture,
( ~ product(e_2,X1,e_2)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_55,c_0_142]) ).
cnf(c_0_155,plain,
( ~ product(e_2,e_1,X1)
| product(e_2,e_2,e_3)
| product(e_2,e_4,e_3)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_41,c_0_146]) ).
cnf(c_0_156,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_2,e_4)
| product(e_2,e_1,e_4) ),
inference(sr,[status(thm)],[c_0_147,c_0_73]) ).
cnf(c_0_157,negated_conjecture,
~ product(e_2,e_2,e_4),
inference(spm,[status(thm)],[c_0_57,c_0_148]) ).
cnf(c_0_158,plain,
( product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_94,c_0_25]) ).
cnf(c_0_159,plain,
~ equalish(e_4,e_1),
c_0_149 ).
cnf(c_0_160,negated_conjecture,
( ~ product(e_4,e_2,X1)
| ~ product(e_4,e_2,e_4)
| product(e_4,e_2,e_3)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_41,c_0_150]) ).
cnf(c_0_161,plain,
( ~ product(e_3,e_3,X1)
| ~ product(e_2,e_1,e_4)
| product(e_3,e_2,e_4)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_41,c_0_151]) ).
cnf(c_0_162,negated_conjecture,
( ~ product(e_2,e_3,e_4)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_113,c_0_152]) ).
cnf(c_0_163,negated_conjecture,
~ product(e_2,e_2,e_3),
inference(spm,[status(thm)],[c_0_96,c_0_148]) ).
cnf(c_0_164,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(sr,[status(thm)],[c_0_153,c_0_73]) ).
cnf(c_0_165,negated_conjecture,
~ product(e_2,e_4,e_2),
inference(spm,[status(thm)],[c_0_57,c_0_154]) ).
cnf(c_0_166,negated_conjecture,
( ~ product(X1,e_2,e_2)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_142]) ).
cnf(c_0_167,negated_conjecture,
( ~ product(X1,e_4,e_3)
| ~ product(e_4,e_2,e_4)
| product(e_4,e_4,e_2)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_33,c_0_68]) ).
cnf(c_0_168,plain,
( ~ product(e_2,e_1,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_44,c_0_155]) ).
cnf(c_0_169,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_3,e_4) ),
inference(sr,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_170,plain,
( ~ product(X1,e_2,e_1)
| product(e_4,e_2,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_2)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_33,c_0_158]) ).
cnf(c_0_171,negated_conjecture,
( ~ product(e_4,e_2,e_4)
| product(e_4,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_172,negated_conjecture,
( ~ product(X2,X3,X4)
| ~ product(X1,X2,X3)
| product(X3,X1,X4) ),
inference(fof_simplification,[status(thm)],[qg3]) ).
cnf(c_0_173,plain,
( ~ product(e_3,e_3,e_3)
| ~ product(e_2,e_1,e_4)
| product(e_3,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_39,c_0_161]) ).
cnf(c_0_174,plain,
( ~ product(e_3,e_3,e_2)
| ~ product(e_2,e_1,e_4)
| product(e_3,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_37,c_0_161]) ).
cnf(c_0_175,negated_conjecture,
( ~ product(e_3,X1,e_3)
| ~ product(e_2,e_3,e_4)
| product(e_3,e_3,e_2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_55,c_0_162]) ).
cnf(c_0_176,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_4,e_3) ),
inference(sr,[status(thm)],[c_0_146,c_0_163]) ).
cnf(c_0_177,negated_conjecture,
( ~ product(X1,e_4,e_1)
| product(e_2,X1,e_4)
| product(e_4,e_2,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_28,c_0_158]) ).
cnf(c_0_178,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_3) ),
inference(sr,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_179,negated_conjecture,
~ product(e_4,e_2,e_2),
inference(spm,[status(thm)],[c_0_57,c_0_166]) ).
cnf(c_0_180,negated_conjecture,
( ~ product(e_2,e_4,e_3)
| ~ product(e_4,e_2,e_4)
| product(e_4,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_37,c_0_167]) ).
cnf(c_0_181,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_3,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_169]),c_0_163]) ).
cnf(c_0_182,plain,
( ~ product(e_3,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_170]),c_0_171]) ).
cnf(c_0_183,negated_conjecture,
( ~ product(X2,X3,X4)
| ~ product(X1,X2,X3)
| product(X3,X1,X4) ),
c_0_172 ).
cnf(c_0_184,negated_conjecture,
( ~ product(e_2,e_1,e_4)
| product(e_3,e_2,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_107]),c_0_174]) ).
cnf(c_0_185,negated_conjecture,
( ~ product(e_3,e_2,e_3)
| ~ product(e_2,e_3,e_4)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_113,c_0_175]) ).
cnf(c_0_186,negated_conjecture,
( ~ product(X1,e_4,e_2)
| ~ product(e_4,e_2,e_4)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_33,c_0_91]) ).
cnf(c_0_187,negated_conjecture,
( ~ product(X1,e_2,e_3)
| product(e_1,X1,e_2)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_28,c_0_176]) ).
cnf(c_0_188,negated_conjecture,
( product(e_4,e_2,e_3)
| product(e_2,e_4,e_3) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_179]),c_0_157]),c_0_171]) ).
cnf(c_0_189,negated_conjecture,
( ~ product(e_4,e_4,X1)
| ~ product(e_2,e_4,e_3)
| ~ product(e_4,e_2,e_4)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_41,c_0_180]) ).
cnf(c_0_190,plain,
( ~ product(X1,e_4,e_3)
| product(e_2,e_3,e_4)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_181]) ).
cnf(c_0_191,plain,
( ~ product(e_4,e_2,X1)
| ~ product(e_3,e_2,e_1)
| product(e_4,e_2,e_2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_41,c_0_182]) ).
cnf(c_0_192,negated_conjecture,
( ~ product(X1,e_3,e_2)
| ~ product(e_2,e_1,e_4)
| product(e_2,X1,e_4) ),
inference(spm,[status(thm)],[c_0_183,c_0_184]) ).
cnf(c_0_193,negated_conjecture,
( ~ product(e_3,X1,e_3)
| product(e_3,e_3,e_2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_55,c_0_107]) ).
cnf(c_0_194,negated_conjecture,
( ~ product(e_3,e_3,X1)
| ~ product(e_3,e_2,e_3)
| ~ product(e_2,e_3,e_4)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_41,c_0_185]) ).
cnf(c_0_195,negated_conjecture,
( ~ product(X1,e_1,e_4)
| product(e_4,X1,e_4)
| product(e_4,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_183,c_0_80]) ).
cnf(c_0_196,negated_conjecture,
( ~ product(e_1,e_4,e_2)
| ~ product(e_4,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_118,c_0_186]) ).
cnf(c_0_197,negated_conjecture,
( product(e_2,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_187,c_0_188]) ).
cnf(c_0_198,negated_conjecture,
( ~ product(e_2,e_4,e_3)
| ~ product(e_4,e_2,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_189]),c_0_183]) ).
cnf(c_0_199,plain,
( ~ product(e_1,e_4,e_3)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_112,c_0_190]) ).
cnf(c_0_200,negated_conjecture,
( ~ product(e_4,e_2,X1)
| product(e_1,e_4,X1)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_79,c_0_169]) ).
cnf(c_0_201,plain,
( ~ product(e_4,e_2,e_1)
| ~ product(e_3,e_2,e_1)
| product(e_4,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_136,c_0_191]) ).
cnf(c_0_202,plain,
( product(e_4,e_2,e_3)
| product(e_4,e_2,e_1) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[c_0_158,c_0_179]),c_0_171]) ).
cnf(c_0_203,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_94,c_0_61]) ).
cnf(c_0_204,negated_conjecture,
~ product(e_3,e_2,e_2),
inference(spm,[status(thm)],[c_0_96,c_0_166]) ).
cnf(c_0_205,negated_conjecture,
( ~ product(X1,e_3,e_2)
| product(e_2,X1,e_4)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_192,c_0_169]) ).
cnf(c_0_206,negated_conjecture,
( ~ product(e_3,e_2,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_113,c_0_193]) ).
cnf(c_0_207,negated_conjecture,
( ~ product(e_3,e_2,e_3)
| ~ product(e_2,e_3,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_194]),c_0_183]) ).
cnf(c_0_208,negated_conjecture,
( product(e_4,e_4,e_4)
| product(e_4,e_2,e_4)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_195,c_0_169]) ).
cnf(c_0_209,negated_conjecture,
~ product(e_4,e_2,e_4),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_197]),c_0_198]) ).
cnf(c_0_210,negated_conjecture,
( ~ product(e_4,e_2,e_3)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_199,c_0_200]) ).
cnf(c_0_211,plain,
( ~ product(e_3,e_2,e_1)
| product(e_4,e_2,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_202]),c_0_179]) ).
cnf(c_0_212,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_1) ),
inference(sr,[status(thm)],[c_0_203,c_0_204]) ).
cnf(c_0_213,negated_conjecture,
~ product(e_3,e_2,e_3),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_206]),c_0_207]) ).
cnf(c_0_214,negated_conjecture,
( ~ product(e_4,e_4,e_4)
| ~ product(e_4,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_57,c_0_98]) ).
cnf(c_0_215,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_4,e_4,e_4) ),
inference(sr,[status(thm)],[c_0_208,c_0_209]) ).
cnf(c_0_216,negated_conjecture,
( ~ product(e_3,e_2,e_1)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_210,c_0_211]) ).
cnf(c_0_217,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_4) ),
inference(sr,[status(thm)],[c_0_212,c_0_213]) ).
cnf(c_0_218,negated_conjecture,
( ~ product(e_4,e_3,e_4)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_214,c_0_215]) ).
cnf(c_0_219,negated_conjecture,
( ~ product(e_3,e_2,X1)
| product(e_4,e_3,X1)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_79,c_0_181]) ).
cnf(c_0_220,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_3,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_216,c_0_217]) ).
cnf(c_0_221,plain,
( ~ product(X1,e_2,e_1)
| product(e_3,e_2,e_4)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_33,c_0_217]) ).
cnf(c_0_222,negated_conjecture,
product(e_2,e_3,e_4),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_219]),c_0_220]) ).
cnf(c_0_223,plain,
( ~ product(e_4,e_2,e_1)
| product(e_3,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_44,c_0_221]) ).
cnf(c_0_224,negated_conjecture,
( ~ product(X1,e_2,e_3)
| product(e_3,X1,e_4) ),
inference(spm,[status(thm)],[c_0_183,c_0_222]) ).
cnf(c_0_225,plain,
( product(e_3,e_2,e_4)
| product(e_4,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_223,c_0_202]) ).
cnf(c_0_226,negated_conjecture,
( ~ product(X1,e_2,e_4)
| product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_28,c_0_222]) ).
cnf(c_0_227,negated_conjecture,
product(e_3,e_2,e_4),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_225]),c_0_74]) ).
cnf(c_0_228,negated_conjecture,
product(e_3,e_3,e_2),
inference(spm,[status(thm)],[c_0_226,c_0_227]) ).
cnf(c_0_229,negated_conjecture,
product(e_2,e_4,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_188]),c_0_74]) ).
cnf(c_0_230,negated_conjecture,
( ~ product(X1,e_3,e_2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_33,c_0_228]) ).
cnf(c_0_231,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_2,e_3)
| product(e_3,e_3,e_3)
| product(e_3,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_101,c_0_61]) ).
cnf(c_0_232,negated_conjecture,
( ~ product(X1,e_4,e_3)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_229]) ).
cnf(c_0_233,negated_conjecture,
~ product(e_1,e_3,e_2),
inference(spm,[status(thm)],[c_0_136,c_0_230]) ).
cnf(c_0_234,negated_conjecture,
( ~ product(e_3,e_3,X1)
| product(e_1,e_3,X1)
| product(e_3,e_4,e_3)
| product(e_3,e_3,e_3)
| product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_79,c_0_231]) ).
cnf(c_0_235,negated_conjecture,
~ product(e_3,e_4,e_3),
inference(spm,[status(thm)],[c_0_96,c_0_232]) ).
cnf(c_0_236,negated_conjecture,
( ~ product(e_3,e_3,X1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_41,c_0_228]) ).
cnf(c_0_237,negated_conjecture,
product(e_3,e_3,e_3),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_233,c_0_234]),c_0_228])]),c_0_213]),c_0_235]) ).
cnf(c_0_238,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_236]),c_0_237])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP129-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.44 % Computer : n010.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sun Sep 20 20:01:09 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.52 Running first-order theorem proving
% 0.22/0.52 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.59/0.77 % Version: 3.5.1
% 1.59/0.77 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.59/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.59/0.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.59/0.77 % Starting new_bool_3 with 300s (1) cores
% 1.59/0.77 % Starting new_bool_1 with 300s (1) cores
% 1.59/0.77 % Starting sh5l with 300s (1) cores
% 1.59/0.77 % new_bool_1 with pid 3389254 completed with status 0
% 1.59/0.77 % Result found by new_bool_1
% 1.59/0.77 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.59/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.59/0.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.59/0.77 % Starting new_bool_3 with 300s (1) cores
% 1.59/0.77 % Starting new_bool_1 with 300s (1) cores
% 1.59/0.77 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.59/0.77 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.59/0.77 % Search class: FGUNF-FFSS00-SFFFFFNN
% 1.59/0.77 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.59/0.77 % Starting SubtermCWHack with 31s (1) cores
% 1.59/0.77 % SubtermCWHack with pid 3389261 completed with status 0
% 1.59/0.77 % Result found by SubtermCWHack
% 1.59/0.77 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.59/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.59/0.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.59/0.77 % Starting new_bool_3 with 300s (1) cores
% 1.59/0.77 % Starting new_bool_1 with 300s (1) cores
% 1.59/0.77 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.59/0.77 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.59/0.77 % Search class: FGUNF-FFSS00-SFFFFFNN
% 1.59/0.77 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.59/0.77 % Starting SubtermCWHack with 31s (1) cores
% 1.59/0.77 % Preprocessing time : 0.001 s
% 1.59/0.77
% 1.59/0.77 % Proof found!
% 1.59/0.77 % SZS status Unsatisfiable
% 1.59/0.77 % SZS output start CNFRefutation
% See solution above
% 1.59/0.77 % Parsed axioms : 25
% 1.59/0.77 % Removed by relevancy pruning/SinE : 0
% 1.59/0.77 % Initial clauses : 25
% 1.59/0.77 % Removed in clause preprocessing : 0
% 1.59/0.77 % Initial clauses in saturation : 25
% 1.59/0.77 % Processed clauses : 2209
% 1.59/0.77 % ...of these trivial : 1
% 1.59/0.77 % ...subsumed : 489
% 1.59/0.77 % ...remaining for further processing : 1719
% 1.59/0.77 % Other redundant clauses eliminated : 0
% 1.59/0.77 % Clauses deleted for lack of memory : 0
% 1.59/0.77 % Backward-subsumed : 1193
% 1.59/0.77 % Backward-rewritten : 208
% 1.59/0.77 % Generated clauses : 7104
% 1.59/0.77 % ...of the previous two non-redundant : 6775
% 1.59/0.77 % ...aggressively subsumed : 0
% 1.59/0.77 % Contextual simplify-reflections : 79
% 1.59/0.77 % Paramodulations : 7024
% 1.59/0.77 % Factorizations : 0
% 1.59/0.77 % NegExts : 0
% 1.59/0.77 % Equation resolutions : 0
% 1.59/0.77 % Disequality decompositions : 0
% 1.59/0.77 % Total rewrite steps : 213
% 1.59/0.77 % ...of those cached : 206
% 1.59/0.77 % Propositional unsat checks : 0
% 1.59/0.77 % Propositional check models : 0
% 1.59/0.77 % Propositional check unsatisfiable : 0
% 1.59/0.77 % Propositional clauses : 0
% 1.59/0.77 % Propositional clauses after purity: 0
% 1.59/0.77 % Propositional unsat core size : 0
% 1.59/0.77 % Propositional preprocessing time : 0.000
% 1.59/0.77 % Propositional encoding time : 0.000
% 1.59/0.77 % Propositional solver time : 0.000
% 1.59/0.77 % Success case prop preproc time : 0.000
% 1.59/0.77 % Success case prop encoding time : 0.000
% 1.59/0.77 % Success case prop solver time : 0.000
% 1.59/0.77 % Current number of processed clauses : 238
% 1.59/0.77 % Positive orientable unit clauses : 11
% 1.59/0.77 % Positive unorientable unit clauses: 0
% 1.59/0.77 % Negative unit clauses : 46
% 1.59/0.77 % Non-unit-clauses : 181
% 1.59/0.77 % Current number of unprocessed clauses: 3957
% 1.59/0.77 % ...number of literals in the above : 19935
% 1.59/0.77 % Current number of archived formulas : 0
% 1.59/0.77 % Current number of archived clauses : 1481
% 1.59/0.77 % Clause-clause subsumption calls (NU) : 59549
% 1.59/0.77 % Rec. Clause-clause subsumption calls : 30406
% 1.59/0.77 % Non-unit clause-clause subsumptions : 1088
% 1.59/0.77 % Unit Clause-clause subsumption calls : 5213
% 1.59/0.77 % Rewrite failures with RHS unbound : 0
% 1.59/0.77 % BW rewrite match attempts : 35
% 1.59/0.77 % BW rewrite match successes : 7
% 1.59/0.77 % Condensation attempts : 0
% 1.59/0.77 % Condensation successes : 0
% 1.59/0.77 % Termbank termtop insertions : 87661
% 1.59/0.77 % Search garbage collected termcells : 60
% 1.59/0.77
% 1.59/0.77 % -------------------------------------------------
% 1.59/0.77 % User time : 0.215 s
% 1.59/0.77 % System time : 0.006 s
% 1.59/0.77 % Total time : 0.221 s
% 1.59/0.77 % Maximum resident set size: 3644 pages
% 1.59/0.77
% 1.59/0.77 % -------------------------------------------------
% 1.59/0.77 % User time : 0.218 s
% 1.59/0.77 % System time : 0.012 s
% 1.59/0.77 % Total time : 0.230 s
% 1.59/0.77 % Maximum resident set size: 4864 pages
% 1.59/0.77 % E exiting
%------------------------------------------------------------------------------