%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP133-1.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 12:38:42 PM UTC 2026
% Result : Unsatisfiable 0.27s 0.65s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 14
% Syntax : Number of clauses : 235 ( 39 unt; 102 nHn; 235 RR)
% Number of literals : 643 ( 0 equ; 318 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 124 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_total_function1,axiom,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
cnf(product_right_cancellation,axiom,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
cnf(product_left_cancellation,axiom,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
cnf(qg3,negated_conjecture,
( ~ product(X2,X1,X4)
| ~ product(X1,X2,X3)
| product(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
cnf(product_total_function2,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
cnf(c_0_14,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| 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_15,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
c_0_14 ).
cnf(c_0_16,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_17,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_18,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
inference(fof_simplification,[status(thm)],[product_right_cancellation]) ).
cnf(c_0_19,plain,
( ~ group_element(X1)
| product(X1,e_3,e_3)
| product(X1,e_3,e_2)
| product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
( ~ group_element(X1)
| product(X1,e_1,e_3)
| product(X1,e_1,e_2)
| product(X1,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_21,plain,
~ equalish(e_2,e_3),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_3]) ).
cnf(c_0_22,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_18 ).
cnf(c_0_23,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_24,plain,
~ equalish(e_2,e_1),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_1]) ).
cnf(c_0_25,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_26,plain,
~ equalish(e_2,e_3),
c_0_21 ).
cnf(c_0_27,plain,
( ~ product(e_1,X1,e_1)
| equalish(X1,e_3)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
inference(fof_simplification,[status(thm)],[product_left_cancellation]) ).
cnf(c_0_29,plain,
~ equalish(e_2,e_1),
c_0_24 ).
cnf(c_0_30,plain,
( ~ product(e_1,X1,e_1)
| equalish(X1,e_1)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_22,c_0_25]) ).
cnf(c_0_31,plain,
~ equalish(e_1,e_3),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_3]) ).
cnf(c_0_32,plain,
( ~ product(e_1,e_2,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_28 ).
cnf(c_0_34,plain,
( ~ product(e_1,e_2,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
~ equalish(e_1,e_3),
c_0_31 ).
cnf(c_0_36,plain,
( ~ product(e_1,X1,e_3)
| ~ product(e_1,e_2,e_1)
| equalish(X1,e_3)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_22,c_0_32]) ).
cnf(c_0_37,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_20,c_0_16]) ).
cnf(c_0_38,plain,
( ~ product(X1,e_1,e_3)
| ~ product(e_1,e_2,e_1)
| equalish(X1,e_1)
| product(e_1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,plain,
( ~ product(e_1,e_1,e_3)
| ~ product(e_1,e_2,e_1)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,plain,
( ~ product(X1,e_1,e_1)
| equalish(X1,e_3)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_37]) ).
cnf(c_0_41,plain,
( ~ product(X1,e_1,e_1)
| equalish(X1,e_1)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_25]) ).
cnf(c_0_42,plain,
~ equalish(e_3,e_1),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_1]) ).
cnf(c_0_43,plain,
( ~ product(e_2,e_1,e_3)
| ~ product(e_1,e_2,e_1)
| product(e_1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_29,c_0_38]) ).
cnf(c_0_44,plain,
( ~ product(e_1,e_2,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_39,c_0_34]) ).
cnf(c_0_45,plain,
( ~ product(e_2,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_26,c_0_40]) ).
cnf(c_0_46,plain,
( ~ product(e_2,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_29,c_0_41]) ).
cnf(c_0_47,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_48,plain,
~ equalish(e_3,e_1),
c_0_42 ).
cnf(c_0_49,plain,
( ~ product(e_1,X1,e_2)
| ~ product(e_2,e_1,e_3)
| ~ product(e_1,e_2,e_1)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_22,c_0_43]) ).
cnf(c_0_50,plain,
( ~ product(X1,e_1,e_2)
| ~ product(e_1,e_2,e_1)
| equalish(X1,e_1)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_44]) ).
cnf(c_0_51,negated_conjecture,
( ~ product(X2,X1,X4)
| ~ product(X1,X2,X3)
| product(X3,X4,X1) ),
inference(fof_simplification,[status(thm)],[qg3]) ).
cnf(c_0_52,plain,
( ~ product(X1,e_1,e_3)
| ~ product(e_2,e_1,e_1)
| equalish(X1,e_3)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_45]) ).
cnf(c_0_53,plain,
( ~ product(e_1,X1,e_3)
| ~ product(e_2,e_1,e_1)
| equalish(X1,e_1)
| product(e_1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_22,c_0_46]) ).
cnf(c_0_54,plain,
~ equalish(e_1,e_2),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_2]) ).
cnf(c_0_55,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_20,c_0_47]) ).
cnf(c_0_56,plain,
( ~ product(e_1,e_3,e_2)
| ~ product(e_2,e_1,e_3)
| ~ product(e_1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_57,plain,
( ~ product(e_3,e_1,e_2)
| ~ product(e_1,e_2,e_1)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_48,c_0_50]) ).
cnf(c_0_58,negated_conjecture,
( ~ product(X2,X1,X4)
| ~ product(X1,X2,X3)
| product(X3,X4,X1) ),
c_0_51 ).
cnf(c_0_59,plain,
( ~ group_element(X1)
| product(X1,e_2,e_3)
| product(X1,e_2,e_2)
| product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_15,c_0_47]) ).
cnf(c_0_60,plain,
( ~ product(e_1,e_1,e_3)
| ~ product(e_2,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_35,c_0_52]) ).
cnf(c_0_61,plain,
( ~ product(e_1,e_2,e_3)
| ~ product(e_2,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_29,c_0_53]) ).
cnf(c_0_62,plain,
~ equalish(e_1,e_2),
c_0_54 ).
cnf(c_0_63,plain,
( ~ product(X1,e_1,e_1)
| equalish(X1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_55]) ).
cnf(c_0_64,plain,
( ~ product(e_2,e_1,e_3)
| ~ product(e_1,e_2,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]) ).
cnf(c_0_65,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_59,c_0_17]) ).
cnf(c_0_66,plain,
( ~ product(e_2,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_60,c_0_46]) ).
cnf(c_0_67,plain,
( ~ product(e_1,X1,e_2)
| ~ product(e_1,e_2,e_3)
| ~ product(e_2,e_1,e_1)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_22,c_0_61]) ).
cnf(c_0_68,negated_conjecture,
( ~ product(e_1,e_2,X1)
| product(X1,e_1,e_1)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_58,c_0_55]) ).
cnf(c_0_69,plain,
( ~ product(e_1,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_70,plain,
( ~ product(e_2,e_1,e_3)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_71,plain,
( ~ product(e_1,X1,e_2)
| ~ product(e_2,e_1,e_1)
| equalish(X1,e_1)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_22,c_0_66]) ).
cnf(c_0_72,plain,
( ~ product(e_1,e_2,e_3)
| ~ product(e_2,e_1,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_67]),c_0_58]) ).
cnf(c_0_73,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_65]),c_0_69]),c_0_70]) ).
cnf(c_0_74,plain,
( ~ product(X1,e_1,e_2)
| ~ product(e_2,e_1,e_1)
| equalish(X1,e_1)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_66]) ).
cnf(c_0_75,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_2,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_29,c_0_71]) ).
cnf(c_0_76,negated_conjecture,
( ~ product(e_2,e_1,e_1)
| product(e_1,e_2,e_2)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_77,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_2,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_29,c_0_74]) ).
cnf(c_0_78,negated_conjecture,
( ~ product(e_2,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]) ).
cnf(c_0_79,plain,
( ~ product(X1,e_3,e_1)
| equalish(X1,e_1)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_23]) ).
cnf(c_0_80,negated_conjecture,
( ~ product(X1,e_1,e_2)
| ~ product(e_2,e_1,e_1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_33,c_0_78]) ).
cnf(c_0_81,negated_conjecture,
( ~ product(e_1,e_1,X1)
| ~ product(e_2,e_1,e_1)
| product(X1,e_3,e_1)
| product(e_1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_58,c_0_46]) ).
cnf(c_0_82,plain,
( ~ product(e_3,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_48,c_0_79]) ).
cnf(c_0_83,negated_conjecture,
( ~ product(e_1,e_1,e_2)
| ~ product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_35,c_0_80]) ).
cnf(c_0_84,plain,
( ~ product(e_1,e_3,e_3)
| ~ product(e_2,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_48,c_0_53]) ).
cnf(c_0_85,negated_conjecture,
( ~ product(e_2,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_81,c_0_46]) ).
cnf(c_0_86,plain,
( ~ product(X1,e_3,e_3)
| ~ product(e_1,e_2,e_1)
| equalish(X1,e_1)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_32]) ).
cnf(c_0_87,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
inference(fof_simplification,[status(thm)],[product_total_function2]) ).
cnf(c_0_88,plain,
( ~ product(X1,e_3,e_3)
| ~ product(e_3,e_3,e_1)
| equalish(X1,e_1)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_82]) ).
cnf(c_0_89,negated_conjecture,
( ~ product(e_1,e_3,e_3)
| ~ product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_90,negated_conjecture,
( ~ product(e_2,e_1,e_1)
| product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_83,c_0_85]) ).
cnf(c_0_91,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_92,plain,
( ~ product(e_3,X1,e_3)
| ~ product(e_2,e_1,e_1)
| equalish(X1,e_1)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_22,c_0_45]) ).
cnf(c_0_93,plain,
( ~ product(e_3,e_3,e_3)
| ~ product(e_1,e_2,e_1)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_48,c_0_86]) ).
cnf(c_0_94,plain,
~ equalish(e_3,e_2),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_2]) ).
cnf(c_0_95,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
c_0_87 ).
cnf(c_0_96,plain,
( ~ product(e_3,e_3,e_3)
| ~ product(e_3,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_48,c_0_88]) ).
cnf(c_0_97,negated_conjecture,
( ~ product(e_2,e_1,e_1)
| product(e_1,e_3,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_82]),c_0_90]) ).
cnf(c_0_98,plain,
( ~ product(X1,e_2,e_1)
| equalish(X1,e_1)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_65]) ).
cnf(c_0_99,negated_conjecture,
( ~ product(e_3,e_3,X1)
| product(X1,e_1,e_3)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_58,c_0_91]) ).
cnf(c_0_100,plain,
( ~ product(e_2,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_29,c_0_79]) ).
cnf(c_0_101,plain,
( ~ product(e_3,e_3,e_3)
| ~ product(e_2,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_48,c_0_92]) ).
cnf(c_0_102,plain,
( ~ product(e_1,X1,e_2)
| ~ product(e_3,e_3,e_3)
| ~ product(e_1,e_2,e_1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_22,c_0_93]) ).
cnf(c_0_103,negated_conjecture,
( ~ product(e_1,e_1,X1)
| ~ product(e_1,e_2,e_1)
| product(X1,e_3,e_1)
| product(e_1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_58,c_0_34]) ).
cnf(c_0_104,plain,
~ equalish(e_3,e_2),
c_0_94 ).
cnf(c_0_105,plain,
( ~ product(e_1,e_3,X1)
| ~ product(e_3,e_3,e_3)
| ~ product(e_3,e_3,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_106,negated_conjecture,
( ~ product(e_1,X1,e_2)
| ~ product(e_2,e_1,e_1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_22,c_0_97]) ).
cnf(c_0_107,plain,
( ~ product(e_2,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_29,c_0_98]) ).
cnf(c_0_108,negated_conjecture,
( ~ product(e_1,e_3,X1)
| ~ product(e_2,e_1,e_1)
| product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_58,c_0_78]) ).
cnf(c_0_109,negated_conjecture,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_3)
| product(e_1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_99,c_0_91]) ).
cnf(c_0_110,plain,
( ~ product(X1,e_3,e_3)
| ~ product(e_2,e_3,e_1)
| equalish(X1,e_1)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_100]) ).
cnf(c_0_111,plain,
( ~ product(X1,e_1,e_2)
| ~ product(e_3,e_3,e_3)
| ~ product(e_2,e_1,e_1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_33,c_0_101]) ).
cnf(c_0_112,plain,
( ~ product(e_1,e_1,e_2)
| ~ product(e_3,e_3,e_3)
| ~ product(e_1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_35,c_0_102]) ).
cnf(c_0_113,negated_conjecture,
( ~ product(e_1,e_2,e_1)
| product(e_1,e_1,e_2)
| product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_103,c_0_34]) ).
cnf(c_0_114,plain,
( ~ product(e_3,e_3,e_3)
| ~ product(e_3,e_3,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_58]) ).
cnf(c_0_115,negated_conjecture,
( ~ product(e_1,e_2,e_2)
| ~ product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_26,c_0_106]) ).
cnf(c_0_116,plain,
( ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_1,e_1)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_72,c_0_107]) ).
cnf(c_0_117,negated_conjecture,
( ~ product(e_2,e_1,e_1)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_108,c_0_97]) ).
cnf(c_0_118,plain,
( ~ product(e_3,X1,e_1)
| equalish(X1,e_3)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_22,c_0_91]) ).
cnf(c_0_119,negated_conjecture,
( ~ product(X1,e_1,e_3)
| equalish(X1,e_1)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_109]) ).
cnf(c_0_120,plain,
( ~ product(e_3,e_3,e_3)
| ~ product(e_2,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_48,c_0_110]) ).
cnf(c_0_121,plain,
( ~ product(e_1,e_1,e_2)
| ~ product(e_3,e_3,e_3)
| ~ product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_35,c_0_111]) ).
cnf(c_0_122,negated_conjecture,
( ~ product(e_3,e_3,e_3)
| ~ product(e_1,e_2,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_114]) ).
cnf(c_0_123,negated_conjecture,
~ product(e_2,e_1,e_1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_117]) ).
cnf(c_0_124,plain,
( ~ product(e_3,e_1,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_35,c_0_118]) ).
cnf(c_0_125,negated_conjecture,
( ~ product(e_3,e_1,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_48,c_0_119]) ).
cnf(c_0_126,plain,
( ~ product(X1,e_3,e_1)
| equalish(X1,e_3)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_91]) ).
cnf(c_0_127,plain,
( ~ product(e_1,X1,e_2)
| ~ product(e_3,e_3,e_3)
| ~ product(e_2,e_3,e_1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_22,c_0_120]) ).
cnf(c_0_128,plain,
( ~ product(e_1,e_2,e_3)
| ~ product(e_3,e_3,e_3)
| ~ product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_121,c_0_61]) ).
cnf(c_0_129,negated_conjecture,
( ~ product(e_3,e_3,e_3)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_122,c_0_65]) ).
cnf(c_0_130,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(sr,[status(thm)],[c_0_55,c_0_123]) ).
cnf(c_0_131,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_37]),c_0_125]) ).
cnf(c_0_132,plain,
( ~ product(e_2,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_26,c_0_126]) ).
cnf(c_0_133,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_3,e_3,e_3)
| ~ product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_26,c_0_127]) ).
cnf(c_0_134,negated_conjecture,
( ~ product(e_3,e_3,e_3)
| ~ product(e_2,e_1,e_1)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_135,plain,
( ~ product(X1,e_1,e_3)
| equalish(X1,e_2)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_130]) ).
cnf(c_0_136,plain,
( ~ product(X1,e_1,e_2)
| equalish(X1,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_33,c_0_131]) ).
cnf(c_0_137,plain,
( ~ product(e_1,X1,e_3)
| ~ product(e_3,e_3,e_1)
| equalish(X1,e_3)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_22,c_0_82]) ).
cnf(c_0_138,plain,
( ~ product(X1,e_3,e_3)
| ~ product(e_2,e_3,e_1)
| equalish(X1,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_132]) ).
cnf(c_0_139,negated_conjecture,
( ~ product(e_3,X1,e_2)
| ~ product(e_2,e_1,e_1)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_22,c_0_78]) ).
cnf(c_0_140,negated_conjecture,
( ~ product(e_2,e_1,e_1)
| ~ product(e_3,e_3,e_3)
| ~ product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_141,plain,
( ~ product(e_1,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_62,c_0_135]) ).
cnf(c_0_142,plain,
( ~ product(e_2,e_1,e_2)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_26,c_0_136]) ).
cnf(c_0_143,plain,
( ~ product(e_1,e_2,e_3)
| ~ product(e_3,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_26,c_0_137]) ).
cnf(c_0_144,plain,
( ~ product(e_2,X1,e_3)
| equalish(X1,e_1)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_22,c_0_130]) ).
cnf(c_0_145,plain,
( ~ product(e_1,e_3,e_3)
| ~ product(e_2,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_35,c_0_138]) ).
cnf(c_0_146,negated_conjecture,
( ~ product(e_3,e_3,e_2)
| ~ product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_48,c_0_139]) ).
cnf(c_0_147,negated_conjecture,
( ~ product(e_2,e_1,e_1)
| ~ product(e_2,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_140,c_0_132]) ).
cnf(c_0_148,plain,
( ~ product(e_3,X1,e_3)
| ~ product(e_2,e_3,e_1)
| equalish(X1,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_22,c_0_132]) ).
cnf(c_0_149,negated_conjecture,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_109]),c_0_142]) ).
cnf(c_0_150,plain,
( ~ product(X1,e_3,e_2)
| ~ product(e_1,e_2,e_3)
| ~ product(e_3,e_3,e_1)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_33,c_0_143]) ).
cnf(c_0_151,plain,
( ~ product(e_2,e_2,e_3)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_29,c_0_144]) ).
cnf(c_0_152,plain,
( ~ product(e_2,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_145,c_0_100]) ).
cnf(c_0_153,negated_conjecture,
( ~ product(e_1,e_3,X1)
| product(X1,e_1,e_1)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_58,c_0_37]) ).
cnf(c_0_154,negated_conjecture,
( ~ product(e_2,e_3,e_1)
| ~ product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_155,plain,
( ~ product(e_3,e_1,e_3)
| ~ product(e_2,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_35,c_0_148]) ).
cnf(c_0_156,negated_conjecture,
( ~ product(e_3,e_3,X1)
| equalish(X1,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_95,c_0_149]) ).
cnf(c_0_157,plain,
( ~ product(e_3,e_3,e_2)
| ~ product(e_3,e_3,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_150]),c_0_58]) ).
cnf(c_0_158,plain,
( ~ product(X1,e_1,e_2)
| ~ product(e_2,e_2,e_3)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_151]) ).
cnf(c_0_159,negated_conjecture,
( ~ product(e_3,e_1,X1)
| ~ product(e_2,e_3,e_1)
| product(X1,e_2,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_58,c_0_152]) ).
cnf(c_0_160,negated_conjecture,
( ~ product(e_2,e_3,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_3,e_2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_152]),c_0_154]),c_0_155]) ).
cnf(c_0_161,negated_conjecture,
( ~ product(e_1,e_2,X1)
| product(X1,e_3,e_1)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_58,c_0_130]) ).
cnf(c_0_162,negated_conjecture,
~ product(e_3,e_3,e_1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_156]),c_0_157]) ).
cnf(c_0_163,plain,
( ~ product(e_3,e_1,e_2)
| ~ product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_104,c_0_158]) ).
cnf(c_0_164,negated_conjecture,
( ~ product(e_2,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_165,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_19,c_0_47]) ).
cnf(c_0_166,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_59,c_0_47]) ).
cnf(c_0_167,plain,
( ~ product(e_3,e_2,e_3)
| ~ product(e_2,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_26,c_0_148]) ).
cnf(c_0_168,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_59,c_0_16]) ).
cnf(c_0_169,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_1,e_2,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_73]),c_0_162]) ).
cnf(c_0_170,negated_conjecture,
( ~ product(e_2,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_160]),c_0_164]) ).
cnf(c_0_171,plain,
( ~ product(e_2,X1,e_1)
| equalish(X1,e_3)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_22,c_0_165]) ).
cnf(c_0_172,negated_conjecture,
( ~ product(e_2,e_2,X1)
| product(X1,e_1,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_58,c_0_166]) ).
cnf(c_0_173,plain,
( ~ product(X1,e_3,e_2)
| ~ product(e_3,e_2,e_3)
| ~ product(e_2,e_3,e_1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_33,c_0_167]) ).
cnf(c_0_174,plain,
( ~ product(X1,e_2,e_1)
| equalish(X1,e_3)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_168]) ).
cnf(c_0_175,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_161,c_0_169]) ).
cnf(c_0_176,negated_conjecture,
( ~ product(X1,e_3,e_2)
| ~ product(e_2,e_3,e_1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_33,c_0_170]) ).
cnf(c_0_177,plain,
( ~ product(e_2,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_26,c_0_171]) ).
cnf(c_0_178,plain,
( ~ product(e_2,X1,e_1)
| equalish(X1,e_1)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_22,c_0_55]) ).
cnf(c_0_179,plain,
( ~ product(e_3,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_48,c_0_41]) ).
cnf(c_0_180,negated_conjecture,
( ~ product(e_3,X1,e_2)
| ~ product(e_2,e_3,e_1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_22,c_0_170]) ).
cnf(c_0_181,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_172,c_0_166]) ).
cnf(c_0_182,plain,
( ~ product(e_2,e_3,e_3)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_48,c_0_144]) ).
cnf(c_0_183,plain,
( ~ product(e_3,e_2,e_3)
| ~ product(e_2,e_3,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_173]),c_0_58]) ).
cnf(c_0_184,plain,
( ~ product(e_2,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_26,c_0_174]) ).
cnf(c_0_185,negated_conjecture,
( ~ product(e_2,X1,e_2)
| equalish(X1,e_1)
| product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_22,c_0_175]) ).
cnf(c_0_186,negated_conjecture,
( ~ product(e_2,e_3,e_2)
| ~ product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_26,c_0_176]) ).
cnf(c_0_187,plain,
( ~ product(e_2,X1,e_3)
| ~ product(e_2,e_2,e_1)
| equalish(X1,e_3)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_22,c_0_177]) ).
cnf(c_0_188,plain,
( ~ product(e_2,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_29,c_0_178]) ).
cnf(c_0_189,negated_conjecture,
( ~ product(e_1,X1,e_2)
| equalish(X1,e_2)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_22,c_0_169]) ).
cnf(c_0_190,negated_conjecture,
( ~ product(e_1,e_1,X1)
| ~ product(e_3,e_1,e_1)
| product(X1,e_3,e_1)
| product(e_1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_58,c_0_179]) ).
cnf(c_0_191,negated_conjecture,
( ~ product(X1,e_1,e_2)
| equalish(X1,e_2)
| product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_33,c_0_175]) ).
cnf(c_0_192,negated_conjecture,
( ~ product(e_3,e_1,e_2)
| ~ product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_35,c_0_180]) ).
cnf(c_0_193,negated_conjecture,
( ~ product(X1,e_1,e_2)
| equalish(X1,e_1)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_181]) ).
cnf(c_0_194,plain,
( ~ product(e_2,X1,e_2)
| ~ product(e_2,e_3,e_3)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_22,c_0_182]) ).
cnf(c_0_195,negated_conjecture,
( ~ product(e_3,e_2,e_2)
| ~ product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_26,c_0_180]) ).
cnf(c_0_196,plain,
( ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_3,e_1)
| product(e_3,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_183,c_0_184]) ).
cnf(c_0_197,negated_conjecture,
~ product(e_2,e_3,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_185]),c_0_186]) ).
cnf(c_0_198,plain,
( ~ product(e_2,e_2,e_3)
| ~ product(e_2,e_2,e_1)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_26,c_0_187]) ).
cnf(c_0_199,plain,
( ~ product(e_2,X1,e_3)
| ~ product(e_2,e_2,e_1)
| equalish(X1,e_1)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_22,c_0_188]) ).
cnf(c_0_200,negated_conjecture,
( ~ product(e_1,e_1,e_2)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_62,c_0_189]) ).
cnf(c_0_201,negated_conjecture,
( ~ product(e_3,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_190,c_0_179]) ).
cnf(c_0_202,negated_conjecture,
~ product(e_3,e_1,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_191]),c_0_192]) ).
cnf(c_0_203,negated_conjecture,
( ~ product(e_2,e_1,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_29,c_0_193]) ).
cnf(c_0_204,plain,
( ~ product(e_2,e_2,e_2)
| ~ product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_29,c_0_194]) ).
cnf(c_0_205,negated_conjecture,
( ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_195,c_0_196]) ).
cnf(c_0_206,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_1) ),
inference(sr,[status(thm)],[c_0_165,c_0_197]) ).
cnf(c_0_207,plain,
( ~ product(e_2,X1,e_2)
| ~ product(e_2,e_2,e_3)
| ~ product(e_2,e_2,e_1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_22,c_0_198]) ).
cnf(c_0_208,plain,
( ~ product(e_2,e_2,e_3)
| ~ product(e_2,e_2,e_1)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_29,c_0_199]) ).
cnf(c_0_209,negated_conjecture,
( ~ product(e_3,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_201]),c_0_162]) ).
cnf(c_0_210,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_1) ),
inference(sr,[status(thm)],[c_0_37,c_0_202]) ).
cnf(c_0_211,plain,
( ~ product(e_3,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_104,c_0_135]) ).
cnf(c_0_212,negated_conjecture,
( ~ product(e_2,e_3,e_3)
| product(e_2,e_2,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_182]),c_0_204]) ).
cnf(c_0_213,negated_conjecture,
( ~ product(e_2,e_2,e_1)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_205,c_0_206]) ).
cnf(c_0_214,plain,
( ~ product(e_2,e_2,e_3)
| ~ product(e_2,e_2,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_207]),c_0_208]) ).
cnf(c_0_215,negated_conjecture,
product(e_2,e_1,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_210]),c_0_211]) ).
cnf(c_0_216,negated_conjecture,
~ product(e_2,e_2,e_1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_213]),c_0_214]) ).
cnf(c_0_217,negated_conjecture,
( ~ product(e_2,X1,e_2)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_22,c_0_215]) ).
cnf(c_0_218,plain,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2) ),
inference(sr,[status(thm)],[c_0_166,c_0_216]) ).
cnf(c_0_219,negated_conjecture,
~ product(e_2,e_2,e_2),
inference(spm,[status(thm)],[c_0_29,c_0_217]) ).
cnf(c_0_220,plain,
( ~ product(e_1,e_1,e_2)
| ~ product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_62,c_0_158]) ).
cnf(c_0_221,plain,
product(e_2,e_2,e_3),
inference(sr,[status(thm)],[c_0_218,c_0_219]) ).
cnf(c_0_222,negated_conjecture,
( ~ product(e_3,e_1,e_1)
| ~ product(e_2,e_2,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_201]),c_0_162]) ).
cnf(c_0_223,plain,
( ~ product(e_2,X1,e_3)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_22,c_0_221]) ).
cnf(c_0_224,negated_conjecture,
( ~ product(e_2,e_2,e_3)
| product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_222,c_0_210]) ).
cnf(c_0_225,plain,
~ product(e_2,e_3,e_3),
inference(spm,[status(thm)],[c_0_104,c_0_223]) ).
cnf(c_0_226,negated_conjecture,
product(e_3,e_1,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_224,c_0_221])]) ).
cnf(c_0_227,negated_conjecture,
( ~ product(e_3,e_2,X1)
| product(X1,e_1,e_3)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_58,c_0_165]) ).
cnf(c_0_228,plain,
product(e_2,e_3,e_1),
inference(sr,[status(thm)],[c_0_206,c_0_225]) ).
cnf(c_0_229,negated_conjecture,
( ~ product(X1,e_1,e_3)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_33,c_0_226]) ).
cnf(c_0_230,negated_conjecture,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_3)
| product(e_1,e_1,e_3)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_227,c_0_168]) ).
cnf(c_0_231,negated_conjecture,
~ product(e_3,e_2,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_195,c_0_228])]) ).
cnf(c_0_232,plain,
~ product(e_3,e_2,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_183,c_0_228])]) ).
cnf(c_0_233,negated_conjecture,
~ product(e_1,e_1,e_3),
inference(spm,[status(thm)],[c_0_35,c_0_229]) ).
cnf(c_0_234,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_230,c_0_197]),c_0_231]),c_0_232]),c_0_233]),c_0_225]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP133-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.43 % Computer : n019.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 20 20:01:36 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.51 Running first-order theorem proving
% 0.18/0.51 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.27/0.65 % Version: 3.5.1
% 0.27/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.27/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.27/0.65 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.65 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.65 % Starting sh5l with 300s (1) cores
% 0.27/0.65 % new_bool_3 with pid 799916 completed with status 0
% 0.27/0.65 % Result found by new_bool_3
% 0.27/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.27/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.27/0.65 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.65 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.27/0.65 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.27/0.65 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.27/0.65 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.27/0.65 % Starting SubtermCWHack with 31s (1) cores
% 0.27/0.65 % SubtermCWHack with pid 799919 completed with status 0
% 0.27/0.65 % Result found by SubtermCWHack
% 0.27/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.27/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.27/0.65 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.65 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.27/0.65 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.27/0.65 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.27/0.65 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.27/0.65 % Starting SubtermCWHack with 31s (1) cores
% 0.27/0.65 % Preprocessing time : 0.001 s
% 0.27/0.65
% 0.27/0.65 % Proof found!
% 0.27/0.65 % SZS status Unsatisfiable
% 0.27/0.65 % SZS output start CNFRefutation
% See solution above
% 0.27/0.65 % Parsed axioms : 14
% 0.27/0.65 % Removed by relevancy pruning/SinE : 0
% 0.27/0.65 % Initial clauses : 14
% 0.27/0.65 % Removed in clause preprocessing : 0
% 0.27/0.65 % Initial clauses in saturation : 14
% 0.27/0.65 % Processed clauses : 1210
% 0.27/0.65 % ...of these trivial : 0
% 0.27/0.65 % ...subsumed : 278
% 0.27/0.65 % ...remaining for further processing : 931
% 0.27/0.65 % Other redundant clauses eliminated : 0
% 0.27/0.65 % Clauses deleted for lack of memory : 0
% 0.27/0.65 % Backward-subsumed : 738
% 0.27/0.65 % Backward-rewritten : 102
% 0.27/0.65 % Generated clauses : 4438
% 0.27/0.65 % ...of the previous two non-redundant : 4134
% 0.27/0.65 % ...aggressively subsumed : 0
% 0.27/0.65 % Contextual simplify-reflections : 42
% 0.27/0.65 % Paramodulations : 4417
% 0.27/0.65 % Factorizations : 0
% 0.27/0.65 % NegExts : 0
% 0.27/0.65 % Equation resolutions : 0
% 0.27/0.65 % Disequality decompositions : 0
% 0.27/0.65 % Total rewrite steps : 104
% 0.27/0.65 % ...of those cached : 98
% 0.27/0.65 % Propositional unsat checks : 0
% 0.27/0.65 % Propositional check models : 0
% 0.27/0.65 % Propositional check unsatisfiable : 0
% 0.27/0.65 % Propositional clauses : 0
% 0.27/0.65 % Propositional clauses after purity: 0
% 0.27/0.65 % Propositional unsat core size : 0
% 0.27/0.65 % Propositional preprocessing time : 0.000
% 0.27/0.65 % Propositional encoding time : 0.000
% 0.27/0.65 % Propositional solver time : 0.000
% 0.27/0.65 % Success case prop preproc time : 0.000
% 0.27/0.65 % Success case prop encoding time : 0.000
% 0.27/0.65 % Success case prop solver time : 0.000
% 0.27/0.65 % Current number of processed clauses : 70
% 0.27/0.65 % Positive orientable unit clauses : 9
% 0.27/0.65 % Positive unorientable unit clauses: 0
% 0.27/0.65 % Negative unit clauses : 25
% 0.27/0.65 % Non-unit-clauses : 36
% 0.27/0.65 % Current number of unprocessed clauses: 198
% 0.27/0.65 % ...number of literals in the above : 559
% 0.27/0.65 % Current number of archived formulas : 0
% 0.27/0.65 % Current number of archived clauses : 861
% 0.27/0.65 % Clause-clause subsumption calls (NU) : 20349
% 0.27/0.65 % Rec. Clause-clause subsumption calls : 9434
% 0.27/0.65 % Non-unit clause-clause subsumptions : 706
% 0.27/0.65 % Unit Clause-clause subsumption calls : 1819
% 0.27/0.65 % Rewrite failures with RHS unbound : 0
% 0.27/0.65 % BW rewrite match attempts : 23
% 0.27/0.65 % BW rewrite match successes : 6
% 0.27/0.65 % Condensation attempts : 0
% 0.27/0.65 % Condensation successes : 0
% 0.27/0.65 % Termbank termtop insertions : 54206
% 0.27/0.65 % Search garbage collected termcells : 36
% 0.27/0.65
% 0.27/0.65 % -------------------------------------------------
% 0.27/0.65 % User time : 0.102 s
% 0.27/0.65 % System time : 0.007 s
% 0.27/0.65 % Total time : 0.109 s
% 0.27/0.65 % Maximum resident set size: 3636 pages
% 0.27/0.65
% 0.27/0.65 % -------------------------------------------------
% 0.27/0.65 % User time : 0.103 s
% 0.27/0.65 % System time : 0.014 s
% 0.27/0.65 % Total time : 0.117 s
% 0.27/0.65 % Maximum resident set size: 4608 pages
% 0.27/0.65 % E exiting
%------------------------------------------------------------------------------