TSTP Solution File: GRP129-3.004 by E-SAT---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : GRP129-3.004 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n008.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 : Sat May 4 07:57:27 EDT 2024
% Result : Unsatisfiable 2.16s 0.75s
% Output : CNFRefutation 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 79
% Number of leaves : 37
% Syntax : Number of clauses : 402 ( 78 unt; 259 nHn; 402 RR)
% Number of literals : 1428 ( 0 equ; 380 neg)
% Maximal clause size : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 249 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',e_1_is_not_e_2) ).
cnf(cycle4,axiom,
( equalish(X2,X5)
| ~ cycle(X1,X2)
| ~ cycle(X3,X4)
| ~ next(X1,X3)
| ~ greater(X2,e_0)
| ~ next(X4,X5) ),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',cycle4) ).
cnf(cycle2,axiom,
( cycle(X1,e_0)
| cycle(X1,e_1)
| cycle(X1,e_2)
| cycle(X1,e_3)
| ~ group_element(X1) ),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',cycle2) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',e_3_is_not_e_2) ).
cnf(e_1_greater_e_0,axiom,
greater(e_1,e_0),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',e_1_greater_e_0) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',element_2) ).
cnf(e_3_greater_e_0,axiom,
greater(e_3,e_0),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',e_3_greater_e_0) ).
cnf(e_1_then_e_2,axiom,
next(e_1,e_2),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',e_1_then_e_2) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',element_3) ).
cnf(cycle5,axiom,
( ~ cycle(X1,X2)
| ~ cycle(X3,e_0)
| ~ cycle(X4,X5)
| ~ next(X3,X4)
| ~ greater(X3,X1)
| ~ greater(X2,X5) ),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',cycle5) ).
cnf(e_2_then_e_3,axiom,
next(e_2,e_3),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',e_2_then_e_3) ).
cnf(e_1_is_not_e_4,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',e_1_is_not_e_4) ).
cnf(e_2_is_not_e_4,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',e_2_is_not_e_4) ).
cnf(e_3_is_not_e_4,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',e_3_is_not_e_4) ).
cnf(e_3_greater_e_2,axiom,
greater(e_3,e_2),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',e_3_greater_e_2) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',e_1_is_not_e_3) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',e_2_is_not_e_3) ).
cnf(e_2_greater_e_0,axiom,
greater(e_2,e_0),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',e_2_greater_e_0) ).
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/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',product_total_function1) ).
cnf(e_3_then_e_4,axiom,
next(e_3,e_4),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',e_3_then_e_4) ).
cnf(cycle3,axiom,
cycle(e_4,e_0),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',cycle3) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',e_2_is_not_e_1) ).
cnf(product_right_cancellation,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',product_right_cancellation) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',element_1) ).
cnf(cycle6,axiom,
( ~ cycle(X1,e_0)
| ~ product(X1,e_1,X2)
| ~ greater(X2,X1) ),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',cycle6) ).
cnf(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',e_4_is_not_e_3) ).
cnf(cycle7,axiom,
( equalish(X3,X4)
| ~ cycle(X1,X2)
| ~ product(X1,e_1,X3)
| ~ greater(X2,e_0)
| ~ next(X1,X4) ),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',cycle7) ).
cnf(e_4_greater_e_2,axiom,
greater(e_4,e_2),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',e_4_greater_e_2) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',e_3_is_not_e_1) ).
cnf(e_0_then_e_1,axiom,
next(e_0,e_1),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',e_0_then_e_1) ).
cnf(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',e_4_is_not_e_2) ).
cnf(qg3,negated_conjecture,
( product(X3,X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X2,X3,X4) ),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',qg3) ).
cnf(product_left_cancellation,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',product_left_cancellation) ).
cnf(element_4,axiom,
group_element(e_4),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',element_4) ).
cnf(e_4_greater_e_1,axiom,
greater(e_4,e_1),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',e_4_greater_e_1) ).
cnf(e_3_greater_e_1,axiom,
greater(e_3,e_1),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',e_3_greater_e_1) ).
cnf(product_total_function2,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p',product_total_function2) ).
cnf(c_0_37,plain,
~ equalish(e_1,e_2),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_2]) ).
cnf(c_0_38,plain,
( equalish(X2,X5)
| ~ cycle(X1,X2)
| ~ cycle(X3,X4)
| ~ next(X1,X3)
| ~ greater(X2,e_0)
| ~ next(X4,X5) ),
inference(fof_simplification,[status(thm)],[cycle4]) ).
cnf(c_0_39,plain,
( cycle(X1,e_0)
| cycle(X1,e_1)
| cycle(X1,e_2)
| cycle(X1,e_3)
| ~ group_element(X1) ),
inference(fof_simplification,[status(thm)],[cycle2]) ).
cnf(c_0_40,plain,
~ equalish(e_3,e_2),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_2]) ).
cnf(c_0_41,plain,
~ equalish(e_1,e_2),
c_0_37 ).
cnf(c_0_42,plain,
( equalish(X2,X5)
| ~ cycle(X1,X2)
| ~ cycle(X3,X4)
| ~ next(X1,X3)
| ~ greater(X2,e_0)
| ~ next(X4,X5) ),
c_0_38 ).
cnf(c_0_43,axiom,
greater(e_1,e_0),
e_1_greater_e_0 ).
cnf(c_0_44,plain,
( cycle(X1,e_0)
| cycle(X1,e_1)
| cycle(X1,e_2)
| cycle(X1,e_3)
| ~ group_element(X1) ),
c_0_39 ).
cnf(c_0_45,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_46,plain,
~ equalish(e_3,e_2),
c_0_40 ).
cnf(c_0_47,axiom,
greater(e_3,e_0),
e_3_greater_e_0 ).
cnf(c_0_48,plain,
( ~ cycle(X1,e_1)
| ~ cycle(X2,X3)
| ~ next(X3,e_2)
| ~ next(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).
cnf(c_0_49,plain,
( cycle(e_2,e_3)
| cycle(e_2,e_2)
| cycle(e_2,e_1)
| cycle(e_2,e_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,plain,
( ~ cycle(X1,e_3)
| ~ cycle(X2,X3)
| ~ next(X3,e_2)
| ~ next(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_42]),c_0_47])]) ).
cnf(c_0_51,plain,
( cycle(e_2,e_0)
| cycle(e_2,e_2)
| ~ cycle(X1,X2)
| ~ next(X2,e_2)
| ~ next(e_2,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_52,axiom,
next(e_1,e_2),
e_1_then_e_2 ).
cnf(c_0_53,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_54,plain,
( ~ cycle(X1,X2)
| ~ cycle(X3,e_0)
| ~ cycle(X4,X5)
| ~ next(X3,X4)
| ~ greater(X3,X1)
| ~ greater(X2,X5) ),
inference(fof_simplification,[status(thm)],[cycle5]) ).
cnf(c_0_55,plain,
( cycle(e_2,e_2)
| cycle(e_2,e_0)
| ~ cycle(X1,e_1)
| ~ next(e_2,X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,plain,
( cycle(e_3,e_3)
| cycle(e_3,e_2)
| cycle(e_3,e_1)
| cycle(e_3,e_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_53]) ).
cnf(c_0_57,axiom,
next(e_2,e_3),
e_2_then_e_3 ).
cnf(c_0_58,plain,
( ~ cycle(X1,X2)
| ~ cycle(X3,e_0)
| ~ cycle(X4,X5)
| ~ next(X3,X4)
| ~ greater(X3,X1)
| ~ greater(X2,X5) ),
c_0_54 ).
cnf(c_0_59,plain,
( cycle(e_3,e_0)
| cycle(e_3,e_2)
| cycle(e_3,e_3)
| cycle(e_2,e_0)
| cycle(e_2,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57])]) ).
cnf(c_0_60,plain,
~ equalish(e_1,e_4),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_4]) ).
cnf(c_0_61,plain,
~ equalish(e_2,e_4),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_4]) ).
cnf(c_0_62,plain,
~ equalish(e_3,e_4),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_4]) ).
cnf(c_0_63,plain,
( cycle(e_2,e_2)
| cycle(e_2,e_0)
| cycle(e_3,e_3)
| cycle(e_3,e_2)
| ~ cycle(X1,X2)
| ~ cycle(X3,X4)
| ~ greater(e_3,X3)
| ~ greater(X4,X2)
| ~ next(e_3,X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_64,axiom,
greater(e_3,e_2),
e_3_greater_e_2 ).
cnf(c_0_65,plain,
~ equalish(e_1,e_3),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_3]) ).
cnf(c_0_66,plain,
~ equalish(e_2,e_3),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_3]) ).
cnf(c_0_67,plain,
~ equalish(e_1,e_4),
c_0_60 ).
cnf(c_0_68,plain,
~ equalish(e_2,e_4),
c_0_61 ).
cnf(c_0_69,axiom,
greater(e_2,e_0),
e_2_greater_e_0 ).
cnf(c_0_70,plain,
~ equalish(e_3,e_4),
c_0_62 ).
cnf(c_0_71,plain,
( cycle(e_3,e_2)
| cycle(e_3,e_3)
| cycle(e_2,e_0)
| cycle(e_2,e_2)
| ~ cycle(e_2,X1)
| ~ cycle(X2,X3)
| ~ greater(X1,X3)
| ~ next(e_3,X2) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_72,plain,
~ equalish(e_1,e_3),
c_0_65 ).
cnf(c_0_73,plain,
~ equalish(e_2,e_3),
c_0_66 ).
cnf(c_0_74,plain,
( ~ cycle(X1,e_1)
| ~ cycle(X2,X3)
| ~ next(X3,e_4)
| ~ next(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_42]),c_0_43])]) ).
cnf(c_0_75,plain,
( ~ cycle(X1,e_2)
| ~ cycle(X2,X3)
| ~ next(X3,e_4)
| ~ next(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_42]),c_0_69])]) ).
cnf(c_0_76,plain,
( ~ cycle(X1,e_3)
| ~ cycle(X2,X3)
| ~ next(X3,e_4)
| ~ next(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_42]),c_0_47])]) ).
cnf(c_0_77,plain,
( cycle(e_2,e_3)
| cycle(e_2,e_2)
| cycle(e_2,e_0)
| cycle(e_3,e_3)
| cycle(e_3,e_2)
| ~ cycle(X1,X2)
| ~ greater(e_1,X2)
| ~ next(e_3,X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_49]) ).
cnf(c_0_78,plain,
( 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) ),
inference(fof_simplification,[status(thm)],[product_total_function1]) ).
cnf(c_0_79,plain,
( ~ cycle(X1,e_1)
| ~ cycle(X2,X3)
| ~ next(X3,e_3)
| ~ next(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_42]),c_0_43])]) ).
cnf(c_0_80,plain,
( ~ cycle(X1,e_2)
| ~ cycle(X2,X3)
| ~ next(X3,e_3)
| ~ next(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_42]),c_0_69])]) ).
cnf(c_0_81,plain,
( cycle(e_2,e_0)
| ~ cycle(X1,X2)
| ~ next(X2,e_4)
| ~ next(e_2,X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_49]),c_0_75]),c_0_76]) ).
cnf(c_0_82,axiom,
next(e_3,e_4),
e_3_then_e_4 ).
cnf(c_0_83,plain,
( cycle(e_3,e_2)
| cycle(e_3,e_3)
| cycle(e_2,e_0)
| cycle(e_2,e_2)
| cycle(e_2,e_3)
| ~ cycle(X1,e_0)
| ~ next(e_3,X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_43]) ).
cnf(c_0_84,axiom,
cycle(e_4,e_0),
cycle3 ).
cnf(c_0_85,plain,
~ equalish(e_2,e_1),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_1]) ).
cnf(c_0_86,plain,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
inference(fof_simplification,[status(thm)],[product_right_cancellation]) ).
cnf(c_0_87,plain,
( 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) ),
c_0_78 ).
cnf(c_0_88,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_89,plain,
( cycle(e_2,e_0)
| cycle(e_2,e_3)
| ~ cycle(X1,X2)
| ~ next(X2,e_3)
| ~ next(e_2,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_49]),c_0_80]) ).
cnf(c_0_90,plain,
( cycle(e_2,e_0)
| ~ cycle(X1,e_3)
| ~ next(e_2,X1) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_91,plain,
( cycle(e_2,e_3)
| cycle(e_2,e_2)
| cycle(e_2,e_0)
| cycle(e_3,e_3)
| cycle(e_3,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_82])]) ).
cnf(c_0_92,plain,
~ equalish(e_2,e_1),
c_0_85 ).
cnf(c_0_93,plain,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
c_0_86 ).
cnf(c_0_94,plain,
( product(X1,e_1,e_4)
| product(X1,e_1,e_3)
| product(X1,e_1,e_2)
| product(X1,e_1,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_95,plain,
( ~ cycle(X1,e_0)
| ~ product(X1,e_1,X2)
| ~ greater(X2,X1) ),
inference(fof_simplification,[status(thm)],[cycle6]) ).
cnf(c_0_96,plain,
( cycle(e_2,e_3)
| cycle(e_2,e_0)
| ~ cycle(X1,e_2)
| ~ next(e_2,X1) ),
inference(spm,[status(thm)],[c_0_89,c_0_57]) ).
cnf(c_0_97,plain,
( cycle(e_3,e_2)
| cycle(e_2,e_2)
| cycle(e_2,e_3)
| cycle(e_2,e_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_57])]) ).
cnf(c_0_98,plain,
( ~ product(X1,e_1,X2)
| ~ product(X1,e_2,X2) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_99,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_94,c_0_45]) ).
cnf(c_0_100,plain,
( product(X1,e_2,e_4)
| product(X1,e_2,e_3)
| product(X1,e_2,e_2)
| product(X1,e_2,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_87,c_0_45]) ).
cnf(c_0_101,plain,
~ equalish(e_4,e_3),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_3]) ).
cnf(c_0_102,plain,
( equalish(X3,X4)
| ~ cycle(X1,X2)
| ~ product(X1,e_1,X3)
| ~ greater(X2,e_0)
| ~ next(X1,X4) ),
inference(fof_simplification,[status(thm)],[cycle7]) ).
cnf(c_0_103,plain,
( ~ cycle(X1,e_0)
| ~ product(X1,e_1,X2)
| ~ greater(X2,X1) ),
c_0_95 ).
cnf(c_0_104,plain,
( cycle(e_2,e_2)
| cycle(e_2,e_0)
| cycle(e_2,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_57])]) ).
cnf(c_0_105,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| ~ product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_106,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_100,c_0_45]) ).
cnf(c_0_107,plain,
~ equalish(e_4,e_3),
c_0_101 ).
cnf(c_0_108,plain,
( equalish(X3,X4)
| ~ cycle(X1,X2)
| ~ product(X1,e_1,X3)
| ~ greater(X2,e_0)
| ~ next(X1,X4) ),
c_0_102 ).
cnf(c_0_109,plain,
( cycle(e_2,e_3)
| cycle(e_2,e_2)
| ~ product(e_2,e_1,X1)
| ~ greater(X1,e_2) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_110,plain,
( product(e_2,e_2,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_111,axiom,
greater(e_4,e_2),
e_4_greater_e_2 ).
cnf(c_0_112,plain,
( ~ product(X1,e_1,e_4)
| ~ cycle(X1,X2)
| ~ greater(X2,e_0)
| ~ next(X1,e_3) ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_113,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_4)
| cycle(e_2,e_2)
| cycle(e_2,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_111])]) ).
cnf(c_0_114,plain,
~ equalish(e_3,e_1),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_1]) ).
cnf(c_0_115,plain,
( product(e_2,e_2,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| cycle(e_2,e_2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_47]),c_0_57])]),c_0_110]) ).
cnf(c_0_116,plain,
~ equalish(e_3,e_1),
c_0_114 ).
cnf(c_0_117,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_4) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_115]),c_0_69]),c_0_57])]),c_0_110]) ).
cnf(c_0_118,plain,
( ~ cycle(X1,e_3)
| ~ cycle(X2,X3)
| ~ next(X3,e_1)
| ~ next(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_42]),c_0_47])]) ).
cnf(c_0_119,plain,
( product(e_2,e_2,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_1,e_2)
| cycle(e_2,e_2)
| cycle(e_2,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_117]),c_0_64])]) ).
cnf(c_0_120,plain,
( ~ cycle(X1,e_2)
| ~ cycle(X2,X3)
| ~ next(X3,e_1)
| ~ next(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_42]),c_0_69])]) ).
cnf(c_0_121,plain,
( ~ product(X1,e_1,e_1)
| ~ cycle(X1,X2)
| ~ greater(X2,e_0)
| ~ next(X1,e_4) ),
inference(spm,[status(thm)],[c_0_67,c_0_108]) ).
cnf(c_0_122,plain,
( ~ product(X1,e_1,e_3)
| ~ cycle(X1,X2)
| ~ greater(X2,e_0)
| ~ next(X1,e_4) ),
inference(spm,[status(thm)],[c_0_70,c_0_108]) ).
cnf(c_0_123,plain,
( ~ product(X1,e_1,e_2)
| ~ cycle(X1,X2)
| ~ greater(X2,e_0)
| ~ next(X1,e_4) ),
inference(spm,[status(thm)],[c_0_68,c_0_108]) ).
cnf(c_0_124,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_4)
| ~ cycle(X1,X2)
| ~ next(X2,e_1)
| ~ next(e_2,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_120]) ).
cnf(c_0_125,axiom,
next(e_0,e_1),
e_0_then_e_1 ).
cnf(c_0_126,plain,
( cycle(e_3,e_0)
| cycle(e_3,e_2)
| cycle(e_3,e_3)
| ~ product(e_3,e_1,e_1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_56]),c_0_43]),c_0_82])]) ).
cnf(c_0_127,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_94,c_0_53]) ).
cnf(c_0_128,plain,
( cycle(e_3,e_0)
| cycle(e_3,e_2)
| cycle(e_3,e_3)
| ~ product(e_3,e_1,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_56]),c_0_43]),c_0_82])]) ).
cnf(c_0_129,plain,
( cycle(e_3,e_0)
| cycle(e_3,e_2)
| cycle(e_3,e_3)
| ~ product(e_3,e_1,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_56]),c_0_43]),c_0_82])]) ).
cnf(c_0_130,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_4)
| ~ cycle(X1,X2)
| ~ next(X2,e_4)
| ~ next(e_2,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_119]),c_0_75]) ).
cnf(c_0_131,plain,
( product(e_2,e_2,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_1,e_2)
| ~ cycle(X1,e_0)
| ~ next(e_2,X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_132,plain,
( product(e_3,e_1,e_4)
| cycle(e_3,e_3)
| cycle(e_3,e_2)
| cycle(e_3,e_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_128]),c_0_129]) ).
cnf(c_0_133,plain,
~ equalish(e_4,e_2),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_2]) ).
cnf(c_0_134,negated_conjecture,
( product(X3,X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X2,X3,X4) ),
inference(fof_simplification,[status(thm)],[qg3]) ).
cnf(c_0_135,plain,
( product(e_2,e_2,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_1,e_2)
| ~ cycle(X1,e_3)
| ~ next(e_2,X1) ),
inference(spm,[status(thm)],[c_0_130,c_0_82]) ).
cnf(c_0_136,plain,
( product(e_3,e_1,e_4)
| product(e_2,e_1,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_4)
| cycle(e_3,e_2)
| cycle(e_3,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_57])]) ).
cnf(c_0_137,plain,
~ equalish(e_4,e_2),
c_0_133 ).
cnf(c_0_138,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_94,c_0_88]) ).
cnf(c_0_139,negated_conjecture,
( product(X3,X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X2,X3,X4) ),
c_0_134 ).
cnf(c_0_140,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_100,c_0_88]) ).
cnf(c_0_141,plain,
( product(e_3,e_1,e_4)
| product(e_2,e_1,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_4)
| cycle(e_3,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_57])]) ).
cnf(c_0_142,plain,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
inference(fof_simplification,[status(thm)],[product_left_cancellation]) ).
cnf(c_0_143,plain,
( ~ product(X1,e_1,e_4)
| ~ cycle(X1,X2)
| ~ greater(X2,e_0)
| ~ next(X1,e_2) ),
inference(spm,[status(thm)],[c_0_137,c_0_108]) ).
cnf(c_0_144,plain,
( cycle(e_1,e_3)
| cycle(e_1,e_2)
| cycle(e_1,e_1)
| cycle(e_1,e_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_88]) ).
cnf(c_0_145,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_2)
| ~ product(e_1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_98,c_0_138]) ).
cnf(c_0_146,negated_conjecture,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| ~ product(X1,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_139]) ).
cnf(c_0_147,plain,
( ~ product(X1,e_1,e_3)
| ~ cycle(X1,X2)
| ~ greater(X2,e_0)
| ~ next(X1,e_2) ),
inference(spm,[status(thm)],[c_0_46,c_0_108]) ).
cnf(c_0_148,plain,
( product(e_2,e_2,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_4)
| ~ cycle(X1,X2)
| ~ next(X2,e_1)
| ~ next(e_3,X1) ),
inference(spm,[status(thm)],[c_0_120,c_0_141]) ).
cnf(c_0_149,plain,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
c_0_142 ).
cnf(c_0_150,plain,
( cycle(e_1,e_0)
| cycle(e_1,e_2)
| cycle(e_1,e_3)
| ~ product(e_1,e_1,e_4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_43]),c_0_52])]) ).
cnf(c_0_151,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_140]),c_0_146]) ).
cnf(c_0_152,plain,
( cycle(e_1,e_0)
| cycle(e_1,e_2)
| cycle(e_1,e_3)
| ~ product(e_1,e_1,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_144]),c_0_43]),c_0_52])]) ).
cnf(c_0_153,plain,
( product(e_3,e_1,e_4)
| product(e_2,e_1,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_4)
| ~ cycle(X1,e_0)
| ~ next(e_3,X1) ),
inference(spm,[status(thm)],[c_0_148,c_0_125]) ).
cnf(c_0_154,plain,
( ~ product(e_3,X1,X2)
| ~ product(e_2,X1,X2) ),
inference(spm,[status(thm)],[c_0_73,c_0_149]) ).
cnf(c_0_155,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_100,c_0_53]) ).
cnf(c_0_156,negated_conjecture,
( product(e_2,e_2,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_1,e_2)
| product(e_1,X1,e_3)
| ~ product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_139,c_0_117]) ).
cnf(c_0_157,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4)
| cycle(e_1,e_3)
| cycle(e_1,e_2)
| cycle(e_1,e_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_152]) ).
cnf(c_0_158,plain,
( product(e_2,e_2,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_84]),c_0_82])]) ).
cnf(c_0_159,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| ~ product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_154,c_0_155]) ).
cnf(c_0_160,plain,
( ~ product(e_3,X1,X2)
| ~ product(e_1,X1,X2) ),
inference(spm,[status(thm)],[c_0_72,c_0_149]) ).
cnf(c_0_161,negated_conjecture,
( product(e_1,e_2,e_3)
| product(e_2,e_1,e_2)
| 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_156,c_0_106]) ).
cnf(c_0_162,axiom,
group_element(e_4),
element_4 ).
cnf(c_0_163,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| cycle(e_1,e_2)
| cycle(e_1,e_3)
| ~ product(e_1,e_1,X1)
| ~ greater(X1,e_1) ),
inference(spm,[status(thm)],[c_0_103,c_0_157]) ).
cnf(c_0_164,axiom,
greater(e_4,e_1),
e_4_greater_e_1 ).
cnf(c_0_165,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| ~ product(e_3,e_2,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_158]),c_0_154]) ).
cnf(c_0_166,plain,
( product(e_2,e_2,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| 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_159,c_0_106]) ).
cnf(c_0_167,negated_conjecture,
( product(e_2,e_2,e_4)
| product(e_2,e_2,e_2)
| product(e_2,e_1,e_2)
| ~ product(e_3,e_2,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_154]) ).
cnf(c_0_168,plain,
( ~ product(X1,e_1,e_1)
| ~ cycle(X1,X2)
| ~ greater(X2,e_0)
| ~ next(X1,e_2) ),
inference(spm,[status(thm)],[c_0_41,c_0_108]) ).
cnf(c_0_169,plain,
( product(X1,e_4,e_4)
| product(X1,e_4,e_3)
| product(X1,e_4,e_2)
| product(X1,e_4,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_87,c_0_162]) ).
cnf(c_0_170,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4)
| cycle(e_1,e_3)
| cycle(e_1,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_151]),c_0_164])]) ).
cnf(c_0_171,negated_conjecture,
( product(e_2,e_2,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,X1,e_1)
| ~ product(X1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_139,c_0_106]) ).
cnf(c_0_172,plain,
( product(e_3,e_2,e_2)
| product(e_2,e_2,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_167]) ).
cnf(c_0_173,plain,
( cycle(e_1,e_0)
| cycle(e_1,e_2)
| cycle(e_1,e_3)
| ~ product(e_1,e_1,e_1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_144]),c_0_43]),c_0_52])]) ).
cnf(c_0_174,plain,
( ~ product(X1,e_4,X2)
| ~ product(X1,e_1,X2) ),
inference(spm,[status(thm)],[c_0_67,c_0_93]) ).
cnf(c_0_175,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_169,c_0_88]) ).
cnf(c_0_176,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_1,e_3)
| cycle(e_1,e_2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_170]),c_0_47]),c_0_52])]),c_0_151]) ).
cnf(c_0_177,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_2,e_3,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_171,c_0_172]) ).
cnf(c_0_178,plain,
( product(e_1,e_1,e_2)
| cycle(e_1,e_3)
| cycle(e_1,e_2)
| cycle(e_1,e_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_138]),c_0_150]),c_0_152]) ).
cnf(c_0_179,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_2)
| ~ product(e_1,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_174,c_0_138]) ).
cnf(c_0_180,negated_conjecture,
( product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| ~ product(X1,e_1,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_175]),c_0_139]) ).
cnf(c_0_181,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_176]),c_0_69]),c_0_52])]),c_0_151]) ).
cnf(c_0_182,axiom,
greater(e_3,e_1),
e_3_greater_e_1 ).
cnf(c_0_183,plain,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
inference(fof_simplification,[status(thm)],[product_total_function2]) ).
cnf(c_0_184,negated_conjecture,
( product(e_2,e_2,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_3,e_1)
| product(e_1,X1,e_2)
| ~ product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_139,c_0_177]) ).
cnf(c_0_185,plain,
( product(e_1,e_1,e_2)
| cycle(e_1,e_2)
| cycle(e_1,e_3)
| ~ product(e_1,e_1,X1)
| ~ greater(X1,e_1) ),
inference(spm,[status(thm)],[c_0_103,c_0_178]) ).
cnf(c_0_186,plain,
( product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_175]),c_0_180]) ).
cnf(c_0_187,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4)
| cycle(e_1,e_3)
| cycle(e_1,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_181]),c_0_182])]) ).
cnf(c_0_188,plain,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
c_0_183 ).
cnf(c_0_189,negated_conjecture,
( product(e_1,e_2,e_2)
| product(e_2,e_3,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_184,c_0_106]) ).
cnf(c_0_190,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4)
| product(e_1,e_1,e_2)
| cycle(e_1,e_3)
| cycle(e_1,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_186]),c_0_182])]) ).
cnf(c_0_191,plain,
( product(X1,e_3,e_4)
| product(X1,e_3,e_3)
| product(X1,e_3,e_2)
| product(X1,e_3,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_87,c_0_53]) ).
cnf(c_0_192,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| cycle(e_1,e_2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_187]),c_0_47]),c_0_52])]),c_0_181]) ).
cnf(c_0_193,plain,
( ~ product(X1,X2,e_1)
| ~ product(X1,X2,e_2) ),
inference(spm,[status(thm)],[c_0_92,c_0_188]) ).
cnf(c_0_194,negated_conjecture,
( product(e_2,e_3,e_1)
| product(e_2,e_1,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_171,c_0_189]) ).
cnf(c_0_195,plain,
( ~ product(e_4,X1,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_70,c_0_149]) ).
cnf(c_0_196,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_100,c_0_162]) ).
cnf(c_0_197,plain,
( ~ product(e_1,X1,X2)
| ~ product(e_2,X1,X2) ),
inference(spm,[status(thm)],[c_0_92,c_0_149]) ).
cnf(c_0_198,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| cycle(e_1,e_2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_190]),c_0_47]),c_0_52])]),c_0_186]) ).
cnf(c_0_199,plain,
( ~ product(X1,e_3,X2)
| ~ product(X1,e_1,X2) ),
inference(spm,[status(thm)],[c_0_72,c_0_93]) ).
cnf(c_0_200,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_191,c_0_88]) ).
cnf(c_0_201,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_192]),c_0_69]),c_0_52])]),c_0_181]) ).
cnf(c_0_202,plain,
( ~ product(X1,e_3,X2)
| ~ product(X1,e_2,X2) ),
inference(spm,[status(thm)],[c_0_73,c_0_93]) ).
cnf(c_0_203,negated_conjecture,
( product(e_2,e_2,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_3,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_194]),c_0_177]) ).
cnf(c_0_204,plain,
( product(e_4,e_2,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_2)
| ~ product(e_3,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_195,c_0_196]) ).
cnf(c_0_205,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_2)
| ~ product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_197,c_0_138]) ).
cnf(c_0_206,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4)
| product(e_1,e_1,e_2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_198]),c_0_69]),c_0_52])]),c_0_186]) ).
cnf(c_0_207,plain,
( ~ product(X1,e_4,X2)
| ~ product(X1,e_2,X2) ),
inference(spm,[status(thm)],[c_0_68,c_0_93]) ).
cnf(c_0_208,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_2)
| ~ product(e_1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_199,c_0_138]) ).
cnf(c_0_209,negated_conjecture,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| ~ product(X1,e_1,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_200]),c_0_139]) ).
cnf(c_0_210,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| ~ product(e_2,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_197,c_0_201]) ).
cnf(c_0_211,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_203]),c_0_106]) ).
cnf(c_0_212,plain,
( ~ product(e_4,X1,X2)
| ~ product(e_2,X1,X2) ),
inference(spm,[status(thm)],[c_0_68,c_0_149]) ).
cnf(c_0_213,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| 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_204,c_0_155]) ).
cnf(c_0_214,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_205,c_0_99]) ).
cnf(c_0_215,negated_conjecture,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_2,X1,e_4)
| ~ product(X1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_139,c_0_201]) ).
cnf(c_0_216,plain,
( product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| ~ product(e_1,e_2,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_206]),c_0_207]) ).
cnf(c_0_217,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_200]),c_0_209]) ).
cnf(c_0_218,plain,
( ~ product(e_4,X1,X2)
| ~ product(e_1,X1,X2) ),
inference(spm,[status(thm)],[c_0_67,c_0_149]) ).
cnf(c_0_219,negated_conjecture,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_210,c_0_211]) ).
cnf(c_0_220,plain,
( product(e_4,e_2,e_3)
| product(e_4,e_2,e_2)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3)
| ~ product(e_2,e_2,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_213]),c_0_154]) ).
cnf(c_0_221,plain,
( product(e_1,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_4)
| ~ product(e_1,e_2,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_214]),c_0_139]) ).
cnf(c_0_222,negated_conjecture,
( product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| product(e_1,e_2,e_3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_206]),c_0_180]),c_0_216]) ).
cnf(c_0_223,plain,
( ~ product(X1,X2,e_4)
| ~ product(X1,X2,e_3) ),
inference(spm,[status(thm)],[c_0_70,c_0_188]) ).
cnf(c_0_224,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| ~ product(e_1,e_2,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_217]),c_0_202]) ).
cnf(c_0_225,negated_conjecture,
( product(e_1,e_2,e_2)
| product(e_2,e_2,e_2)
| ~ product(e_4,e_2,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_219]),c_0_212]) ).
cnf(c_0_226,negated_conjecture,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_220,c_0_211]) ).
cnf(c_0_227,negated_conjecture,
( product(e_1,e_2,e_2)
| product(e_2,e_2,e_2)
| ~ product(e_3,e_2,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_219]),c_0_154]) ).
cnf(c_0_228,plain,
( ~ product(X1,X2,e_4)
| ~ product(X1,X2,e_2) ),
inference(spm,[status(thm)],[c_0_68,c_0_188]) ).
cnf(c_0_229,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_2,e_1,e_4)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_221,c_0_201]) ).
cnf(c_0_230,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| ~ product(e_1,e_2,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_222]),c_0_223]) ).
cnf(c_0_231,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_224,c_0_201]) ).
cnf(c_0_232,negated_conjecture,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,X1,e_4)
| ~ product(X1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_139,c_0_211]) ).
cnf(c_0_233,negated_conjecture,
( product(e_4,e_2,e_2)
| product(e_3,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_1,e_2,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_226]),c_0_227]) ).
cnf(c_0_234,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| ~ product(e_2,e_1,e_4) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_158]),c_0_228]),c_0_98]) ).
cnf(c_0_235,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_4)
| product(e_1,e_2,e_2)
| ~ product(e_1,e_4,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_229]),c_0_207]) ).
cnf(c_0_236,negated_conjecture,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_230,c_0_201]) ).
cnf(c_0_237,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_4)
| product(e_1,e_2,e_2)
| ~ product(e_1,e_3,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_229]),c_0_202]) ).
cnf(c_0_238,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_2,e_1,e_4)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_215,c_0_231]) ).
cnf(c_0_239,negated_conjecture,
( product(e_3,e_2,e_2)
| product(e_4,e_2,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_232,c_0_233]),c_0_234]) ).
cnf(c_0_240,plain,
( ~ product(X1,X2,e_4)
| ~ product(X1,X2,e_1) ),
inference(spm,[status(thm)],[c_0_67,c_0_188]) ).
cnf(c_0_241,plain,
( ~ product(X1,e_4,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_70,c_0_93]) ).
cnf(c_0_242,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_2,e_1,e_4)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_235,c_0_236]) ).
cnf(c_0_243,negated_conjecture,
( product(e_1,e_2,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_2,e_1,e_4)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_237,c_0_238]) ).
cnf(c_0_244,negated_conjecture,
( product(e_3,e_2,e_2)
| product(e_2,e_4,e_4)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_232,c_0_239]) ).
cnf(c_0_245,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| ~ product(e_2,e_3,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_240,c_0_203]),c_0_202]) ).
cnf(c_0_246,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_4)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_242]),c_0_243]) ).
cnf(c_0_247,negated_conjecture,
( product(e_2,e_4,e_4)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_232,c_0_244]),c_0_245]) ).
cnf(c_0_248,negated_conjecture,
( product(e_2,e_1,e_4)
| product(e_2,e_1,e_2)
| ~ product(e_2,e_2,e_3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_246]),c_0_139]),c_0_98]) ).
cnf(c_0_249,negated_conjecture,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_247]),c_0_211]) ).
cnf(c_0_250,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_248,c_0_249]) ).
cnf(c_0_251,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_2,e_2,e_2)
| cycle(e_2,e_2)
| cycle(e_2,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_250]),c_0_111])]) ).
cnf(c_0_252,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| ~ product(e_2,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_174,c_0_99]) ).
cnf(c_0_253,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_169,c_0_45]) ).
cnf(c_0_254,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_2,e_1,e_2)
| cycle(e_2,e_2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_251]),c_0_47]),c_0_57])]),c_0_250]) ).
cnf(c_0_255,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_252,c_0_253]) ).
cnf(c_0_256,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_2,e_2,e_2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_254]),c_0_69]),c_0_57])]),c_0_250]) ).
cnf(c_0_257,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_4)
| cycle(e_2,e_2)
| cycle(e_2,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_255]),c_0_111])]) ).
cnf(c_0_258,negated_conjecture,
~ product(e_2,e_4,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_256]),c_0_207]) ).
cnf(c_0_259,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| cycle(e_2,e_3)
| cycle(e_2,e_2) ),
inference(sr,[status(thm)],[c_0_257,c_0_258]) ).
cnf(c_0_260,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_4) ),
inference(sr,[status(thm)],[c_0_255,c_0_258]) ).
cnf(c_0_261,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_4)
| cycle(e_2,e_2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_259]),c_0_47]),c_0_57])]),c_0_260]) ).
cnf(c_0_262,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_169,c_0_162]) ).
cnf(c_0_263,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_261]),c_0_69]),c_0_57])]),c_0_260]) ).
cnf(c_0_264,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_1) ),
inference(sr,[status(thm)],[c_0_253,c_0_258]) ).
cnf(c_0_265,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_191,c_0_45]) ).
cnf(c_0_266,negated_conjecture,
~ product(e_2,e_3,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_256]),c_0_202]) ).
cnf(c_0_267,plain,
( product(e_4,e_4,e_4)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| ~ product(e_4,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_207,c_0_262]) ).
cnf(c_0_268,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_256]),c_0_210]) ).
cnf(c_0_269,plain,
( product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_94,c_0_162]) ).
cnf(c_0_270,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_4)
| cycle(e_2,e_2)
| cycle(e_2,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_263]),c_0_64])]) ).
cnf(c_0_271,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_4,e_4)
| ~ product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_241,c_0_264]) ).
cnf(c_0_272,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_1) ),
inference(sr,[status(thm)],[c_0_265,c_0_266]) ).
cnf(c_0_273,plain,
( product(e_4,e_2,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_2)
| 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_267,c_0_196]) ).
cnf(c_0_274,negated_conjecture,
( product(e_1,e_2,e_2)
| product(e_2,e_2,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_268]),c_0_249]) ).
cnf(c_0_275,negated_conjecture,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| product(e_1,X1,e_1)
| ~ product(X1,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_139,c_0_269]) ).
cnf(c_0_276,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_1,e_2)
| ~ cycle(X1,X2)
| ~ next(X2,e_1)
| ~ next(e_2,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_270]),c_0_120]) ).
cnf(c_0_277,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_4)
| product(e_2,e_4,e_4)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_271,c_0_272]) ).
cnf(c_0_278,plain,
( product(e_4,e_2,e_2)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_4)
| ~ product(e_2,e_4,e_4) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_273]),c_0_139]),c_0_139]) ).
cnf(c_0_279,negated_conjecture,
~ product(e_4,e_2,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_274]),c_0_212]) ).
cnf(c_0_280,negated_conjecture,
( product(e_2,e_4,e_3)
| product(e_2,e_4,e_4)
| product(e_1,e_2,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_275,c_0_264]) ).
cnf(c_0_281,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_1,e_2)
| ~ cycle(X1,X2)
| ~ next(X2,e_4)
| ~ next(e_2,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_270]),c_0_75]) ).
cnf(c_0_282,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_4)
| ~ cycle(X1,e_0)
| ~ next(e_2,X1) ),
inference(spm,[status(thm)],[c_0_276,c_0_125]) ).
cnf(c_0_283,negated_conjecture,
( product(e_2,e_4,e_3)
| product(e_2,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_4,X1,e_4)
| ~ product(X1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_139,c_0_277]) ).
cnf(c_0_284,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_4,e_2,e_4)
| product(e_4,e_2,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_278,c_0_277]),c_0_279]) ).
cnf(c_0_285,plain,
( ~ product(X1,X2,e_3)
| ~ product(X1,X2,e_1) ),
inference(spm,[status(thm)],[c_0_72,c_0_188]) ).
cnf(c_0_286,negated_conjecture,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| ~ product(e_1,e_2,e_4) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_240,c_0_280]),c_0_139]),c_0_139]),c_0_139]) ).
cnf(c_0_287,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_4)
| ~ cycle(X1,e_3)
| ~ next(e_2,X1) ),
inference(spm,[status(thm)],[c_0_281,c_0_82]) ).
cnf(c_0_288,plain,
( product(e_3,e_1,e_4)
| product(e_2,e_4,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_1,e_2)
| cycle(e_3,e_2)
| cycle(e_3,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_282,c_0_132]),c_0_57])]) ).
cnf(c_0_289,negated_conjecture,
( product(e_4,e_2,e_3)
| product(e_4,e_4,e_4)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_283,c_0_284]) ).
cnf(c_0_290,negated_conjecture,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_2,e_4,e_4)
| product(e_2,e_4,e_3)
| ~ product(e_1,e_2,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_285,c_0_280]),c_0_139]) ).
cnf(c_0_291,negated_conjecture,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_286,c_0_201]) ).
cnf(c_0_292,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_2,X1,e_2)
| ~ product(X1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_139,c_0_274]) ).
cnf(c_0_293,plain,
( product(e_3,e_1,e_4)
| product(e_2,e_4,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_1,e_2)
| cycle(e_3,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_287,c_0_288]),c_0_57])]) ).
cnf(c_0_294,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_4)
| product(e_3,X1,e_1)
| ~ product(X1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_139,c_0_272]) ).
cnf(c_0_295,negated_conjecture,
( product(e_2,e_4,e_3)
| product(e_2,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_4,e_2,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_289]),c_0_284]) ).
cnf(c_0_296,negated_conjecture,
( product(e_1,e_2,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_290,c_0_291]) ).
cnf(c_0_297,negated_conjecture,
product(e_2,e_2,e_2),
inference(spm,[status(thm)],[c_0_292,c_0_256]) ).
cnf(c_0_298,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_4)
| product(e_3,e_1,e_4)
| ~ cycle(X1,X2)
| ~ next(X2,e_1)
| ~ next(e_3,X1) ),
inference(spm,[status(thm)],[c_0_120,c_0_293]) ).
cnf(c_0_299,negated_conjecture,
( product(e_2,e_4,e_3)
| product(e_3,e_4,e_1)
| product(e_2,e_3,e_4)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_294,c_0_295]) ).
cnf(c_0_300,negated_conjecture,
~ product(e_3,e_2,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_274]),c_0_154]) ).
cnf(c_0_301,negated_conjecture,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_2,e_4,e_4)
| product(e_2,e_4,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_296]),c_0_297])]) ).
cnf(c_0_302,plain,
( product(e_3,e_1,e_4)
| product(e_2,e_4,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_1,e_2)
| ~ cycle(X1,e_0)
| ~ next(e_3,X1) ),
inference(spm,[status(thm)],[c_0_298,c_0_125]) ).
cnf(c_0_303,plain,
( product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| ~ product(e_1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_241,c_0_175]) ).
cnf(c_0_304,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_4)
| product(e_2,e_4,e_3)
| ~ product(e_3,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_207,c_0_299]) ).
cnf(c_0_305,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_155,c_0_300]) ).
cnf(c_0_306,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_4)
| product(e_2,e_4,e_3)
| ~ product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_195,c_0_295]) ).
cnf(c_0_307,negated_conjecture,
( product(e_2,e_4,e_3)
| product(e_2,e_4,e_4)
| product(e_4,e_1,e_3)
| ~ product(e_3,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_195,c_0_301]) ).
cnf(c_0_308,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_4)
| product(e_3,e_1,e_4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_302,c_0_84]),c_0_82])]) ).
cnf(c_0_309,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_303,c_0_200]) ).
cnf(c_0_310,negated_conjecture,
( product(e_3,e_2,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_3,e_4)
| product(e_2,e_3,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_304,c_0_305]),c_0_306]) ).
cnf(c_0_311,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_2,e_4,e_4)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_307,c_0_308]) ).
cnf(c_0_312,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| ~ product(e_1,e_4,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_217]),c_0_241]) ).
cnf(c_0_313,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_2,e_3)
| ~ product(e_1,e_4,e_2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_231]),c_0_241]),c_0_207]) ).
cnf(c_0_314,plain,
( product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| ~ product(e_1,e_2,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_309]),c_0_202]) ).
cnf(c_0_315,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_4)
| product(e_2,e_4,e_3)
| product(e_4,X1,e_1)
| ~ product(X1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_139,c_0_299]) ).
cnf(c_0_316,negated_conjecture,
( product(e_4,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_283,c_0_310]) ).
cnf(c_0_317,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_191,c_0_162]) ).
cnf(c_0_318,negated_conjecture,
( product(e_2,e_4,e_3)
| product(e_2,e_4,e_4)
| product(e_2,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_311]),c_0_263]) ).
cnf(c_0_319,negated_conjecture,
( product(e_1,e_2,e_3)
| product(e_1,e_4,e_3)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_312,c_0_222]),c_0_313]) ).
cnf(c_0_320,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_4,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_314,c_0_201]),c_0_313]) ).
cnf(c_0_321,negated_conjecture,
( product(e_4,e_4,e_1)
| product(e_2,e_4,e_3)
| product(e_2,e_3,e_4)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_315,c_0_316]) ).
cnf(c_0_322,plain,
( product(e_4,e_3,e_4)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| ~ product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_212,c_0_317]) ).
cnf(c_0_323,negated_conjecture,
( product(e_2,e_4,e_4)
| product(e_2,e_4,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_318]),c_0_297])]) ).
cnf(c_0_324,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_4,e_3)
| product(e_1,e_2,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_319]),c_0_320]) ).
cnf(c_0_325,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_197,c_0_236]) ).
cnf(c_0_326,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_4)
| product(e_2,e_4,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_321]),c_0_299]) ).
cnf(c_0_327,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_322,c_0_265]) ).
cnf(c_0_328,negated_conjecture,
( product(e_2,e_4,e_3)
| product(e_4,X1,e_4)
| ~ product(X1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_139,c_0_323]) ).
cnf(c_0_329,negated_conjecture,
( product(e_2,e_4,e_3)
| product(e_4,e_2,e_4)
| product(e_4,e_2,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_278,c_0_323]),c_0_279]) ).
cnf(c_0_330,negated_conjecture,
( product(e_1,e_2,e_3)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_197,c_0_324]) ).
cnf(c_0_331,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_325,c_0_326]) ).
cnf(c_0_332,negated_conjecture,
( product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4)
| ~ product(X1,e_4,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_327]),c_0_139]) ).
cnf(c_0_333,negated_conjecture,
( product(e_4,e_2,e_3)
| product(e_4,e_4,e_4)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_328,c_0_329]) ).
cnf(c_0_334,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_330,c_0_326]) ).
cnf(c_0_335,negated_conjecture,
( product(e_1,e_2,e_3)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4)
| ~ product(e_1,e_3,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_331]),c_0_202]) ).
cnf(c_0_336,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_332,c_0_326]),c_0_266]) ).
cnf(c_0_337,negated_conjecture,
( product(e_4,e_1,e_4)
| product(e_1,e_2,e_2)
| ~ product(e_4,e_2,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_291]),c_0_98]) ).
cnf(c_0_338,negated_conjecture,
( product(e_2,e_4,e_3)
| product(e_4,e_2,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_333]),c_0_329]) ).
cnf(c_0_339,negated_conjecture,
( product(e_1,e_2,e_3)
| product(e_2,e_3,e_4)
| ~ product(e_4,e_3,e_3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_334]),c_0_335]),c_0_212]) ).
cnf(c_0_340,negated_conjecture,
( product(e_4,e_3,e_2)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4)
| product(e_3,X1,e_3)
| ~ product(X1,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_139,c_0_336]) ).
cnf(c_0_341,negated_conjecture,
( product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| product(e_1,X1,e_2)
| ~ product(X1,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_139,c_0_206]) ).
cnf(c_0_342,plain,
( product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| ~ product(e_4,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_218,c_0_206]) ).
cnf(c_0_343,negated_conjecture,
( product(e_2,e_4,e_3)
| product(e_1,e_2,e_2)
| product(e_4,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_337,c_0_338]) ).
cnf(c_0_344,negated_conjecture,
( product(e_4,e_3,e_2)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_339,c_0_336]) ).
cnf(c_0_345,negated_conjecture,
( product(e_3,e_2,e_3)
| product(e_2,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_4,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_340,c_0_326]) ).
cnf(c_0_346,negated_conjecture,
( product(e_4,e_1,e_3)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_341,c_0_269]),c_0_180]),c_0_342]) ).
cnf(c_0_347,negated_conjecture,
( product(e_4,e_1,e_4)
| product(e_2,e_4,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_343]),c_0_297])]) ).
cnf(c_0_348,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_4,e_3,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_344]),c_0_345]) ).
cnf(c_0_349,plain,
( product(e_4,e_2,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_1) ),
inference(sr,[status(thm)],[c_0_196,c_0_279]) ).
cnf(c_0_350,negated_conjecture,
( product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| product(e_4,e_1,e_3)
| ~ product(e_2,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_197,c_0_346]) ).
cnf(c_0_351,negated_conjecture,
( product(e_2,e_4,e_3)
| ~ product(e_4,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_223,c_0_347]) ).
cnf(c_0_352,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_4)
| product(e_3,X1,e_2)
| ~ product(X1,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_139,c_0_348]) ).
cnf(c_0_353,plain,
( product(e_4,e_2,e_3)
| product(e_4,e_2,e_4)
| ~ product(e_3,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_195,c_0_349]) ).
cnf(c_0_354,negated_conjecture,
( product(e_2,e_4,e_3)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_350,c_0_323]),c_0_351]) ).
cnf(c_0_355,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_352,c_0_326]),c_0_300]) ).
cnf(c_0_356,plain,
( product(e_4,e_4,e_4)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| ~ product(e_2,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_212,c_0_262]) ).
cnf(c_0_357,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| ~ product(e_4,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_218,c_0_201]) ).
cnf(c_0_358,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_4)
| product(e_4,e_2,e_4)
| product(e_4,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_353,c_0_305]) ).
cnf(c_0_359,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| ~ product(e_3,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_160,c_0_201]) ).
cnf(c_0_360,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_2,e_4,e_3)
| product(e_4,X1,e_3)
| ~ product(X1,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_139,c_0_354]) ).
cnf(c_0_361,negated_conjecture,
~ product(e_4,e_4,e_3),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_223,c_0_333]),c_0_212]),c_0_207]) ).
cnf(c_0_362,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_3,X1,e_4)
| ~ product(X1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_139,c_0_355]) ).
cnf(c_0_363,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| 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_356,c_0_253]) ).
cnf(c_0_364,plain,
( product(e_4,e_2,e_3)
| product(e_3,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_357,c_0_358]),c_0_359]) ).
cnf(c_0_365,negated_conjecture,
( product(e_2,e_4,e_3)
| product(e_2,X1,e_3)
| ~ product(X1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_139,c_0_338]) ).
cnf(c_0_366,negated_conjecture,
( product(e_2,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_360,c_0_347]),c_0_361]) ).
cnf(c_0_367,negated_conjecture,
( product(e_2,e_4,e_3)
| product(e_3,e_4,e_4)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_362,c_0_338]) ).
cnf(c_0_368,plain,
( product(e_4,e_4,e_4)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_4) ),
inference(sr,[status(thm)],[c_0_363,c_0_258]) ).
cnf(c_0_369,negated_conjecture,
( product(e_1,e_2,e_2)
| product(e_3,e_2,e_3)
| product(e_4,e_2,e_3)
| product(e_3,e_1,e_4)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_362,c_0_364]) ).
cnf(c_0_370,negated_conjecture,
( product(e_2,e_1,e_3)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_365,c_0_366]) ).
cnf(c_0_371,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_2,e_4,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_367]),c_0_323]) ).
cnf(c_0_372,plain,
( product(e_2,e_4,e_4)
| product(e_4,e_4,e_3)
| ~ product(e_4,e_2,e_4) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_368]),c_0_139]),c_0_139]) ).
cnf(c_0_373,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_3,e_1,e_4)
| product(e_4,e_2,e_3)
| product(e_3,e_2,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_369]),c_0_297])]) ).
cnf(c_0_374,negated_conjecture,
product(e_2,e_4,e_3),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_370]),c_0_371]) ).
cnf(c_0_375,plain,
( product(e_4,e_2,e_3)
| product(e_3,e_2,e_4)
| product(e_3,e_2,e_3)
| product(e_4,e_4,e_3)
| product(e_2,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_372,c_0_358]) ).
cnf(c_0_376,negated_conjecture,
( product(e_3,e_2,e_3)
| product(e_3,e_1,e_4)
| product(e_3,e_4,e_4)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_362,c_0_373]) ).
cnf(c_0_377,negated_conjecture,
~ product(e_2,e_3,e_3),
inference(spm,[status(thm)],[c_0_241,c_0_374]) ).
cnf(c_0_378,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4)
| product(e_1,e_1,e_2)
| cycle(e_1,e_3)
| cycle(e_1,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_217]),c_0_164])]) ).
cnf(c_0_379,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_4)
| product(e_4,e_2,e_3)
| ~ product(e_2,e_4,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_375]),c_0_223]) ).
cnf(c_0_380,negated_conjecture,
( product(e_3,e_4,e_4)
| product(e_3,e_1,e_4)
| product(e_3,e_2,e_3) ),
inference(sr,[status(thm)],[c_0_376,c_0_377]) ).
cnf(c_0_381,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| cycle(e_1,e_2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_378]),c_0_47]),c_0_52])]),c_0_217]) ).
cnf(c_0_382,negated_conjecture,
product(e_2,e_3,e_4),
inference(sr,[status(thm)],[c_0_355,c_0_377]) ).
cnf(c_0_383,plain,
( product(e_4,e_2,e_3)
| product(e_3,e_2,e_4)
| product(e_3,e_2,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_379,c_0_374])]) ).
cnf(c_0_384,negated_conjecture,
~ product(e_3,e_2,e_4),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_380]),c_0_223]),c_0_207]) ).
cnf(c_0_385,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4)
| product(e_1,e_1,e_2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_381]),c_0_69]),c_0_52])]),c_0_217]) ).
cnf(c_0_386,negated_conjecture,
( product(e_3,X1,e_4)
| ~ product(X1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_139,c_0_382]) ).
cnf(c_0_387,plain,
( product(e_3,e_2,e_3)
| product(e_4,e_2,e_3) ),
inference(sr,[status(thm)],[c_0_383,c_0_384]) ).
cnf(c_0_388,negated_conjecture,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,X1,e_2)
| ~ product(X1,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_139,c_0_385]) ).
cnf(c_0_389,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| ~ product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_160,c_0_385]) ).
cnf(c_0_390,negated_conjecture,
( product(e_3,e_2,e_3)
| product(e_3,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_386,c_0_387]) ).
cnf(c_0_391,negated_conjecture,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_4,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_325,c_0_374])]) ).
cnf(c_0_392,negated_conjecture,
( product(e_3,e_1,e_4)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_388,c_0_127]),c_0_209]),c_0_389]) ).
cnf(c_0_393,negated_conjecture,
( product(e_3,e_2,e_3)
| product(e_4,X1,e_4)
| ~ product(X1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_139,c_0_390]) ).
cnf(c_0_394,negated_conjecture,
( product(e_1,e_2,e_3)
| ~ product(e_1,e_3,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_391]),c_0_202]) ).
cnf(c_0_395,negated_conjecture,
( product(e_1,e_3,e_2)
| ~ product(e_3,e_3,e_4) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_392]),c_0_139]),c_0_199]) ).
cnf(c_0_396,negated_conjecture,
( product(e_4,X1,e_3)
| ~ product(X1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_139,c_0_374]) ).
cnf(c_0_397,negated_conjecture,
( product(e_4,e_2,e_4)
| product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_393,c_0_382]) ).
cnf(c_0_398,negated_conjecture,
( product(e_1,e_2,e_3)
| ~ product(e_3,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_394,c_0_395]) ).
cnf(c_0_399,negated_conjecture,
product(e_3,e_2,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_396,c_0_397]),c_0_361]) ).
cnf(c_0_400,negated_conjecture,
~ product(e_3,e_3,e_4),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_386,c_0_398]),c_0_199]) ).
cnf(c_0_401,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_386,c_0_399]),c_0_400]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP129-3.004 : TPTP v8.1.2. Released v1.2.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 16:20:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.49 Running first-order model finding
% 0.21/0.49 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.IOfWYx2kfE/E---3.1_10237.p
% 2.16/0.75 # Version: 3.1.0
% 2.16/0.75 # Preprocessing class: FSMSSMSSSSSNFFN.
% 2.16/0.75 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.16/0.75 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.16/0.75 # Starting new_bool_3 with 300s (1) cores
% 2.16/0.75 # Starting new_bool_1 with 300s (1) cores
% 2.16/0.75 # Starting sh5l with 300s (1) cores
% 2.16/0.75 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 10368 completed with status 0
% 2.16/0.75 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 2.16/0.75 # Preprocessing class: FSMSSMSSSSSNFFN.
% 2.16/0.75 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.16/0.75 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.16/0.75 # No SInE strategy applied
% 2.16/0.75 # Search class: FGHNF-FFMM00-SFFFFFNN
% 2.16/0.75 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 2.16/0.75 # Starting H----_011_C07_F1_PI_AE_OS_S1U with 811s (1) cores
% 2.16/0.75 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.16/0.75 # Starting G----_425_C05_02_F1_SE_CS_SP_PS_RG_S04AI with 136s (1) cores
% 2.16/0.75 # Starting G-E--_208_B07--C_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.16/0.75 # Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 2.16/0.75 # G----_425_C05_02_F1_SE_CS_SP_PS_RG_S04AI with pid 10377 completed with status 0
% 2.16/0.75 # Result found by G----_425_C05_02_F1_SE_CS_SP_PS_RG_S04AI
% 2.16/0.75 # Preprocessing class: FSMSSMSSSSSNFFN.
% 2.16/0.75 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.16/0.75 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.16/0.75 # No SInE strategy applied
% 2.16/0.75 # Search class: FGHNF-FFMM00-SFFFFFNN
% 2.16/0.75 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 2.16/0.75 # Starting H----_011_C07_F1_PI_AE_OS_S1U with 811s (1) cores
% 2.16/0.75 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.16/0.75 # Starting G----_425_C05_02_F1_SE_CS_SP_PS_RG_S04AI with 136s (1) cores
% 2.16/0.75 # Preprocessing time : 0.001 s
% 2.16/0.75 # Presaturation interreduction done
% 2.16/0.75
% 2.16/0.75 # Proof found!
% 2.16/0.75 # SZS status Unsatisfiable
% 2.16/0.75 # SZS output start CNFRefutation
% See solution above
% 2.16/0.76 # Parsed axioms : 42
% 2.16/0.76 # Removed by relevancy pruning/SinE : 0
% 2.16/0.76 # Initial clauses : 42
% 2.16/0.76 # Removed in clause preprocessing : 0
% 2.16/0.76 # Initial clauses in saturation : 42
% 2.16/0.76 # Processed clauses : 1851
% 2.16/0.76 # ...of these trivial : 0
% 2.16/0.76 # ...subsumed : 433
% 2.16/0.76 # ...remaining for further processing : 1418
% 2.16/0.76 # Other redundant clauses eliminated : 0
% 2.16/0.76 # Clauses deleted for lack of memory : 0
% 2.16/0.76 # Backward-subsumed : 711
% 2.16/0.76 # Backward-rewritten : 78
% 2.16/0.76 # Generated clauses : 5755
% 2.16/0.76 # ...of the previous two non-redundant : 5192
% 2.16/0.76 # ...aggressively subsumed : 0
% 2.16/0.76 # Contextual simplify-reflections : 396
% 2.16/0.76 # Paramodulations : 5691
% 2.16/0.76 # Factorizations : 0
% 2.16/0.76 # NegExts : 0
% 2.16/0.76 # Equation resolutions : 0
% 2.16/0.76 # Disequality decompositions : 0
% 2.16/0.76 # Total rewrite steps : 806
% 2.16/0.76 # ...of those cached : 788
% 2.16/0.76 # Propositional unsat checks : 0
% 2.16/0.76 # Propositional check models : 0
% 2.16/0.76 # Propositional check unsatisfiable : 0
% 2.16/0.76 # Propositional clauses : 0
% 2.16/0.76 # Propositional clauses after purity: 0
% 2.16/0.76 # Propositional unsat core size : 0
% 2.16/0.76 # Propositional preprocessing time : 0.000
% 2.16/0.76 # Propositional encoding time : 0.000
% 2.16/0.76 # Propositional solver time : 0.000
% 2.16/0.76 # Success case prop preproc time : 0.000
% 2.16/0.76 # Success case prop encoding time : 0.000
% 2.16/0.76 # Success case prop solver time : 0.000
% 2.16/0.76 # Current number of processed clauses : 523
% 2.16/0.76 # Positive orientable unit clauses : 23
% 2.16/0.76 # Positive unorientable unit clauses: 0
% 2.16/0.76 # Negative unit clauses : 25
% 2.16/0.76 # Non-unit-clauses : 475
% 2.16/0.76 # Current number of unprocessed clauses: 2902
% 2.16/0.76 # ...number of literals in the above : 22967
% 2.16/0.76 # Current number of archived formulas : 0
% 2.16/0.76 # Current number of archived clauses : 895
% 2.16/0.76 # Clause-clause subsumption calls (NU) : 176003
% 2.16/0.76 # Rec. Clause-clause subsumption calls : 28903
% 2.16/0.76 # Non-unit clause-clause subsumptions : 1383
% 2.16/0.76 # Unit Clause-clause subsumption calls : 6331
% 2.16/0.76 # Rewrite failures with RHS unbound : 0
% 2.16/0.76 # BW rewrite match attempts : 16
% 2.16/0.76 # BW rewrite match successes : 4
% 2.16/0.76 # Condensation attempts : 0
% 2.16/0.76 # Condensation successes : 0
% 2.16/0.76 # Termbank termtop insertions : 104937
% 2.16/0.76 # Search garbage collected termcells : 98
% 2.16/0.76
% 2.16/0.76 # -------------------------------------------------
% 2.16/0.76 # User time : 0.247 s
% 2.16/0.76 # System time : 0.005 s
% 2.16/0.76 # Total time : 0.252 s
% 2.16/0.76 # Maximum resident set size: 1684 pages
% 2.16/0.76
% 2.16/0.76 # -------------------------------------------------
% 2.16/0.76 # User time : 1.210 s
% 2.16/0.76 # System time : 0.035 s
% 2.16/0.76 # Total time : 1.245 s
% 2.16/0.76 # Maximum resident set size: 1756 pages
% 2.16/0.76 % E---3.1 exiting
%------------------------------------------------------------------------------