%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP126-3.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 12:41:57 PM UTC 2026
% Result : Unsatisfiable 0.24s 5.60s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 27
% Syntax : Number of clauses : 131 ( 52 unt; 52 nHn; 129 RR)
% Number of literals : 322 ( 0 equ; 115 neg)
% Maximal clause size : 6 ( 2 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 : 105 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_total_function1,axiom,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_4)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
cnf(cycle2,axiom,
( ~ group_element(X1)
| cycle(X1,e_3)
| cycle(X1,e_2)
| cycle(X1,e_1)
| cycle(X1,e_0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle2) ).
cnf(product_left_cancellation,axiom,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(element_4,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
cnf(cycle6,axiom,
( ~ greater(X2,X1)
| ~ product(X1,e_1,X2)
| ~ cycle(X1,e_0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle6) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
cnf(product_right_cancellation,axiom,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(product_idempotence,axiom,
product(X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
cnf(e_3_is_not_e_4,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
cnf(cycle7,axiom,
( ~ next(X1,X4)
| ~ greater(X2,e_0)
| ~ product(X1,e_1,X3)
| ~ cycle(X1,X2)
| equalish(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cycle7) ).
cnf(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
cnf(e_3_greater_e_1,axiom,
greater(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_1) ).
cnf(qg4,negated_conjecture,
( ~ product(X2,X1,X4)
| ~ product(X1,X2,X3)
| product(X3,X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg4) ).
cnf(e_3_greater_e_0,axiom,
greater(e_3,e_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_0) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
cnf(e_1_then_e_2,axiom,
next(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_then_e_2) ).
cnf(e_2_greater_e_0,axiom,
greater(e_2,e_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_greater_e_0) ).
cnf(e_1_greater_e_0,axiom,
greater(e_1,e_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_greater_e_0) ).
cnf(product_total_function2,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
cnf(e_1_is_not_e_4,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
cnf(e_2_is_not_e_4,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
cnf(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
cnf(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
cnf(c_0_27,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_4)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
inference(fof_simplification,[status(thm)],[product_total_function1]) ).
cnf(c_0_28,plain,
( ~ group_element(X1)
| cycle(X1,e_3)
| cycle(X1,e_2)
| cycle(X1,e_1)
| cycle(X1,e_0) ),
inference(fof_simplification,[status(thm)],[cycle2]) ).
cnf(c_0_29,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
inference(fof_simplification,[status(thm)],[product_left_cancellation]) ).
cnf(c_0_30,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_4)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
c_0_27 ).
cnf(c_0_31,axiom,
group_element(e_4),
element_4 ).
cnf(c_0_32,plain,
( ~ greater(X2,X1)
| ~ product(X1,e_1,X2)
| ~ cycle(X1,e_0) ),
inference(fof_simplification,[status(thm)],[cycle6]) ).
cnf(c_0_33,plain,
( ~ group_element(X1)
| cycle(X1,e_3)
| cycle(X1,e_2)
| cycle(X1,e_1)
| cycle(X1,e_0) ),
c_0_28 ).
cnf(c_0_34,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_35,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
inference(fof_simplification,[status(thm)],[product_right_cancellation]) ).
cnf(c_0_36,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_29 ).
cnf(c_0_37,axiom,
product(X1,X1,X1),
product_idempotence ).
cnf(c_0_38,plain,
( ~ group_element(X1)
| product(X1,e_4,e_4)
| product(X1,e_4,e_3)
| product(X1,e_4,e_2)
| product(X1,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_39,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_40,plain,
~ equalish(e_3,e_4),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_4]) ).
cnf(c_0_41,plain,
( ~ next(X1,X4)
| ~ greater(X2,e_0)
| ~ product(X1,e_1,X3)
| ~ cycle(X1,X2)
| equalish(X3,X4) ),
inference(fof_simplification,[status(thm)],[cycle7]) ).
cnf(c_0_42,plain,
( ~ greater(X2,X1)
| ~ product(X1,e_1,X2)
| ~ cycle(X1,e_0) ),
c_0_32 ).
cnf(c_0_43,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_33,c_0_34]) ).
cnf(c_0_44,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_35 ).
cnf(c_0_45,plain,
( ~ product(X1,X2,X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_46,plain,
( product(e_3,e_4,e_1)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_47,plain,
~ equalish(e_3,e_4),
c_0_40 ).
cnf(c_0_48,plain,
~ equalish(e_4,e_3),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_3]) ).
cnf(c_0_49,plain,
( ~ group_element(X1)
| product(X1,e_3,e_4)
| product(X1,e_3,e_3)
| product(X1,e_3,e_2)
| product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_30,c_0_39]) ).
cnf(c_0_50,plain,
( ~ next(X1,X4)
| ~ greater(X2,e_0)
| ~ product(X1,e_1,X3)
| ~ cycle(X1,X2)
| equalish(X3,X4) ),
c_0_41 ).
cnf(c_0_51,plain,
( ~ greater(X1,e_1)
| ~ product(e_1,e_1,X1)
| cycle(e_1,e_1)
| cycle(e_1,e_2)
| cycle(e_1,e_3) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_52,axiom,
greater(e_3,e_1),
e_3_greater_e_1 ).
cnf(c_0_53,negated_conjecture,
( ~ product(X2,X1,X4)
| ~ product(X1,X2,X3)
| product(X3,X4,X2) ),
inference(fof_simplification,[status(thm)],[qg4]) ).
cnf(c_0_54,plain,
( ~ product(X2,X1,X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_37]) ).
cnf(c_0_55,plain,
( product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_56,plain,
~ equalish(e_4,e_3),
c_0_48 ).
cnf(c_0_57,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_49,c_0_31]) ).
cnf(c_0_58,plain,
( ~ next(e_1,X1)
| ~ greater(X2,e_0)
| ~ cycle(e_1,X2)
| equalish(e_1,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_37]) ).
cnf(c_0_59,plain,
( ~ product(e_1,e_1,e_3)
| cycle(e_1,e_3)
| cycle(e_1,e_2)
| cycle(e_1,e_1) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_60,axiom,
greater(e_3,e_0),
e_3_greater_e_0 ).
cnf(c_0_61,plain,
~ equalish(e_1,e_2),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_2]) ).
cnf(c_0_62,negated_conjecture,
( ~ product(X2,X1,X4)
| ~ product(X1,X2,X3)
| product(X3,X4,X2) ),
c_0_53 ).
cnf(c_0_63,plain,
( product(e_3,e_4,e_1)
| product(e_3,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]) ).
cnf(c_0_64,plain,
( product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_57]),c_0_47]) ).
cnf(c_0_65,plain,
( ~ next(e_1,X1)
| ~ product(e_1,e_1,e_3)
| cycle(e_1,e_1)
| cycle(e_1,e_2)
| equalish(e_1,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60])]) ).
cnf(c_0_66,axiom,
next(e_1,e_2),
e_1_then_e_2 ).
cnf(c_0_67,plain,
~ equalish(e_1,e_2),
c_0_61 ).
cnf(c_0_68,negated_conjecture,
( ~ product(e_4,e_3,X1)
| product(X1,e_2,e_3)
| product(e_3,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_69,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_64]),c_0_56]) ).
cnf(c_0_70,plain,
( ~ product(e_1,e_1,e_3)
| cycle(e_1,e_2)
| cycle(e_1,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]) ).
cnf(c_0_71,axiom,
greater(e_2,e_0),
e_2_greater_e_0 ).
cnf(c_0_72,negated_conjecture,
( product(e_3,e_4,e_1)
| product(e_2,e_2,e_3)
| product(e_4,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_73,plain,
( ~ next(e_1,X1)
| ~ product(e_1,e_1,e_3)
| cycle(e_1,e_1)
| equalish(e_1,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_70]),c_0_71])]) ).
cnf(c_0_74,negated_conjecture,
( product(e_3,e_4,e_1)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_68,c_0_72]) ).
cnf(c_0_75,plain,
( ~ product(e_1,e_1,e_3)
| cycle(e_1,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_66]),c_0_67]) ).
cnf(c_0_76,axiom,
greater(e_1,e_0),
e_1_greater_e_0 ).
cnf(c_0_77,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
inference(fof_simplification,[status(thm)],[product_total_function2]) ).
cnf(c_0_78,negated_conjecture,
( ~ product(e_4,e_3,X1)
| product(X1,e_1,e_3)
| product(e_2,e_2,e_3)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_62,c_0_74]) ).
cnf(c_0_79,plain,
( ~ next(e_1,X1)
| ~ product(e_1,e_1,e_3)
| equalish(e_1,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_75]),c_0_76])]) ).
cnf(c_0_80,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
c_0_77 ).
cnf(c_0_81,negated_conjecture,
( product(e_1,e_2,e_3)
| product(e_2,e_2,e_3)
| product(e_2,e_1,e_3)
| product(e_4,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_78,c_0_69]) ).
cnf(c_0_82,plain,
~ product(e_1,e_1,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_66]),c_0_67]) ).
cnf(c_0_83,plain,
~ equalish(e_3,e_2),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_2]) ).
cnf(c_0_84,negated_conjecture,
( ~ product(e_3,e_4,X1)
| product(X1,e_2,e_4)
| product(e_4,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_62,c_0_69]) ).
cnf(c_0_85,plain,
( ~ product(X2,X2,X1)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_80,c_0_37]) ).
cnf(c_0_86,negated_conjecture,
( product(e_1,e_2,e_3)
| product(e_2,e_2,e_3)
| product(e_2,e_1,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_81]),c_0_82]) ).
cnf(c_0_87,plain,
~ equalish(e_3,e_2),
c_0_83 ).
cnf(c_0_88,negated_conjecture,
( product(e_4,e_3,e_1)
| product(e_1,e_2,e_4)
| product(e_2,e_2,e_3)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_84,c_0_74]) ).
cnf(c_0_89,plain,
( ~ group_element(X1)
| product(X1,e_1,e_4)
| product(X1,e_1,e_3)
| product(X1,e_1,e_2)
| product(X1,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_30,c_0_34]) ).
cnf(c_0_90,plain,
~ equalish(e_1,e_4),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_4]) ).
cnf(c_0_91,negated_conjecture,
( product(e_2,e_1,e_3)
| product(e_1,e_2,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87]) ).
cnf(c_0_92,negated_conjecture,
( product(e_1,e_2,e_3)
| product(e_2,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_88]),c_0_82]) ).
cnf(c_0_93,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_89,c_0_31]) ).
cnf(c_0_94,plain,
~ equalish(e_1,e_4),
c_0_90 ).
cnf(c_0_95,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_96,negated_conjecture,
( ~ product(e_1,e_2,X1)
| product(X1,e_3,e_2)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_62,c_0_91]) ).
cnf(c_0_97,negated_conjecture,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_92]),c_0_87]) ).
cnf(c_0_98,plain,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_93]),c_0_94]) ).
cnf(c_0_99,plain,
~ equalish(e_2,e_4),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_4]) ).
cnf(c_0_100,plain,
( ~ group_element(X1)
| product(X1,e_2,e_4)
| product(X1,e_2,e_3)
| product(X1,e_2,e_2)
| product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_30,c_0_95]) ).
cnf(c_0_101,negated_conjecture,
( product(e_1,e_2,e_3)
| product(e_4,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_102,plain,
( ~ product(X1,e_1,e_3)
| equalish(X1,e_4)
| product(e_4,e_1,e_1)
| product(e_4,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_36,c_0_98]) ).
cnf(c_0_103,plain,
~ equalish(e_2,e_4),
c_0_99 ).
cnf(c_0_104,plain,
~ equalish(e_1,e_3),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_3]) ).
cnf(c_0_105,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_31]) ).
cnf(c_0_106,negated_conjecture,
( ~ product(e_4,X1,e_2)
| equalish(X1,e_3)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_44,c_0_101]) ).
cnf(c_0_107,negated_conjecture,
( product(e_4,e_1,e_2)
| product(e_4,e_1,e_1)
| product(e_1,e_2,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_91]),c_0_103]) ).
cnf(c_0_108,plain,
~ equalish(e_1,e_3),
c_0_104 ).
cnf(c_0_109,plain,
~ equalish(e_4,e_1),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_1]) ).
cnf(c_0_110,negated_conjecture,
( ~ product(e_3,e_4,X1)
| product(X1,e_1,e_4)
| product(e_2,e_2,e_3)
| product(e_3,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_62,c_0_72]) ).
cnf(c_0_111,plain,
( product(e_4,e_2,e_3)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_105]),c_0_103]) ).
cnf(c_0_112,negated_conjecture,
( product(e_1,e_2,e_3)
| product(e_4,e_1,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108]) ).
cnf(c_0_113,plain,
~ equalish(e_4,e_1),
c_0_109 ).
cnf(c_0_114,negated_conjecture,
( product(e_3,e_4,e_1)
| product(e_2,e_2,e_3)
| product(e_2,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_110,c_0_63]) ).
cnf(c_0_115,plain,
( ~ product(X1,e_2,e_3)
| equalish(X1,e_4)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_36,c_0_111]) ).
cnf(c_0_116,negated_conjecture,
product(e_1,e_2,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_112]),c_0_113]) ).
cnf(c_0_117,plain,
~ equalish(e_4,e_2),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_2]) ).
cnf(c_0_118,negated_conjecture,
( ~ product(e_4,e_3,X1)
| product(X1,e_1,e_3)
| product(e_2,e_1,e_4)
| product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_62,c_0_114]) ).
cnf(c_0_119,negated_conjecture,
( product(e_4,e_3,e_1)
| product(e_1,e_2,e_4)
| product(e_2,e_1,e_4)
| product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_84,c_0_114]) ).
cnf(c_0_120,negated_conjecture,
( product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_94]) ).
cnf(c_0_121,plain,
~ equalish(e_4,e_2),
c_0_117 ).
cnf(c_0_122,negated_conjecture,
( product(e_2,e_2,e_3)
| product(e_2,e_1,e_4)
| product(e_1,e_2,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_82]) ).
cnf(c_0_123,negated_conjecture,
product(e_4,e_2,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_120]),c_0_121]) ).
cnf(c_0_124,negated_conjecture,
( ~ product(e_2,e_1,X1)
| product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_62,c_0_116]) ).
cnf(c_0_125,negated_conjecture,
( product(e_1,e_2,e_4)
| product(e_2,e_1,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_122]),c_0_87]) ).
cnf(c_0_126,negated_conjecture,
( ~ product(e_4,X1,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_44,c_0_123]) ).
cnf(c_0_127,negated_conjecture,
( product(e_4,e_3,e_1)
| product(e_1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_128,negated_conjecture,
( ~ product(e_1,e_2,X1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_80,c_0_116]) ).
cnf(c_0_129,negated_conjecture,
product(e_1,e_2,e_4),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_87]) ).
cnf(c_0_130,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_56]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP126-3.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/5.47 % Computer : n019.cluster.edu
% 0.19/5.47 % Model : x86_64 x86_64
% 0.19/5.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.47 % Memory : 8046.5625MB
% 0.19/5.47 % OS : Linux 6.8.0-71-generic
% 0.19/5.47 % CPULimit : 300
% 0.19/5.47 % WCLimit : 300
% 0.19/5.47 % DateTime : Sun Sep 20 19:59:41 UTC 2026
% 0.19/5.47 % CPUTime :
% 0.19/5.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/5.52 Running first-order theorem proving
% 0.24/5.52 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.24/5.60 % Version: 3.5.1
% 0.24/5.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/5.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/5.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/5.60 % Starting new_bool_3 with 300s (1) cores
% 0.24/5.60 % Starting new_bool_1 with 300s (1) cores
% 0.24/5.60 % Starting sh5l with 300s (1) cores
% 0.24/5.60 % new_bool_1 with pid 795066 completed with status 0
% 0.24/5.60 % Result found by new_bool_1
% 0.24/5.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/5.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/5.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/5.60 % Starting new_bool_3 with 300s (1) cores
% 0.24/5.60 % Starting new_bool_1 with 300s (1) cores
% 0.24/5.60 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/5.60 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/5.60 % Search class: FGHNF-FFMM00-SFFFFFNN
% 0.24/5.60 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/5.60 % Starting SubtermCWHack with 28s (1) cores
% 0.24/5.60 % SubtermCWHack with pid 795074 completed with status 0
% 0.24/5.60 % Result found by SubtermCWHack
% 0.24/5.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/5.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/5.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/5.60 % Starting new_bool_3 with 300s (1) cores
% 0.24/5.60 % Starting new_bool_1 with 300s (1) cores
% 0.24/5.60 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/5.60 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/5.60 % Search class: FGHNF-FFMM00-SFFFFFNN
% 0.24/5.60 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/5.60 % Starting SubtermCWHack with 28s (1) cores
% 0.24/5.60 % Preprocessing time : 0.002 s
% 0.24/5.60
% 0.24/5.60 % Proof found!
% 0.24/5.60 % SZS status Unsatisfiable
% 0.24/5.60 % SZS output start CNFRefutation
% See solution above
% 0.24/5.60 % Parsed axioms : 43
% 0.24/5.60 % Removed by relevancy pruning/SinE : 0
% 0.24/5.60 % Initial clauses : 43
% 0.24/5.60 % Removed in clause preprocessing : 0
% 0.24/5.60 % Initial clauses in saturation : 43
% 0.24/5.60 % Processed clauses : 367
% 0.24/5.60 % ...of these trivial : 0
% 0.24/5.60 % ...subsumed : 72
% 0.24/5.60 % ...remaining for further processing : 295
% 0.24/5.60 % Other redundant clauses eliminated : 0
% 0.24/5.60 % Clauses deleted for lack of memory : 0
% 0.24/5.60 % Backward-subsumed : 99
% 0.24/5.60 % Backward-rewritten : 34
% 0.24/5.60 % Generated clauses : 989
% 0.24/5.60 % ...of the previous two non-redundant : 730
% 0.24/5.60 % ...aggressively subsumed : 0
% 0.24/5.60 % Contextual simplify-reflections : 0
% 0.24/5.60 % Paramodulations : 989
% 0.24/5.60 % Factorizations : 0
% 0.24/5.60 % NegExts : 0
% 0.24/5.60 % Equation resolutions : 0
% 0.24/5.60 % Disequality decompositions : 0
% 0.24/5.60 % Total rewrite steps : 363
% 0.24/5.60 % ...of those cached : 342
% 0.24/5.60 % Propositional unsat checks : 0
% 0.24/5.60 % Propositional check models : 0
% 0.24/5.60 % Propositional check unsatisfiable : 0
% 0.24/5.60 % Propositional clauses : 0
% 0.24/5.60 % Propositional clauses after purity: 0
% 0.24/5.60 % Propositional unsat core size : 0
% 0.24/5.60 % Propositional preprocessing time : 0.000
% 0.24/5.60 % Propositional encoding time : 0.000
% 0.24/5.60 % Propositional solver time : 0.000
% 0.24/5.60 % Success case prop preproc time : 0.000
% 0.24/5.60 % Success case prop encoding time : 0.000
% 0.24/5.60 % Success case prop solver time : 0.000
% 0.24/5.60 % Current number of processed clauses : 162
% 0.24/5.60 % Positive orientable unit clauses : 24
% 0.24/5.60 % Positive unorientable unit clauses: 0
% 0.24/5.60 % Negative unit clauses : 16
% 0.24/5.60 % Non-unit-clauses : 122
% 0.24/5.60 % Current number of unprocessed clauses: 255
% 0.24/5.60 % ...number of literals in the above : 1217
% 0.24/5.60 % Current number of archived formulas : 0
% 0.24/5.60 % Current number of archived clauses : 133
% 0.24/5.60 % Clause-clause subsumption calls (NU) : 7597
% 0.24/5.60 % Rec. Clause-clause subsumption calls : 3024
% 0.24/5.60 % Non-unit clause-clause subsumptions : 150
% 0.24/5.60 % Unit Clause-clause subsumption calls : 333
% 0.24/5.60 % Rewrite failures with RHS unbound : 0
% 0.24/5.60 % BW rewrite match attempts : 24
% 0.24/5.60 % BW rewrite match successes : 4
% 0.24/5.60 % Condensation attempts : 0
% 0.24/5.60 % Condensation successes : 0
% 0.24/5.60 % Termbank termtop insertions : 17505
% 0.24/5.60 % Search garbage collected termcells : 98
% 0.24/5.60
% 0.24/5.60 % -------------------------------------------------
% 0.24/5.60 % User time : 0.061 s
% 0.24/5.60 % System time : 0.003 s
% 0.24/5.60 % Total time : 0.064 s
% 0.24/5.60 % Maximum resident set size: 3604 pages
% 0.24/5.60
% 0.24/5.60 % -------------------------------------------------
% 0.24/5.60 % User time : 0.062 s
% 0.24/5.60 % System time : 0.007 s
% 0.24/5.60 % Total time : 0.069 s
% 0.24/5.60 % Maximum resident set size: 4864 pages
% 0.24/5.60 % E exiting
%------------------------------------------------------------------------------