%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP124-3.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:41:54 PM UTC 2026
% Result : Unsatisfiable 0.22s 0.60s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 21
% Syntax : Number of clauses : 121 ( 54 unt; 30 nHn; 119 RR)
% Number of literals : 263 ( 0 equ; 148 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 112 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(e_1_is_not_e_4,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
cnf(product_right_cancellation,axiom,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(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/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
cnf(qg2_2,negated_conjecture,
( ~ product(X6,X4,X5)
| ~ product(X6,X1,X2)
| ~ product(X4,X5,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2_2) ).
cnf(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
cnf(product_left_cancellation,axiom,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(element_4,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
cnf(product_idempotence,axiom,
product(X1,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
cnf(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
cnf(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
cnf(e_3_is_not_e_4,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
cnf(qg2_1,negated_conjecture,
( ~ product(X6,X4,X5)
| ~ product(X6,X1,X2)
| ~ product(X4,X5,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2_1) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
cnf(e_2_is_not_e_4,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
cnf(c_0_21,plain,
~ equalish(e_1,e_4),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_4]) ).
cnf(c_0_22,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
inference(fof_simplification,[status(thm)],[product_right_cancellation]) ).
cnf(c_0_23,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_4)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
inference(fof_simplification,[status(thm)],[product_total_function1]) ).
cnf(c_0_24,plain,
~ equalish(e_1,e_4),
c_0_21 ).
cnf(c_0_25,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_22 ).
cnf(c_0_26,plain,
~ equalish(e_3,e_1),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_1]) ).
cnf(c_0_27,negated_conjecture,
( ~ product(X6,X4,X5)
| ~ product(X6,X1,X2)
| ~ product(X4,X5,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X5) ),
inference(fof_simplification,[status(thm)],[qg2_2]) ).
cnf(c_0_28,plain,
~ equalish(e_4,e_1),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_1]) ).
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_23 ).
cnf(c_0_31,axiom,
group_element(e_4),
element_4 ).
cnf(c_0_32,plain,
( ~ product(X1,e_1,X2)
| ~ product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_33,axiom,
product(X1,X1,X1),
product_idempotence ).
cnf(c_0_34,plain,
~ equalish(e_4,e_3),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_3]) ).
cnf(c_0_35,plain,
~ equalish(e_3,e_1),
c_0_26 ).
cnf(c_0_36,negated_conjecture,
( ~ product(X6,X4,X5)
| ~ product(X6,X1,X2)
| ~ product(X4,X5,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X5) ),
c_0_27 ).
cnf(c_0_37,plain,
~ equalish(e_4,e_1),
c_0_28 ).
cnf(c_0_38,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_29 ).
cnf(c_0_39,plain,
( ~ group_element(X1)
| product(X1,e_4,e_1)
| product(X1,e_4,e_2)
| product(X1,e_4,e_3)
| product(X1,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_40,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_41,plain,
~ product(e_1,e_4,e_1),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_42,plain,
~ equalish(e_4,e_3),
c_0_34 ).
cnf(c_0_43,plain,
~ equalish(e_4,e_2),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_2]) ).
cnf(c_0_44,negated_conjecture,
( ~ product(X3,e_3,X4)
| ~ product(X2,e_1,X4)
| ~ product(X1,X3,e_3)
| ~ product(X1,X2,e_1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_45,plain,
( ~ product(e_4,X1,X2)
| ~ product(e_1,X1,X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_46,plain,
( product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_47,plain,
~ equalish(e_3,e_4),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_4]) ).
cnf(c_0_48,plain,
~ equalish(e_3,e_2),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_2]) ).
cnf(c_0_49,plain,
( ~ product(e_4,X1,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_38]) ).
cnf(c_0_50,plain,
~ equalish(e_4,e_2),
c_0_43 ).
cnf(c_0_51,negated_conjecture,
( ~ product(X1,e_3,X2)
| ~ product(e_1,e_1,X2)
| ~ product(e_1,X1,e_3) ),
inference(spm,[status(thm)],[c_0_44,c_0_33]) ).
cnf(c_0_52,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_33])]) ).
cnf(c_0_53,plain,
~ equalish(e_3,e_4),
c_0_47 ).
cnf(c_0_54,plain,
~ equalish(e_3,e_2),
c_0_48 ).
cnf(c_0_55,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_56,plain,
~ product(e_3,e_4,e_4),
inference(spm,[status(thm)],[c_0_49,c_0_33]) ).
cnf(c_0_57,plain,
( ~ product(e_4,X1,X2)
| ~ product(e_2,X1,X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_38]) ).
cnf(c_0_58,plain,
~ equalish(e_2,e_1),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_1]) ).
cnf(c_0_59,negated_conjecture,
( ~ product(e_4,e_3,X1)
| ~ product(e_1,e_1,X1)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_60,plain,
( ~ product(X1,e_3,X2)
| ~ product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_53,c_0_25]) ).
cnf(c_0_61,plain,
( ~ product(e_3,X1,X2)
| ~ product(e_2,X1,X2) ),
inference(spm,[status(thm)],[c_0_54,c_0_38]) ).
cnf(c_0_62,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_39,c_0_55]),c_0_56]) ).
cnf(c_0_63,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_64,plain,
~ product(e_2,e_4,e_4),
inference(spm,[status(thm)],[c_0_57,c_0_33]) ).
cnf(c_0_65,plain,
~ equalish(e_2,e_1),
c_0_58 ).
cnf(c_0_66,plain,
( ~ product(e_3,X1,X2)
| ~ product(e_1,X1,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_38]) ).
cnf(c_0_67,negated_conjecture,
( ~ product(e_4,e_3,e_1)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_59,c_0_33]) ).
cnf(c_0_68,plain,
( ~ group_element(X1)
| product(X1,e_3,e_1)
| product(X1,e_3,e_2)
| product(X1,e_3,e_3)
| product(X1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_30,c_0_55]) ).
cnf(c_0_69,plain,
~ product(e_4,e_3,e_4),
inference(spm,[status(thm)],[c_0_60,c_0_33]) ).
cnf(c_0_70,plain,
( ~ product(e_2,e_4,e_1)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_71,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_63]),c_0_64]) ).
cnf(c_0_72,plain,
( ~ product(e_2,X1,X2)
| ~ product(e_1,X1,X2) ),
inference(spm,[status(thm)],[c_0_65,c_0_38]) ).
cnf(c_0_73,negated_conjecture,
( ~ product(X6,X4,X5)
| ~ product(X6,X1,X2)
| ~ product(X4,X5,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
inference(fof_simplification,[status(thm)],[qg2_1]) ).
cnf(c_0_74,negated_conjecture,
( ~ product(e_4,e_3,e_1)
| ~ product(e_3,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_75,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_68,c_0_31]),c_0_69]) ).
cnf(c_0_76,plain,
( product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_77,negated_conjecture,
( ~ product(e_4,e_3,e_1)
| ~ product(e_2,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_72,c_0_67]) ).
cnf(c_0_78,negated_conjecture,
( ~ product(X6,X4,X5)
| ~ product(X6,X1,X2)
| ~ product(X4,X5,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_73 ).
cnf(c_0_79,negated_conjecture,
( ~ product(e_3,e_4,e_2)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_80,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| product(e_3,e_4,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_76]),c_0_33])]) ).
cnf(c_0_81,negated_conjecture,
( ~ product(e_2,e_4,e_2)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_77,c_0_75]) ).
cnf(c_0_82,negated_conjecture,
( ~ product(e_3,X3,X4)
| ~ product(e_2,X2,X4)
| ~ product(X1,e_3,X3)
| ~ product(X1,e_2,X2) ),
inference(spm,[status(thm)],[c_0_54,c_0_78]) ).
cnf(c_0_83,negated_conjecture,
( product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_2,e_4,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]) ).
cnf(c_0_84,plain,
~ equalish(e_1,e_3),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_3]) ).
cnf(c_0_85,plain,
~ product(e_2,e_3,e_3),
inference(spm,[status(thm)],[c_0_61,c_0_33]) ).
cnf(c_0_86,negated_conjecture,
( ~ product(e_3,X1,X2)
| ~ product(e_2,e_2,X2)
| ~ product(e_2,e_3,X1) ),
inference(spm,[status(thm)],[c_0_82,c_0_33]) ).
cnf(c_0_87,negated_conjecture,
( product(e_2,e_4,e_3)
| product(e_4,e_3,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_83]),c_0_33])]) ).
cnf(c_0_88,plain,
~ equalish(e_1,e_3),
c_0_84 ).
cnf(c_0_89,negated_conjecture,
( ~ product(X3,e_3,X4)
| ~ product(X2,e_2,X4)
| ~ product(X1,X3,e_3)
| ~ product(X1,X2,e_2) ),
inference(spm,[status(thm)],[c_0_54,c_0_36]) ).
cnf(c_0_90,plain,
( ~ product(e_2,e_3,e_1)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_60,c_0_71]) ).
cnf(c_0_91,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_63]),c_0_85]) ).
cnf(c_0_92,negated_conjecture,
( ~ product(e_2,e_3,e_4)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_80]),c_0_33])]) ).
cnf(c_0_93,negated_conjecture,
( ~ product(e_2,e_3,e_2)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_57,c_0_87]) ).
cnf(c_0_94,plain,
( ~ product(e_2,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_57,c_0_75]) ).
cnf(c_0_95,plain,
( ~ product(X1,e_1,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_88,c_0_25]) ).
cnf(c_0_96,plain,
~ equalish(e_2,e_4),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_4]) ).
cnf(c_0_97,negated_conjecture,
( ~ product(X1,e_3,X2)
| ~ product(e_2,e_2,X2)
| ~ product(e_2,X1,e_3) ),
inference(spm,[status(thm)],[c_0_89,c_0_33]) ).
cnf(c_0_98,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_4,e_2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]),c_0_93]) ).
cnf(c_0_99,plain,
( 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_4) ),
inference(spm,[status(thm)],[c_0_94,c_0_91]) ).
cnf(c_0_100,plain,
~ product(e_1,e_3,e_1),
inference(spm,[status(thm)],[c_0_95,c_0_33]) ).
cnf(c_0_101,plain,
~ equalish(e_2,e_4),
c_0_96 ).
cnf(c_0_102,negated_conjecture,
( ~ product(e_4,e_3,X1)
| ~ product(e_2,e_2,X1)
| product(e_2,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_103,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_2)
| product(e_4,e_3,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_99]),c_0_33])]) ).
cnf(c_0_104,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_40]),c_0_100]) ).
cnf(c_0_105,plain,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_101,c_0_25]) ).
cnf(c_0_106,negated_conjecture,
( product(e_2,e_4,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_33])]) ).
cnf(c_0_107,plain,
( ~ product(e_2,e_3,e_4)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_72,c_0_104]) ).
cnf(c_0_108,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_33])]) ).
cnf(c_0_109,negated_conjecture,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_110,negated_conjecture,
( product(e_2,e_3,e_2)
| product(e_1,e_3,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_109]),c_0_33])]) ).
cnf(c_0_111,plain,
( ~ product(e_2,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_72,c_0_52]) ).
cnf(c_0_112,negated_conjecture,
~ product(e_4,e_3,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_110]),c_0_57]) ).
cnf(c_0_113,plain,
~ equalish(e_2,e_3),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_3]) ).
cnf(c_0_114,plain,
( ~ product(e_2,e_4,e_3)
| ~ product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_60,c_0_111]) ).
cnf(c_0_115,negated_conjecture,
product(e_2,e_4,e_3),
inference(sr,[status(thm)],[c_0_87,c_0_112]) ).
cnf(c_0_116,plain,
~ equalish(e_2,e_3),
c_0_113 ).
cnf(c_0_117,plain,
~ product(e_1,e_3,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_115])]) ).
cnf(c_0_118,plain,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_116,c_0_25]) ).
cnf(c_0_119,negated_conjecture,
product(e_2,e_3,e_2),
inference(sr,[status(thm)],[c_0_110,c_0_117]) ).
cnf(c_0_120,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP124-3.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.43 % Computer : n008.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sun Sep 20 20:00:09 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.48 Running first-order theorem proving
% 0.16/0.48 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.60 % Version: 3.5.1
% 0.22/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.22/0.60 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.60 % Starting sh5l with 300s (1) cores
% 0.22/0.60 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3482894 completed with status 0
% 0.22/0.60 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.22/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.60 % No SInE strategy applied
% 0.22/0.60 % Search class: FGHNF-FFMM00-SFFFFFNN
% 0.22/0.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.60 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.22/0.60 % Starting H----_011_C07_F1_PI_AE_OS_R8_SP_S1U with 136s (1) cores
% 0.22/0.60 % Starting G----_425_C05_02_F1_SE_CS_SP_PS_RG_S04AI with 136s (1) cores
% 0.22/0.60 % Starting G-E--_208_B07--C_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.22/0.60 % G----_425_C05_02_F1_SE_CS_SP_PS_RG_S04AI with pid 3482901 completed with status 0
% 0.22/0.60 % Result found by G----_425_C05_02_F1_SE_CS_SP_PS_RG_S04AI
% 0.22/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.60 % No SInE strategy applied
% 0.22/0.60 % Search class: FGHNF-FFMM00-SFFFFFNN
% 0.22/0.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.60 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.22/0.60 % Starting H----_011_C07_F1_PI_AE_OS_R8_SP_S1U with 136s (1) cores
% 0.22/0.60 % Starting G----_425_C05_02_F1_SE_CS_SP_PS_RG_S04AI with 136s (1) cores
% 0.22/0.60 % Preprocessing time : 0.002 s
% 0.22/0.60 % Presaturation interreduction done
% 0.22/0.60
% 0.22/0.60 % Proof found!
% 0.22/0.60 % SZS status Unsatisfiable
% 0.22/0.60 % SZS output start CNFRefutation
% See solution above
% 0.22/0.61 % Parsed axioms : 44
% 0.22/0.61 % Removed by relevancy pruning/SinE : 0
% 0.22/0.61 % Initial clauses : 44
% 0.22/0.61 % Removed in clause preprocessing : 0
% 0.22/0.61 % Initial clauses in saturation : 44
% 0.22/0.61 % Processed clauses : 547
% 0.22/0.61 % ...of these trivial : 0
% 0.22/0.61 % ...subsumed : 135
% 0.22/0.61 % ...remaining for further processing : 412
% 0.22/0.61 % Other redundant clauses eliminated : 0
% 0.22/0.61 % Clauses deleted for lack of memory : 0
% 0.22/0.61 % Backward-subsumed : 70
% 0.22/0.61 % Backward-rewritten : 25
% 0.22/0.61 % Generated clauses : 646
% 0.22/0.61 % ...of the previous two non-redundant : 615
% 0.22/0.61 % ...aggressively subsumed : 0
% 0.22/0.61 % Contextual simplify-reflections : 24
% 0.22/0.61 % Paramodulations : 641
% 0.22/0.61 % Factorizations : 0
% 0.22/0.61 % NegExts : 0
% 0.22/0.61 % Equation resolutions : 0
% 0.22/0.61 % Disequality decompositions : 0
% 0.22/0.61 % Total rewrite steps : 130
% 0.22/0.61 % ...of those cached : 115
% 0.22/0.61 % Propositional unsat checks : 0
% 0.22/0.61 % Propositional check models : 0
% 0.22/0.61 % Propositional check unsatisfiable : 0
% 0.22/0.61 % Propositional clauses : 0
% 0.22/0.61 % Propositional clauses after purity: 0
% 0.22/0.61 % Propositional unsat core size : 0
% 0.22/0.61 % Propositional preprocessing time : 0.000
% 0.22/0.61 % Propositional encoding time : 0.000
% 0.22/0.61 % Propositional solver time : 0.000
% 0.22/0.61 % Success case prop preproc time : 0.000
% 0.22/0.61 % Success case prop encoding time : 0.000
% 0.22/0.61 % Success case prop solver time : 0.000
% 0.22/0.61 % Current number of processed clauses : 268
% 0.22/0.61 % Positive orientable unit clauses : 23
% 0.22/0.61 % Positive unorientable unit clauses: 0
% 0.22/0.61 % Negative unit clauses : 38
% 0.22/0.61 % Non-unit-clauses : 207
% 0.22/0.61 % Current number of unprocessed clauses: 107
% 0.22/0.61 % ...number of literals in the above : 460
% 0.22/0.61 % Current number of archived formulas : 0
% 0.22/0.61 % Current number of archived clauses : 144
% 0.22/0.61 % Clause-clause subsumption calls (NU) : 33887
% 0.22/0.61 % Rec. Clause-clause subsumption calls : 9001
% 0.22/0.61 % Non-unit clause-clause subsumptions : 143
% 0.22/0.61 % Unit Clause-clause subsumption calls : 2083
% 0.22/0.61 % Rewrite failures with RHS unbound : 0
% 0.22/0.61 % BW rewrite match attempts : 15
% 0.22/0.61 % BW rewrite match successes : 3
% 0.22/0.61 % Condensation attempts : 0
% 0.22/0.61 % Condensation successes : 0
% 0.22/0.61 % Termbank termtop insertions : 11135
% 0.22/0.61 % Search garbage collected termcells : 107
% 0.22/0.61
% 0.22/0.61 % -------------------------------------------------
% 0.22/0.61 % User time : 0.068 s
% 0.22/0.61 % System time : 0.005 s
% 0.22/0.61 % Total time : 0.074 s
% 0.22/0.61 % Maximum resident set size: 3404 pages
% 0.22/0.61
% 0.22/0.61 % -------------------------------------------------
% 0.22/0.61 % User time : 0.218 s
% 0.22/0.61 % System time : 0.023 s
% 0.22/0.61 % Total time : 0.241 s
% 0.22/0.61 % Maximum resident set size: 4608 pages
% 0.22/0.61 % E exiting
%------------------------------------------------------------------------------