%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP129-1.003 : 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 : n007.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 12:42:31 PM UTC 2026
% Result : Unsatisfiable 0.32s 0.47s
% Output : CNFRefutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 14
% Syntax : Number of clauses : 152 ( 41 unt; 61 nHn; 152 RR)
% Number of literals : 363 ( 0 equ; 162 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 93 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_total_function1,axiom,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
cnf(product_right_cancellation,axiom,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
cnf(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(qg3,negated_conjecture,
( ~ product(X2,X3,X4)
| ~ product(X1,X2,X3)
| product(X3,X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
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(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
cnf(e_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_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
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(c_0_14,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
inference(fof_simplification,[status(thm)],[product_total_function1]) ).
cnf(c_0_15,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
c_0_14 ).
cnf(c_0_16,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_17,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
inference(fof_simplification,[status(thm)],[product_right_cancellation]) ).
cnf(c_0_18,plain,
( ~ group_element(X1)
| product(X1,e_3,e_3)
| product(X1,e_3,e_2)
| product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_20,plain,
~ equalish(e_2,e_3),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_3]) ).
cnf(c_0_21,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_17 ).
cnf(c_0_22,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
inference(fof_simplification,[status(thm)],[product_left_cancellation]) ).
cnf(c_0_24,plain,
( ~ group_element(X1)
| product(X1,e_2,e_3)
| product(X1,e_2,e_2)
| product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_15,c_0_19]) ).
cnf(c_0_25,plain,
~ equalish(e_2,e_3),
c_0_20 ).
cnf(c_0_26,plain,
( ~ product(e_2,X1,e_1)
| equalish(X1,e_3)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_23 ).
cnf(c_0_28,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_29,negated_conjecture,
( ~ product(X2,X3,X4)
| ~ product(X1,X2,X3)
| product(X3,X1,X4) ),
inference(fof_simplification,[status(thm)],[qg3]) ).
cnf(c_0_30,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_31,plain,
~ equalish(e_3,e_2),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_2]) ).
cnf(c_0_32,plain,
( ~ product(e_2,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,plain,
( ~ product(X1,e_2,e_1)
| equalish(X1,e_3)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,negated_conjecture,
( ~ product(X2,X3,X4)
| ~ product(X1,X2,X3)
| product(X3,X1,X4) ),
c_0_29 ).
cnf(c_0_35,plain,
( ~ product(e_3,X1,e_1)
| equalish(X1,e_3)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_21,c_0_30]) ).
cnf(c_0_36,plain,
~ equalish(e_3,e_2),
c_0_31 ).
cnf(c_0_37,plain,
( ~ product(X1,e_3,e_3)
| ~ product(e_2,e_2,e_1)
| equalish(X1,e_2)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_27,c_0_32]) ).
cnf(c_0_38,plain,
( ~ product(e_2,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_33]) ).
cnf(c_0_39,negated_conjecture,
( ~ product(X1,e_3,e_3)
| product(e_3,X1,e_1)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_34,c_0_30]) ).
cnf(c_0_40,plain,
( ~ product(e_3,e_2,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_35]) ).
cnf(c_0_41,plain,
( ~ product(e_3,e_3,e_3)
| ~ product(e_2,e_2,e_1)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,negated_conjecture,
( ~ product(X1,e_3,e_2)
| ~ product(e_2,e_2,e_1)
| product(e_3,e_2,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_38]),c_0_34]) ).
cnf(c_0_43,negated_conjecture,
( ~ product(e_2,e_2,e_1)
| product(e_3,e_3,e_2)
| product(e_2,e_3,e_2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_32]),c_0_40]),c_0_41]) ).
cnf(c_0_44,negated_conjecture,
( ~ product(e_2,e_2,e_1)
| product(e_3,e_2,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_42]) ).
cnf(c_0_45,negated_conjecture,
( ~ product(e_3,X1,e_2)
| ~ product(e_2,e_2,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_21,c_0_44]) ).
cnf(c_0_46,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_47,negated_conjecture,
( ~ product(e_3,e_3,e_2)
| ~ product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_36,c_0_45]) ).
cnf(c_0_48,plain,
~ equalish(e_2,e_1),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_1]) ).
cnf(c_0_49,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_24,c_0_46]) ).
cnf(c_0_50,plain,
~ equalish(e_1,e_3),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_3]) ).
cnf(c_0_51,plain,
~ equalish(e_1,e_2),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_2]) ).
cnf(c_0_52,negated_conjecture,
( ~ product(e_2,e_2,e_1)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_47,c_0_43]) ).
cnf(c_0_53,plain,
~ equalish(e_2,e_1),
c_0_48 ).
cnf(c_0_54,plain,
( ~ product(X1,e_2,e_1)
| equalish(X1,e_1)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_27,c_0_49]) ).
cnf(c_0_55,plain,
~ equalish(e_1,e_3),
c_0_50 ).
cnf(c_0_56,negated_conjecture,
( ~ product(X1,e_2,e_2)
| ~ product(e_2,e_2,e_1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_27,c_0_44]) ).
cnf(c_0_57,plain,
~ equalish(e_1,e_2),
c_0_51 ).
cnf(c_0_58,negated_conjecture,
( ~ product(X1,e_2,e_3)
| ~ product(e_2,e_2,e_1)
| product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_34,c_0_52]) ).
cnf(c_0_59,plain,
( ~ product(e_2,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_60,negated_conjecture,
( ~ product(e_1,e_2,e_2)
| ~ product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_61,negated_conjecture,
( ~ product(e_3,e_1,e_2)
| ~ product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_57,c_0_45]) ).
cnf(c_0_62,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_24,c_0_19]) ).
cnf(c_0_63,negated_conjecture,
~ product(e_2,e_2,e_1),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]),c_0_61]) ).
cnf(c_0_64,plain,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2) ),
inference(sr,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_65,plain,
~ equalish(e_3,e_1),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_1]) ).
cnf(c_0_66,plain,
( ~ product(X1,e_2,e_3)
| equalish(X1,e_2)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_27,c_0_64]) ).
cnf(c_0_67,plain,
~ equalish(e_3,e_1),
c_0_65 ).
cnf(c_0_68,plain,
( ~ product(e_1,e_2,e_3)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_57,c_0_66]) ).
cnf(c_0_69,plain,
( ~ product(e_3,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_67,c_0_54]) ).
cnf(c_0_70,plain,
( ~ product(e_2,X1,e_3)
| equalish(X1,e_2)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_21,c_0_64]) ).
cnf(c_0_71,negated_conjecture,
( ~ product(X1,e_2,e_2)
| product(e_2,X1,e_3)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_34,c_0_64]) ).
cnf(c_0_72,plain,
( ~ product(e_3,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_73,plain,
( ~ product(e_2,e_1,e_3)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_57,c_0_70]) ).
cnf(c_0_74,negated_conjecture,
( ~ product(e_3,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_75,plain,
( ~ product(e_3,e_2,e_3)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_36,c_0_66]) ).
cnf(c_0_76,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_3,e_2,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_28]),c_0_75]) ).
cnf(c_0_77,plain,
( ~ product(e_2,e_3,e_3)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_36,c_0_70]) ).
cnf(c_0_78,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_18,c_0_46]) ).
cnf(c_0_79,negated_conjecture,
product(e_2,e_2,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_76]),c_0_77]) ).
cnf(c_0_80,plain,
( ~ product(X1,e_3,e_3)
| ~ product(e_3,e_2,e_1)
| equalish(X1,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_27,c_0_40]) ).
cnf(c_0_81,plain,
( ~ product(X1,e_3,e_1)
| equalish(X1,e_1)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_27,c_0_78]) ).
cnf(c_0_82,negated_conjecture,
( ~ product(e_2,X1,e_2)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_21,c_0_79]) ).
cnf(c_0_83,plain,
( ~ product(e_2,e_3,e_3)
| ~ product(e_3,e_2,e_1)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_80]) ).
cnf(c_0_84,plain,
( ~ product(e_3,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_67,c_0_81]) ).
cnf(c_0_85,negated_conjecture,
~ product(e_2,e_3,e_2),
inference(spm,[status(thm)],[c_0_36,c_0_82]) ).
cnf(c_0_86,plain,
( ~ product(X1,e_3,e_2)
| ~ product(e_2,e_3,e_3)
| ~ product(e_3,e_2,e_1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_27,c_0_83]) ).
cnf(c_0_87,plain,
( ~ product(X1,e_3,e_3)
| ~ product(e_3,e_3,e_1)
| equalish(X1,e_1)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_27,c_0_84]) ).
cnf(c_0_88,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_1) ),
inference(sr,[status(thm)],[c_0_22,c_0_85]) ).
cnf(c_0_89,plain,
( ~ product(e_1,e_3,e_2)
| ~ product(e_2,e_3,e_3)
| ~ product(e_3,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_55,c_0_86]) ).
cnf(c_0_90,plain,
( ~ product(e_2,e_3,e_3)
| ~ product(e_3,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_53,c_0_87]) ).
cnf(c_0_91,plain,
( ~ product(X1,e_3,e_1)
| equalish(X1,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_27,c_0_88]) ).
cnf(c_0_92,plain,
( ~ product(e_3,e_3,e_1)
| ~ product(e_2,e_3,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_34]) ).
cnf(c_0_93,plain,
~ product(e_3,e_3,e_1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_91]),c_0_92]) ).
cnf(c_0_94,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(sr,[status(thm)],[c_0_30,c_0_93]) ).
cnf(c_0_95,plain,
( ~ product(X1,e_3,e_3)
| equalish(X1,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_27,c_0_94]) ).
cnf(c_0_96,plain,
( ~ product(e_1,X1,e_1)
| equalish(X1,e_3)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_21,c_0_78]) ).
cnf(c_0_97,plain,
( ~ product(e_2,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_95]) ).
cnf(c_0_98,plain,
( ~ product(e_1,e_2,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_96]) ).
cnf(c_0_99,plain,
( ~ group_element(X1)
| product(X1,e_1,e_3)
| product(X1,e_1,e_2)
| product(X1,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_15,c_0_46]) ).
cnf(c_0_100,plain,
( ~ product(X1,e_3,e_2)
| ~ product(e_2,e_3,e_3)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_27,c_0_97]) ).
cnf(c_0_101,plain,
( ~ product(X1,e_3,e_3)
| ~ product(e_1,e_2,e_1)
| equalish(X1,e_1)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_27,c_0_98]) ).
cnf(c_0_102,negated_conjecture,
( ~ product(X1,e_2,e_2)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_27,c_0_79]) ).
cnf(c_0_103,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_99,c_0_19]) ).
cnf(c_0_104,negated_conjecture,
~ product(e_2,e_1,e_2),
inference(spm,[status(thm)],[c_0_57,c_0_82]) ).
cnf(c_0_105,plain,
( ~ product(e_1,e_3,e_2)
| ~ product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_55,c_0_100]) ).
cnf(c_0_106,plain,
( ~ product(e_2,e_3,e_3)
| ~ product(e_1,e_2,e_1)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_53,c_0_101]) ).
cnf(c_0_107,negated_conjecture,
~ product(e_1,e_2,e_2),
inference(spm,[status(thm)],[c_0_57,c_0_102]) ).
cnf(c_0_108,plain,
( ~ product(e_2,e_1,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_55,c_0_26]) ).
cnf(c_0_109,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_1) ),
inference(sr,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_110,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_111,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_1) ),
inference(sr,[status(thm)],[c_0_49,c_0_107]) ).
cnf(c_0_112,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_1,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_85]) ).
cnf(c_0_113,plain,
( ~ product(e_1,X1,e_1)
| equalish(X1,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_21,c_0_49]) ).
cnf(c_0_114,plain,
( ~ product(e_2,e_3,e_3)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_115,plain,
( ~ product(X1,e_1,e_3)
| equalish(X1,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_27,c_0_112]) ).
cnf(c_0_116,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
inference(fof_simplification,[status(thm)],[product_total_function2]) ).
cnf(c_0_117,plain,
( ~ product(e_1,e_1,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_57,c_0_113]) ).
cnf(c_0_118,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_99,c_0_46]) ).
cnf(c_0_119,plain,
( ~ product(e_1,X1,e_3)
| ~ product(e_2,e_3,e_3)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_21,c_0_114]) ).
cnf(c_0_120,plain,
( ~ product(e_1,e_1,e_3)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_57,c_0_115]) ).
cnf(c_0_121,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
c_0_116 ).
cnf(c_0_122,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_107]) ).
cnf(c_0_123,plain,
~ product(e_1,e_1,e_3),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_119]),c_0_120]) ).
cnf(c_0_124,plain,
( ~ product(e_1,e_2,X1)
| ~ product(e_3,e_2,e_1)
| equalish(X1,e_3)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_121,c_0_69]) ).
cnf(c_0_125,negated_conjecture,
( ~ product(X1,e_1,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_49]),c_0_34]) ).
cnf(c_0_126,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_2,e_3) ),
inference(sr,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_127,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_3,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_55,c_0_124]) ).
cnf(c_0_128,negated_conjecture,
product(e_1,e_2,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_107]) ).
cnf(c_0_129,plain,
( ~ product(X1,e_1,e_1)
| equalish(X1,e_2)
| product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_27,c_0_109]) ).
cnf(c_0_130,plain,
( ~ product(e_3,e_2,e_1)
| product(e_1,e_2,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_111]),c_0_107]) ).
cnf(c_0_131,negated_conjecture,
~ product(e_3,e_2,e_2),
inference(spm,[status(thm)],[c_0_36,c_0_102]) ).
cnf(c_0_132,negated_conjecture,
( ~ product(X1,e_2,e_3)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_27,c_0_128]) ).
cnf(c_0_133,plain,
( ~ product(e_1,e_1,e_1)
| product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_57,c_0_129]) ).
cnf(c_0_134,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(sr,[status(thm)],[c_0_118,c_0_123]) ).
cnf(c_0_135,plain,
( ~ product(e_1,X1,e_3)
| ~ product(e_3,e_2,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_21,c_0_130]) ).
cnf(c_0_136,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_1) ),
inference(sr,[status(thm)],[c_0_28,c_0_131]) ).
cnf(c_0_137,negated_conjecture,
~ product(e_3,e_2,e_3),
inference(spm,[status(thm)],[c_0_67,c_0_132]) ).
cnf(c_0_138,negated_conjecture,
( ~ product(X1,e_1,e_2)
| product(e_2,X1,e_3) ),
inference(spm,[status(thm)],[c_0_34,c_0_128]) ).
cnf(c_0_139,plain,
( product(e_2,e_1,e_3)
| product(e_1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_140,plain,
( ~ product(e_1,e_3,e_3)
| ~ product(e_3,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_36,c_0_135]) ).
cnf(c_0_141,plain,
product(e_3,e_2,e_1),
inference(sr,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_142,negated_conjecture,
( ~ product(X1,e_1,e_3)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_78]),c_0_34]) ).
cnf(c_0_143,negated_conjecture,
product(e_2,e_1,e_3),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_144,plain,
~ product(e_1,e_3,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_140,c_0_141])]) ).
cnf(c_0_145,plain,
( ~ product(e_2,X1,e_1)
| equalish(X1,e_3)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_21,c_0_88]) ).
cnf(c_0_146,negated_conjecture,
( ~ product(X1,e_3,e_2)
| product(e_2,X1,e_1)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_34,c_0_28]) ).
cnf(c_0_147,negated_conjecture,
product(e_1,e_3,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_144]) ).
cnf(c_0_148,plain,
( ~ product(e_2,e_1,e_1)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_55,c_0_145]) ).
cnf(c_0_149,negated_conjecture,
product(e_2,e_1,e_1),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_131]),c_0_137]) ).
cnf(c_0_150,plain,
~ product(e_2,e_3,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_147])]) ).
cnf(c_0_151,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_148,c_0_149])]),c_0_150]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP129-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 19:58:21 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.32/0.47 % Version: 3.5.1
% 0.32/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.32/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.32/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.32/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.32/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.32/0.47 % Starting sh5l with 300s (1) cores
% 0.32/0.47 % new_bool_3 with pid 3451258 completed with status 0
% 0.32/0.47 % Result found by new_bool_3
% 0.32/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.32/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.32/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.32/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.32/0.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.32/0.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.32/0.47 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.32/0.47 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.32/0.47 % Starting SubtermCWHack with 31s (1) cores
% 0.32/0.47 % SubtermCWHack with pid 3451263 completed with status 0
% 0.32/0.47 % Result found by SubtermCWHack
% 0.32/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.32/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.32/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.32/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.32/0.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.32/0.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.32/0.47 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.32/0.47 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.32/0.47 % Starting SubtermCWHack with 31s (1) cores
% 0.32/0.47 % Preprocessing time : 0.001 s
% 0.32/0.47
% 0.32/0.47 % Proof found!
% 0.32/0.47 % SZS status Unsatisfiable
% 0.32/0.47 % SZS output start CNFRefutation
% See solution above
% 0.32/0.47 % Parsed axioms : 14
% 0.32/0.47 % Removed by relevancy pruning/SinE : 0
% 0.32/0.47 % Initial clauses : 14
% 0.32/0.47 % Removed in clause preprocessing : 0
% 0.32/0.47 % Initial clauses in saturation : 14
% 0.32/0.47 % Processed clauses : 603
% 0.32/0.47 % ...of these trivial : 0
% 0.32/0.47 % ...subsumed : 122
% 0.32/0.47 % ...remaining for further processing : 481
% 0.32/0.47 % Other redundant clauses eliminated : 0
% 0.32/0.47 % Clauses deleted for lack of memory : 0
% 0.32/0.47 % Backward-subsumed : 313
% 0.32/0.47 % Backward-rewritten : 69
% 0.32/0.47 % Generated clauses : 1594
% 0.32/0.47 % ...of the previous two non-redundant : 1536
% 0.32/0.47 % ...aggressively subsumed : 0
% 0.32/0.47 % Contextual simplify-reflections : 23
% 0.32/0.47 % Paramodulations : 1574
% 0.32/0.47 % Factorizations : 0
% 0.32/0.47 % NegExts : 0
% 0.32/0.47 % Equation resolutions : 0
% 0.32/0.47 % Disequality decompositions : 0
% 0.32/0.47 % Total rewrite steps : 64
% 0.32/0.47 % ...of those cached : 58
% 0.32/0.47 % Propositional unsat checks : 0
% 0.32/0.47 % Propositional check models : 0
% 0.32/0.47 % Propositional check unsatisfiable : 0
% 0.32/0.47 % Propositional clauses : 0
% 0.32/0.47 % Propositional clauses after purity: 0
% 0.32/0.47 % Propositional unsat core size : 0
% 0.32/0.47 % Propositional preprocessing time : 0.000
% 0.32/0.47 % Propositional encoding time : 0.000
% 0.32/0.47 % Propositional solver time : 0.000
% 0.32/0.47 % Success case prop preproc time : 0.000
% 0.32/0.47 % Success case prop encoding time : 0.000
% 0.32/0.47 % Success case prop solver time : 0.000
% 0.32/0.47 % Current number of processed clauses : 79
% 0.32/0.47 % Positive orientable unit clauses : 9
% 0.32/0.47 % Positive unorientable unit clauses: 0
% 0.32/0.47 % Negative unit clauses : 19
% 0.32/0.47 % Non-unit-clauses : 51
% 0.32/0.47 % Current number of unprocessed clauses: 832
% 0.32/0.47 % ...number of literals in the above : 3329
% 0.32/0.47 % Current number of archived formulas : 0
% 0.32/0.47 % Current number of archived clauses : 402
% 0.32/0.47 % Clause-clause subsumption calls (NU) : 5113
% 0.32/0.47 % Rec. Clause-clause subsumption calls : 3761
% 0.32/0.47 % Non-unit clause-clause subsumptions : 283
% 0.32/0.47 % Unit Clause-clause subsumption calls : 955
% 0.32/0.47 % Rewrite failures with RHS unbound : 0
% 0.32/0.47 % BW rewrite match attempts : 24
% 0.32/0.47 % BW rewrite match successes : 6
% 0.32/0.47 % Condensation attempts : 0
% 0.32/0.47 % Condensation successes : 0
% 0.32/0.47 % Termbank termtop insertions : 18351
% 0.32/0.47 % Search garbage collected termcells : 36
% 0.32/0.47
% 0.32/0.47 % -------------------------------------------------
% 0.32/0.47 % User time : 0.026 s
% 0.32/0.47 % System time : 0.002 s
% 0.32/0.47 % Total time : 0.028 s
% 0.32/0.47 % Maximum resident set size: 3636 pages
% 0.32/0.47
% 0.32/0.47 % -------------------------------------------------
% 0.32/0.47 % User time : 0.027 s
% 0.32/0.47 % System time : 0.004 s
% 0.32/0.47 % Total time : 0.032 s
% 0.32/0.47 % Maximum resident set size: 4864 pages
% 0.32/0.47 % E exiting
%------------------------------------------------------------------------------