%------------------------------------------------------------------------------
% File : E---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/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:38:36 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.51s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 14
% Syntax : Number of clauses : 131 ( 35 unt; 46 nHn; 131 RR)
% Number of literals : 323 ( 0 equ; 160 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 : 86 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_total_function1,axiom,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
cnf(product_right_cancellation,axiom,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
cnf(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(product_total_function2,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
cnf(qg3,negated_conjecture,
( ~ product(X2,X3,X4)
| ~ product(X1,X2,X3)
| product(X3,X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
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(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
cnf(c_0_14,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
inference(fof_simplification,[status(thm)],[product_total_function1]) ).
cnf(c_0_15,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
c_0_14 ).
cnf(c_0_16,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_17,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_1)
| product(X1,e_3,e_2)
| product(X1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
~ equalish(e_2,e_3),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_3]) ).
cnf(c_0_20,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_17 ).
cnf(c_0_21,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_22,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
inference(fof_simplification,[status(thm)],[product_left_cancellation]) ).
cnf(c_0_23,plain,
~ equalish(e_2,e_3),
c_0_19 ).
cnf(c_0_24,plain,
( ~ product(e_3,X1,e_1)
| equalish(X1,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_22 ).
cnf(c_0_26,plain,
( ~ product(e_3,e_2,e_1)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
inference(fof_simplification,[status(thm)],[product_total_function2]) ).
cnf(c_0_28,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_25,c_0_26]) ).
cnf(c_0_29,plain,
~ equalish(e_1,e_2),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_2]) ).
cnf(c_0_30,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
c_0_27 ).
cnf(c_0_31,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_23,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( ~ product(X2,X3,X4)
| ~ product(X1,X2,X3)
| product(X3,X1,X4) ),
inference(fof_simplification,[status(thm)],[qg3]) ).
cnf(c_0_33,plain,
~ equalish(e_1,e_2),
c_0_29 ).
cnf(c_0_34,plain,
( ~ product(e_3,e_3,X1)
| ~ product(e_2,e_3,e_3)
| ~ product(e_3,e_2,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( ~ product(X2,X3,X4)
| ~ product(X1,X2,X3)
| product(X3,X1,X4) ),
c_0_32 ).
cnf(c_0_36,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_37,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_33,c_0_34]),c_0_35]) ).
cnf(c_0_38,plain,
( ~ group_element(X1)
| product(X1,e_2,e_1)
| product(X1,e_2,e_2)
| product(X1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_15,c_0_36]) ).
cnf(c_0_39,plain,
( ~ product(e_2,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_37,c_0_21]) ).
cnf(c_0_40,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_38,c_0_16]) ).
cnf(c_0_41,plain,
( ~ product(X1,e_3,e_3)
| ~ product(e_2,e_3,e_3)
| equalish(X1,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_39]) ).
cnf(c_0_42,plain,
( ~ product(X1,e_2,e_1)
| equalish(X1,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_40]) ).
cnf(c_0_43,plain,
( ~ product(e_2,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_23,c_0_41]) ).
cnf(c_0_44,plain,
( ~ product(e_2,e_2,e_1)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_23,c_0_42]) ).
cnf(c_0_45,plain,
( ~ product(e_3,X1,e_2)
| ~ product(e_2,e_3,e_3)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_20,c_0_43]) ).
cnf(c_0_46,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_18,c_0_36]) ).
cnf(c_0_47,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_35,c_0_44]),c_0_35]) ).
cnf(c_0_48,plain,
( ~ product(e_3,e_2,e_2)
| ~ product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_23,c_0_45]) ).
cnf(c_0_49,plain,
( ~ product(e_2,X1,e_1)
| equalish(X1,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_20,c_0_46]) ).
cnf(c_0_50,negated_conjecture,
( ~ product(e_2,e_3,e_3)
| ~ product(e_2,e_2,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_43]),c_0_48]) ).
cnf(c_0_51,plain,
( ~ product(e_2,e_2,e_1)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_23,c_0_49]) ).
cnf(c_0_52,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_53,negated_conjecture,
( ~ product(e_2,e_2,e_1)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,plain,
~ equalish(e_2,e_1),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_1]) ).
cnf(c_0_55,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_38,c_0_52]) ).
cnf(c_0_56,plain,
~ equalish(e_1,e_3),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_3]) ).
cnf(c_0_57,negated_conjecture,
( ~ product(e_2,e_2,e_1)
| product(e_3,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_47,c_0_53]) ).
cnf(c_0_58,plain,
~ equalish(e_2,e_1),
c_0_54 ).
cnf(c_0_59,plain,
( ~ product(X1,e_2,e_1)
| equalish(X1,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_55]) ).
cnf(c_0_60,plain,
~ equalish(e_1,e_3),
c_0_56 ).
cnf(c_0_61,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_25,c_0_57]) ).
cnf(c_0_62,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_20,c_0_57]) ).
cnf(c_0_63,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_35,c_0_53]) ).
cnf(c_0_64,plain,
( ~ product(e_2,e_2,e_1)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_65,negated_conjecture,
( ~ product(e_1,e_2,e_2)
| ~ product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_66,negated_conjecture,
( ~ product(e_3,e_1,e_2)
| ~ product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_33,c_0_62]) ).
cnf(c_0_67,plain,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_38,c_0_36]) ).
cnf(c_0_68,negated_conjecture,
~ product(e_2,e_2,e_1),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]),c_0_66]) ).
cnf(c_0_69,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(sr,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_70,plain,
~ equalish(e_3,e_1),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_1]) ).
cnf(c_0_71,plain,
( ~ product(X1,e_2,e_3)
| equalish(X1,e_2)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_69]) ).
cnf(c_0_72,plain,
~ equalish(e_3,e_1),
c_0_70 ).
cnf(c_0_73,plain,
( ~ product(e_1,e_2,e_3)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_71]) ).
cnf(c_0_74,plain,
( ~ product(e_3,e_2,e_1)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_72,c_0_59]) ).
cnf(c_0_75,plain,
( ~ product(e_2,X1,e_3)
| equalish(X1,e_2)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_20,c_0_69]) ).
cnf(c_0_76,plain,
~ equalish(e_3,e_2),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_2]) ).
cnf(c_0_77,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_35,c_0_69]) ).
cnf(c_0_78,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_73,c_0_74]) ).
cnf(c_0_79,plain,
( ~ product(e_2,e_1,e_3)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_75]) ).
cnf(c_0_80,plain,
~ equalish(e_3,e_2),
c_0_76 ).
cnf(c_0_81,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_18,c_0_52]) ).
cnf(c_0_82,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_77,c_0_78]),c_0_79]) ).
cnf(c_0_83,plain,
( ~ product(e_3,e_2,e_3)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_80,c_0_71]) ).
cnf(c_0_84,plain,
( ~ product(X1,e_3,e_1)
| equalish(X1,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_81]) ).
cnf(c_0_85,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_82,c_0_40]),c_0_83]) ).
cnf(c_0_86,plain,
( ~ product(e_2,e_3,e_3)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_80,c_0_75]) ).
cnf(c_0_87,plain,
( ~ product(e_2,e_3,e_1)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_58,c_0_84]) ).
cnf(c_0_88,negated_conjecture,
product(e_2,e_2,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_85]),c_0_86]) ).
cnf(c_0_89,plain,
( ~ product(e_1,X1,e_1)
| equalish(X1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_20,c_0_81]) ).
cnf(c_0_90,plain,
( ~ product(e_1,X1,e_3)
| ~ product(e_2,e_3,e_1)
| equalish(X1,e_3)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_20,c_0_87]) ).
cnf(c_0_91,negated_conjecture,
( ~ product(X1,e_2,e_2)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_88]) ).
cnf(c_0_92,plain,
( ~ product(e_1,e_2,e_1)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_23,c_0_89]) ).
cnf(c_0_93,plain,
( ~ product(X1,e_3,e_2)
| ~ product(e_2,e_3,e_3)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_43]) ).
cnf(c_0_94,plain,
( ~ product(e_1,e_2,e_3)
| ~ product(e_2,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_23,c_0_90]) ).
cnf(c_0_95,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_30,c_0_74]) ).
cnf(c_0_96,negated_conjecture,
~ product(e_1,e_2,e_2),
inference(spm,[status(thm)],[c_0_33,c_0_91]) ).
cnf(c_0_97,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_25,c_0_92]) ).
cnf(c_0_98,plain,
( ~ product(e_1,e_3,e_2)
| ~ product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_60,c_0_93]) ).
cnf(c_0_99,plain,
( ~ product(X1,e_3,e_1)
| equalish(X1,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_21]) ).
cnf(c_0_100,plain,
( ~ product(X1,e_3,e_2)
| ~ product(e_1,e_2,e_3)
| ~ product(e_2,e_3,e_1)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_25,c_0_94]) ).
cnf(c_0_101,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_60,c_0_95]) ).
cnf(c_0_102,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_3) ),
inference(sr,[status(thm)],[c_0_55,c_0_96]) ).
cnf(c_0_103,plain,
( ~ product(e_2,e_3,e_3)
| ~ product(e_1,e_2,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_97]),c_0_98]) ).
cnf(c_0_104,plain,
( ~ product(e_2,e_3,e_1)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_23,c_0_99]) ).
cnf(c_0_105,plain,
( ~ product(e_3,e_3,e_2)
| ~ product(e_1,e_2,e_3)
| ~ product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_72,c_0_100]) ).
cnf(c_0_106,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_101,c_0_102]),c_0_96]) ).
cnf(c_0_107,plain,
( ~ product(e_2,e_3,e_3)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_103,c_0_102]) ).
cnf(c_0_108,plain,
( ~ product(e_3,X1,e_3)
| ~ product(e_2,e_3,e_1)
| equalish(X1,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_20,c_0_104]) ).
cnf(c_0_109,negated_conjecture,
( ~ product(e_2,X1,e_2)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_20,c_0_88]) ).
cnf(c_0_110,plain,
( ~ product(e_3,e_2,e_1)
| ~ product(e_3,e_3,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_35]) ).
cnf(c_0_111,negated_conjecture,
~ product(e_3,e_2,e_2),
inference(spm,[status(thm)],[c_0_80,c_0_91]) ).
cnf(c_0_112,plain,
( ~ product(X1,e_2,e_3)
| ~ product(e_2,e_3,e_3)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_25,c_0_107]) ).
cnf(c_0_113,plain,
( ~ product(e_3,e_2,e_3)
| ~ product(e_2,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_23,c_0_108]) ).
cnf(c_0_114,negated_conjecture,
~ product(e_2,e_3,e_2),
inference(spm,[status(thm)],[c_0_80,c_0_109]) ).
cnf(c_0_115,plain,
( ~ product(e_2,e_3,e_3)
| ~ product(e_3,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_110,c_0_43]) ).
cnf(c_0_116,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_3) ),
inference(sr,[status(thm)],[c_0_40,c_0_111]) ).
cnf(c_0_117,plain,
( ~ product(e_3,e_2,e_3)
| ~ product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_72,c_0_112]) ).
cnf(c_0_118,plain,
( ~ product(e_3,e_3,X1)
| ~ product(e_3,e_2,e_3)
| ~ product(e_2,e_3,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_30,c_0_113]) ).
cnf(c_0_119,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_3) ),
inference(sr,[status(thm)],[c_0_46,c_0_114]) ).
cnf(c_0_120,plain,
~ product(e_2,e_3,e_3),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_117]) ).
cnf(c_0_121,plain,
( ~ product(e_3,e_2,e_3)
| ~ product(e_2,e_3,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_118]),c_0_35]) ).
cnf(c_0_122,plain,
product(e_2,e_3,e_1),
inference(sr,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_123,negated_conjecture,
( ~ product(X1,e_2,e_3)
| product(e_3,X1,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_35,c_0_46]) ).
cnf(c_0_124,plain,
~ product(e_3,e_2,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_122])]) ).
cnf(c_0_125,plain,
( ~ product(e_3,X1,e_1)
| equalish(X1,e_2)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_20,c_0_40]) ).
cnf(c_0_126,negated_conjecture,
( ~ product(e_3,e_2,e_1)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_3,e_1,e_1)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_123,c_0_74]) ).
cnf(c_0_127,plain,
product(e_3,e_2,e_1),
inference(sr,[status(thm)],[c_0_116,c_0_124]) ).
cnf(c_0_128,plain,
( ~ product(e_3,e_1,e_1)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_125]) ).
cnf(c_0_129,negated_conjecture,
product(e_3,e_1,e_1),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_127])]),c_0_96]),c_0_114]),c_0_120]) ).
cnf(c_0_130,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_128,c_0_129])]),c_0_111]),c_0_124]),
[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/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:00:25 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 0.14/0.51 % Version: 3.5.1
% 0.14/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.51 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.51 % Starting sh5l with 300s (1) cores
% 0.14/0.51 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 41415 completed with status 0
% 0.14/0.51 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.51 % No SInE strategy applied
% 0.14/0.51 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.14/0.51 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.51 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.51 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.14/0.51 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.51 % Starting new_bool_1 with 136s (1) cores
% 0.14/0.51 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 41421 completed with status 0
% 0.14/0.51 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 0.14/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.51 % No SInE strategy applied
% 0.14/0.51 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.14/0.51 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.51 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.51 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.14/0.51 % Preprocessing time : 0.001 s
% 0.14/0.51 % Presaturation interreduction done
% 0.14/0.51
% 0.14/0.51 % Proof found!
% 0.14/0.51 % SZS status Unsatisfiable
% 0.14/0.51 % SZS output start CNFRefutation
% See solution above
% 0.14/0.51 % Parsed axioms : 14
% 0.14/0.51 % Removed by relevancy pruning/SinE : 0
% 0.14/0.51 % Initial clauses : 14
% 0.14/0.51 % Removed in clause preprocessing : 0
% 0.14/0.51 % Initial clauses in saturation : 14
% 0.14/0.51 % Processed clauses : 796
% 0.14/0.51 % ...of these trivial : 1
% 0.14/0.51 % ...subsumed : 233
% 0.14/0.51 % ...remaining for further processing : 562
% 0.14/0.51 % Other redundant clauses eliminated : 0
% 0.14/0.51 % Clauses deleted for lack of memory : 0
% 0.14/0.51 % Backward-subsumed : 341
% 0.14/0.51 % Backward-rewritten : 111
% 0.14/0.51 % Generated clauses : 1692
% 0.14/0.51 % ...of the previous two non-redundant : 1641
% 0.14/0.51 % ...aggressively subsumed : 0
% 0.14/0.51 % Contextual simplify-reflections : 26
% 0.14/0.51 % Paramodulations : 1673
% 0.14/0.51 % Factorizations : 0
% 0.14/0.51 % NegExts : 0
% 0.14/0.51 % Equation resolutions : 0
% 0.14/0.51 % Disequality decompositions : 0
% 0.14/0.51 % Total rewrite steps : 113
% 0.14/0.51 % ...of those cached : 107
% 0.14/0.51 % Propositional unsat checks : 0
% 0.14/0.51 % Propositional check models : 0
% 0.14/0.51 % Propositional check unsatisfiable : 0
% 0.14/0.51 % Propositional clauses : 0
% 0.14/0.51 % Propositional clauses after purity: 0
% 0.14/0.51 % Propositional unsat core size : 0
% 0.14/0.51 % Propositional preprocessing time : 0.000
% 0.14/0.51 % Propositional encoding time : 0.000
% 0.14/0.51 % Propositional solver time : 0.000
% 0.14/0.51 % Success case prop preproc time : 0.000
% 0.14/0.51 % Success case prop encoding time : 0.000
% 0.14/0.51 % Success case prop solver time : 0.000
% 0.14/0.51 % Current number of processed clauses : 77
% 0.14/0.51 % Positive orientable unit clauses : 9
% 0.14/0.51 % Positive unorientable unit clauses: 0
% 0.14/0.51 % Negative unit clauses : 19
% 0.14/0.51 % Non-unit-clauses : 49
% 0.14/0.51 % Current number of unprocessed clauses: 810
% 0.14/0.51 % ...number of literals in the above : 3320
% 0.14/0.51 % Current number of archived formulas : 0
% 0.14/0.51 % Current number of archived clauses : 485
% 0.14/0.51 % Clause-clause subsumption calls (NU) : 11030
% 0.14/0.51 % Rec. Clause-clause subsumption calls : 4276
% 0.14/0.51 % Non-unit clause-clause subsumptions : 444
% 0.14/0.51 % Unit Clause-clause subsumption calls : 1359
% 0.14/0.51 % Rewrite failures with RHS unbound : 0
% 0.14/0.51 % BW rewrite match attempts : 24
% 0.14/0.51 % BW rewrite match successes : 6
% 0.14/0.51 % Condensation attempts : 0
% 0.14/0.51 % Condensation successes : 0
% 0.14/0.51 % Termbank termtop insertions : 20952
% 0.14/0.51 % Search garbage collected termcells : 36
% 0.14/0.51
% 0.14/0.51 % -------------------------------------------------
% 0.14/0.51 % User time : 0.056 s
% 0.14/0.51 % System time : 0.006 s
% 0.14/0.51 % Total time : 0.062 s
% 0.14/0.51 % Maximum resident set size: 3636 pages
% 0.14/0.51
% 0.14/0.51 % -------------------------------------------------
% 0.14/0.51 % User time : 0.291 s
% 0.14/0.51 % System time : 0.026 s
% 0.14/0.51 % Total time : 0.316 s
% 0.14/0.51 % Maximum resident set size: 4864 pages
% 0.14/0.51 % E exiting
%------------------------------------------------------------------------------