%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP130-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:38:41 PM UTC 2026
% Result : Unsatisfiable 0.23s 0.64s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 18
% Syntax : Number of clauses : 112 ( 28 unt; 51 nHn; 112 RR)
% Number of literals : 340 ( 0 equ; 150 neg)
% Maximal clause size : 7 ( 3 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 : 134 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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_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(row_surjectivity,axiom,
( ~ group_element(X2)
| ~ group_element(X1)
| product(e_3,X1,X2)
| product(e_2,X1,X2)
| product(e_1,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',row_surjectivity) ).
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(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_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
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(qg3_2,negated_conjecture,
( ~ product(X1,X4,X2)
| ~ product(X3,X4,X1)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3_2) ).
cnf(qg3_1,negated_conjecture,
( ~ product(X1,X3,X4)
| ~ product(X4,X2,X1)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3_1) ).
cnf(qg3,negated_conjecture,
( ~ product(X1,X3,X4)
| ~ product(X1,X2,X3)
| product(X4,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
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(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_1,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
cnf(column_surjectivity,axiom,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,e_3,X2)
| product(X1,e_2,X2)
| product(X1,e_1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',column_surjectivity) ).
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(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(c_0_18,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
inference(fof_simplification,[status(thm)],[product_right_cancellation]) ).
cnf(c_0_19,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_20,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_18 ).
cnf(c_0_21,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
c_0_19 ).
cnf(c_0_22,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(e_3,X1,X2)
| product(e_2,X1,X2)
| product(e_1,X1,X2) ),
inference(fof_simplification,[status(thm)],[row_surjectivity]) ).
cnf(c_0_23,plain,
~ equalish(e_3,e_2),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_2]) ).
cnf(c_0_24,plain,
( ~ group_element(X3)
| ~ group_element(X2)
| ~ product(X3,X1,e_1)
| product(X3,X2,e_3)
| product(X3,X2,e_2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(e_3,X1,X2)
| product(e_2,X1,X2)
| product(e_1,X1,X2) ),
c_0_22 ).
cnf(c_0_26,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_27,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
inference(fof_simplification,[status(thm)],[product_left_cancellation]) ).
cnf(c_0_28,plain,
~ equalish(e_3,e_2),
c_0_23 ).
cnf(c_0_29,plain,
( ~ group_element(X1)
| ~ group_element(X2)
| product(e_1,X2,e_2)
| product(e_1,X2,e_3)
| product(e_3,X1,e_1)
| product(e_2,X1,e_1)
| equalish(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_30,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_31,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_32,plain,
~ equalish(e_2,e_1),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_1]) ).
cnf(c_0_33,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_27 ).
cnf(c_0_34,plain,
( product(e_2,e_3,e_1)
| product(e_3,e_3,e_1)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31])]) ).
cnf(c_0_35,negated_conjecture,
( ~ product(X1,X4,X2)
| ~ product(X3,X4,X1)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[qg3_2]) ).
cnf(c_0_36,plain,
~ equalish(e_2,e_1),
c_0_32 ).
cnf(c_0_37,plain,
( ~ product(X1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_3,e_3,e_1)
| product(e_2,e_3,e_1)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
( ~ product(X1,X4,X2)
| ~ product(X3,X4,X1)
| product(X1,X2,X3) ),
c_0_35 ).
cnf(c_0_39,negated_conjecture,
( ~ product(X1,X3,X4)
| ~ product(X4,X2,X1)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[qg3_1]) ).
cnf(c_0_40,negated_conjecture,
( ~ product(X1,X3,X4)
| ~ product(X1,X2,X3)
| product(X4,X2,X1) ),
inference(fof_simplification,[status(thm)],[qg3]) ).
cnf(c_0_41,plain,
~ equalish(e_1,e_3),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_3]) ).
cnf(c_0_42,plain,
( ~ product(e_2,e_2,e_3)
| product(e_2,e_3,e_1)
| product(e_3,e_3,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_43,negated_conjecture,
( ~ product(X1,X3,X4)
| ~ product(X4,X2,X1)
| product(X1,X2,X3) ),
c_0_39 ).
cnf(c_0_44,negated_conjecture,
( ~ product(X1,X3,X4)
| ~ product(X1,X2,X3)
| product(X4,X2,X1) ),
c_0_40 ).
cnf(c_0_45,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
inference(fof_simplification,[status(thm)],[product_total_function2]) ).
cnf(c_0_46,plain,
~ equalish(e_1,e_3),
c_0_41 ).
cnf(c_0_47,plain,
( ~ product(X1,e_3,e_1)
| ~ product(e_2,e_2,e_3)
| product(e_2,e_3,e_1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_33,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
( ~ product(e_1,X1,e_3)
| ~ product(e_2,e_2,e_3)
| product(e_1,e_3,X1)
| product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_43,c_0_42]) ).
cnf(c_0_49,negated_conjecture,
( ~ product(e_3,X1,e_3)
| ~ product(e_2,e_2,e_3)
| product(e_1,X1,e_3)
| product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_44,c_0_42]) ).
cnf(c_0_50,plain,
~ equalish(e_3,e_1),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_1]) ).
cnf(c_0_51,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
c_0_45 ).
cnf(c_0_52,plain,
( ~ product(e_1,e_3,e_1)
| ~ product(e_2,e_2,e_3)
| product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_53,negated_conjecture,
( ~ product(e_3,X1,e_3)
| ~ product(e_2,e_2,e_3)
| product(e_1,e_3,X1)
| product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,e_3,X2)
| product(X1,e_2,X2)
| product(X1,e_1,X2) ),
inference(fof_simplification,[status(thm)],[column_surjectivity]) ).
cnf(c_0_55,plain,
~ equalish(e_3,e_1),
c_0_50 ).
cnf(c_0_56,plain,
( ~ product(e_3,e_3,X1)
| ~ product(e_2,e_2,e_3)
| product(e_2,e_3,e_1)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_51,c_0_42]) ).
cnf(c_0_57,negated_conjecture,
( ~ product(e_3,e_1,e_3)
| ~ product(e_2,e_2,e_3)
| product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,e_3,X2)
| product(X1,e_2,X2)
| product(X1,e_1,X2) ),
c_0_54 ).
cnf(c_0_59,plain,
( ~ product(e_3,e_3,e_3)
| ~ product(e_2,e_2,e_3)
| product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_60,plain,
~ equalish(e_2,e_3),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_3]) ).
cnf(c_0_61,negated_conjecture,
( ~ product(e_2,e_2,e_3)
| product(e_2,e_3,e_1)
| product(e_3,e_2,e_3) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_31])]),c_0_59]) ).
cnf(c_0_62,plain,
( ~ group_element(X2)
| ~ group_element(X3)
| ~ product(X2,X3,X1)
| product(X2,X3,e_3)
| product(X2,X3,e_2)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_51,c_0_21]) ).
cnf(c_0_63,plain,
~ equalish(e_2,e_3),
c_0_60 ).
cnf(c_0_64,negated_conjecture,
( ~ product(X1,e_2,e_3)
| ~ product(e_2,e_2,e_3)
| product(e_2,e_3,e_1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_33,c_0_61]) ).
cnf(c_0_65,plain,
( ~ group_element(X1)
| ~ group_element(X2)
| product(e_3,X2,X1)
| product(e_2,X2,X1)
| product(e_1,X2,e_2)
| product(e_1,X2,e_3)
| equalish(X1,e_1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_25]),c_0_26])]) ).
cnf(c_0_66,plain,
~ equalish(e_1,e_2),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_2]) ).
cnf(c_0_67,negated_conjecture,
( ~ product(e_2,e_2,e_3)
| product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_68,plain,
( ~ group_element(X1)
| product(e_2,e_3,X1)
| product(e_3,e_3,X1)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_65,c_0_31]) ).
cnf(c_0_69,plain,
~ equalish(e_1,e_2),
c_0_66 ).
cnf(c_0_70,negated_conjecture,
( ~ product(X1,e_3,e_1)
| ~ product(e_2,e_2,e_3)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_67]) ).
cnf(c_0_71,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_3,e_3,e_3)
| product(e_2,e_3,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_68]),c_0_31])]) ).
cnf(c_0_72,negated_conjecture,
( ~ product(e_1,e_3,e_1)
| ~ product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_73,negated_conjecture,
( ~ product(e_1,X1,e_2)
| ~ product(e_2,e_2,e_3)
| product(e_1,e_3,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_67]) ).
cnf(c_0_74,plain,
( ~ product(e_1,X1,e_3)
| product(e_2,e_3,e_3)
| product(e_3,e_3,e_3)
| product(e_1,e_3,e_2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_20,c_0_71]) ).
cnf(c_0_75,negated_conjecture,
( ~ group_element(X1)
| ~ group_element(X2)
| ~ product(X1,X3,X2)
| product(e_1,X3,X1)
| product(X1,X2,e_3)
| product(X1,X2,e_2) ),
inference(spm,[status(thm)],[c_0_44,c_0_21]) ).
cnf(c_0_76,negated_conjecture,
( ~ product(e_2,e_2,e_3)
| product(e_1,e_3,e_3) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_21]),c_0_31]),c_0_26])]),c_0_73]) ).
cnf(c_0_77,negated_conjecture,
( ~ product(e_1,e_3,X1)
| ~ product(e_2,e_2,e_3)
| product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_38,c_0_67]) ).
cnf(c_0_78,plain,
( ~ product(e_1,e_2,e_3)
| product(e_1,e_3,e_2)
| product(e_3,e_3,e_3)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_63,c_0_74]) ).
cnf(c_0_79,negated_conjecture,
( ~ group_element(X1)
| ~ group_element(X2)
| product(X1,X2,e_2)
| product(X1,X2,e_3)
| product(X1,e_3,X2)
| product(X1,e_2,X2)
| product(e_1,e_1,X1) ),
inference(spm,[status(thm)],[c_0_75,c_0_58]) ).
cnf(c_0_80,negated_conjecture,
( ~ product(e_1,e_3,X1)
| ~ product(e_2,e_2,e_3)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_51,c_0_76]) ).
cnf(c_0_81,negated_conjecture,
( ~ product(e_2,e_2,e_3)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_77,c_0_76]) ).
cnf(c_0_82,plain,
( ~ product(e_1,e_3,X1)
| ~ product(e_1,e_2,e_3)
| product(e_2,e_3,e_3)
| product(e_3,e_3,e_3)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_51,c_0_78]) ).
cnf(c_0_83,negated_conjecture,
( ~ group_element(X1)
| product(e_1,e_1,X1)
| product(X1,e_2,e_3)
| product(X1,e_3,e_3)
| product(X1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_79,c_0_31]) ).
cnf(c_0_84,negated_conjecture,
~ product(e_2,e_2,e_3),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_80]),c_0_81]) ).
cnf(c_0_85,plain,
( ~ product(e_1,e_3,e_3)
| ~ product(e_1,e_2,e_3)
| product(e_3,e_3,e_3)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_28,c_0_82]) ).
cnf(c_0_86,negated_conjecture,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_3)
| product(e_1,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_30]),c_0_84]) ).
cnf(c_0_87,plain,
( ~ product(e_1,e_2,e_3)
| product(e_2,e_3,e_3)
| product(e_3,e_3,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_25]),c_0_31])]) ).
cnf(c_0_88,negated_conjecture,
( ~ product(e_1,X1,e_2)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_20,c_0_86]) ).
cnf(c_0_89,plain,
( product(e_3,e_3,e_3)
| product(e_2,e_3,e_3)
| product(e_3,e_2,e_3)
| product(e_2,e_2,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_25]),c_0_31]),c_0_30])]) ).
cnf(c_0_90,negated_conjecture,
( ~ product(e_1,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_55,c_0_88]) ).
cnf(c_0_91,plain,
( product(e_3,e_2,e_3)
| product(e_2,e_3,e_3)
| product(e_3,e_3,e_3) ),
inference(sr,[status(thm)],[c_0_89,c_0_84]) ).
cnf(c_0_92,negated_conjecture,
( ~ group_element(X1)
| ~ group_element(X2)
| ~ product(X2,X3,X1)
| product(X2,e_1,X3)
| product(X1,e_3,X2)
| product(X1,e_2,X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_58]) ).
cnf(c_0_93,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_3,e_3,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_25]),c_0_30]),c_0_31])]) ).
cnf(c_0_94,plain,
( ~ product(e_3,e_3,X1)
| product(e_2,e_3,e_3)
| product(e_3,e_2,e_3)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_51,c_0_91]) ).
cnf(c_0_95,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_3,e_1,e_3)
| product(e_2,e_3,e_2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_31]),c_0_30])]),c_0_84]) ).
cnf(c_0_96,plain,
( ~ product(e_3,e_3,e_2)
| product(e_3,e_2,e_3)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_63,c_0_94]) ).
cnf(c_0_97,negated_conjecture,
( ~ product(e_3,X1,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_20,c_0_95]) ).
cnf(c_0_98,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_3,e_2,e_3)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_96,c_0_93]) ).
cnf(c_0_99,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_97]),c_0_98]) ).
cnf(c_0_100,negated_conjecture,
( ~ product(e_2,e_3,X1)
| product(e_2,e_3,e_2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_51,c_0_99]) ).
cnf(c_0_101,negated_conjecture,
( ~ group_element(X1)
| ~ group_element(X2)
| ~ product(X2,X1,X3)
| product(X2,X3,e_1)
| product(e_3,X1,X2)
| product(e_2,X1,X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_25]) ).
cnf(c_0_102,negated_conjecture,
( ~ product(e_2,e_3,e_1)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_46,c_0_100]) ).
cnf(c_0_103,negated_conjecture,
( ~ product(X1,e_3,e_3)
| product(e_2,e_3,e_2)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_99]) ).
cnf(c_0_104,negated_conjecture,
( ~ product(e_3,X1,e_2)
| product(e_3,e_3,X1)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_43,c_0_99]) ).
cnf(c_0_105,negated_conjecture,
( product(e_2,e_3,e_2)
| product(e_3,e_3,e_2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_99]),c_0_30]),c_0_31])]),c_0_102]) ).
cnf(c_0_106,negated_conjecture,
( ~ product(e_3,e_3,e_3)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_28,c_0_103]) ).
cnf(c_0_107,negated_conjecture,
product(e_2,e_3,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106]) ).
cnf(c_0_108,negated_conjecture,
( ~ product(e_2,e_3,X1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_51,c_0_107]) ).
cnf(c_0_109,negated_conjecture,
( ~ product(e_2,X1,e_2)
| product(e_2,e_3,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_107]) ).
cnf(c_0_110,negated_conjecture,
~ product(e_2,e_3,e_3),
inference(spm,[status(thm)],[c_0_28,c_0_108]) ).
cnf(c_0_111,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_107]),c_0_110]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP130-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.46 % Computer : n005.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Sun Sep 20 20:01:03 UTC 2026
% 0.18/0.47 % CPUTime :
% 0.18/0.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.55 Running first-order theorem proving
% 0.23/0.55 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
% 0.23/0.64 % Version: 3.5.1
% 0.23/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.64 % Starting sh5l with 300s (1) cores
% 0.23/0.64 % sh5l with pid 1637076 completed with status 0
% 0.23/0.64 % Result found by sh5l
% 0.23/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.64 % Starting sh5l with 300s (1) cores
% 0.23/0.64 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.23/0.64 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.23/0.64 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.23/0.64 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.64 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.64 % SubtermCWHack with pid 1637082 completed with status 0
% 0.23/0.64 % Result found by SubtermCWHack
% 0.23/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.64 % Starting sh5l with 300s (1) cores
% 0.23/0.64 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.23/0.64 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.23/0.64 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.23/0.64 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.64 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.64 % Preprocessing time : 0.001 s
% 0.23/0.64
% 0.23/0.64 % Proof found!
% 0.23/0.64 % SZS status Unsatisfiable
% 0.23/0.64 % SZS output start CNFRefutation
% See solution above
% 0.23/0.64 % Parsed axioms : 18
% 0.23/0.64 % Removed by relevancy pruning/SinE : 0
% 0.23/0.64 % Initial clauses : 18
% 0.23/0.64 % Removed in clause preprocessing : 0
% 0.23/0.64 % Initial clauses in saturation : 18
% 0.23/0.64 % Processed clauses : 366
% 0.23/0.64 % ...of these trivial : 0
% 0.23/0.64 % ...subsumed : 100
% 0.23/0.64 % ...remaining for further processing : 266
% 0.23/0.64 % Other redundant clauses eliminated : 0
% 0.23/0.64 % Clauses deleted for lack of memory : 0
% 0.23/0.64 % Backward-subsumed : 109
% 0.23/0.64 % Backward-rewritten : 24
% 0.23/0.64 % Generated clauses : 1586
% 0.23/0.64 % ...of the previous two non-redundant : 1545
% 0.23/0.64 % ...aggressively subsumed : 0
% 0.23/0.64 % Contextual simplify-reflections : 7
% 0.23/0.64 % Paramodulations : 1564
% 0.23/0.64 % Factorizations : 0
% 0.23/0.64 % NegExts : 0
% 0.23/0.64 % Equation resolutions : 0
% 0.23/0.64 % Disequality decompositions : 0
% 0.23/0.64 % Total rewrite steps : 1156
% 0.23/0.64 % ...of those cached : 1151
% 0.23/0.64 % Propositional unsat checks : 0
% 0.23/0.64 % Propositional check models : 0
% 0.23/0.64 % Propositional check unsatisfiable : 0
% 0.23/0.64 % Propositional clauses : 0
% 0.23/0.64 % Propositional clauses after purity: 0
% 0.23/0.64 % Propositional unsat core size : 0
% 0.23/0.64 % Propositional preprocessing time : 0.000
% 0.23/0.64 % Propositional encoding time : 0.000
% 0.23/0.64 % Propositional solver time : 0.000
% 0.23/0.64 % Success case prop preproc time : 0.000
% 0.23/0.64 % Success case prop encoding time : 0.000
% 0.23/0.64 % Success case prop solver time : 0.000
% 0.23/0.64 % Current number of processed clauses : 111
% 0.23/0.64 % Positive orientable unit clauses : 5
% 0.23/0.64 % Positive unorientable unit clauses: 0
% 0.23/0.64 % Negative unit clauses : 13
% 0.23/0.64 % Non-unit-clauses : 93
% 0.23/0.64 % Current number of unprocessed clauses: 1079
% 0.23/0.64 % ...number of literals in the above : 6131
% 0.23/0.64 % Current number of archived formulas : 0
% 0.23/0.64 % Current number of archived clauses : 155
% 0.23/0.64 % Clause-clause subsumption calls (NU) : 4400
% 0.23/0.64 % Rec. Clause-clause subsumption calls : 1668
% 0.23/0.64 % Non-unit clause-clause subsumptions : 176
% 0.23/0.64 % Unit Clause-clause subsumption calls : 160
% 0.23/0.64 % Rewrite failures with RHS unbound : 0
% 0.23/0.64 % BW rewrite match attempts : 5
% 0.23/0.64 % BW rewrite match successes : 2
% 0.23/0.64 % Condensation attempts : 0
% 0.23/0.64 % Condensation successes : 0
% 0.23/0.64 % Termbank termtop insertions : 28050
% 0.23/0.64 % Search garbage collected termcells : 48
% 0.23/0.64
% 0.23/0.64 % -------------------------------------------------
% 0.23/0.64 % User time : 0.038 s
% 0.23/0.64 % System time : 0.003 s
% 0.23/0.64 % Total time : 0.041 s
% 0.23/0.64 % Maximum resident set size: 3588 pages
% 0.23/0.64
% 0.23/0.64 % -------------------------------------------------
% 0.23/0.64 % User time : 0.039 s
% 0.23/0.64 % System time : 0.011 s
% 0.23/0.64 % Total time : 0.050 s
% 0.23/0.64 % Maximum resident set size: 4608 pages
% 0.23/0.64 % E exiting
%------------------------------------------------------------------------------