%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP128-4.003 : 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 12:38:35 PM UTC 2026
% Result : Unsatisfiable 0.21s 0.53s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 18
% Syntax : Number of clauses : 131 ( 36 unt; 47 nHn; 131 RR)
% Number of literals : 351 ( 0 equ; 168 neg)
% Maximal clause size : 7 ( 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 : 134 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(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(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_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(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
cnf(qg3_2,negated_conjecture,
( ~ product(X4,X2,X1)
| ~ product(X4,X1,X3)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3_2) ).
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_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(qg3_1,negated_conjecture,
( ~ product(X3,X2,X4)
| ~ product(X1,X3,X4)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3_1) ).
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_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
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(qg3,negated_conjecture,
( ~ product(X3,X2,X4)
| ~ product(X1,X2,X3)
| product(X1,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
cnf(c_0_18,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
inference(fof_simplification,[status(thm)],[product_total_function2]) ).
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,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,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,
( ~ 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_20,c_0_21]) ).
cnf(c_0_24,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_25,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_26,plain,
~ equalish(e_2,e_1),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_1]) ).
cnf(c_0_27,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_23,c_0_24]),c_0_25])]) ).
cnf(c_0_28,axiom,
group_element(e_3),
element_3 ).
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,
~ equalish(e_2,e_1),
c_0_26 ).
cnf(c_0_31,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_27,c_0_28]) ).
cnf(c_0_32,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_33,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_29 ).
cnf(c_0_34,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_2,e_3,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_35,negated_conjecture,
( ~ product(X4,X2,X1)
| ~ product(X4,X1,X3)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[qg3_2]) ).
cnf(c_0_36,plain,
( ~ product(X1,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_3,e_3,e_2)
| product(e_1,e_3,e_2)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
( ~ product(X4,X2,X1)
| ~ product(X4,X1,X3)
| product(X1,X2,X3) ),
c_0_35 ).
cnf(c_0_38,plain,
~ equalish(e_1,e_2),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_2]) ).
cnf(c_0_39,plain,
( ~ product(e_2,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_3,e_3,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_36]),c_0_37]) ).
cnf(c_0_40,plain,
~ equalish(e_1,e_2),
c_0_38 ).
cnf(c_0_41,plain,
( ~ product(e_1,e_3,X1)
| ~ product(e_2,e_3,e_3)
| product(e_3,e_3,e_2)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_20,c_0_39]) ).
cnf(c_0_42,plain,
~ equalish(e_3,e_1),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_1]) ).
cnf(c_0_43,plain,
( ~ product(e_1,e_3,e_1)
| ~ product(e_2,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
inference(fof_simplification,[status(thm)],[product_right_cancellation]) ).
cnf(c_0_45,plain,
~ equalish(e_3,e_1),
c_0_42 ).
cnf(c_0_46,negated_conjecture,
( ~ product(X3,X2,X4)
| ~ product(X1,X3,X4)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[qg3_1]) ).
cnf(c_0_47,plain,
( ~ product(e_2,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_24]),c_0_25]),c_0_28])]),c_0_37]) ).
cnf(c_0_48,plain,
~ equalish(e_2,e_3),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_3]) ).
cnf(c_0_49,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_44 ).
cnf(c_0_50,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_45,c_0_31]),c_0_28])]) ).
cnf(c_0_51,negated_conjecture,
( ~ product(X3,X2,X4)
| ~ product(X1,X3,X4)
| product(X1,X2,X3) ),
c_0_46 ).
cnf(c_0_52,plain,
( ~ product(e_3,e_3,X1)
| ~ product(e_2,e_3,e_3)
| product(e_3,e_3,e_2)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_20,c_0_47]) ).
cnf(c_0_53,plain,
~ equalish(e_2,e_3),
c_0_48 ).
cnf(c_0_54,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_49,c_0_50]) ).
cnf(c_0_55,negated_conjecture,
( ~ product(X1,e_3,e_1)
| ~ product(e_2,e_3,e_3)
| product(X1,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_51,c_0_47]) ).
cnf(c_0_56,plain,
( ~ product(e_3,e_3,e_3)
| ~ product(e_2,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_45,c_0_52]) ).
cnf(c_0_57,plain,
~ equalish(e_3,e_2),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_2]) ).
cnf(c_0_58,plain,
( ~ product(e_1,e_2,e_3)
| product(e_1,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_51]) ).
cnf(c_0_59,plain,
~ equalish(e_1,e_3),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_3]) ).
cnf(c_0_60,negated_conjecture,
( ~ product(e_2,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_47]),c_0_56]) ).
cnf(c_0_61,plain,
~ equalish(e_3,e_2),
c_0_57 ).
cnf(c_0_62,plain,
( ~ product(e_1,e_3,X1)
| ~ product(e_1,e_2,e_3)
| product(e_3,e_3,e_3)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_20,c_0_58]) ).
cnf(c_0_63,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_64,plain,
~ equalish(e_1,e_3),
c_0_59 ).
cnf(c_0_65,negated_conjecture,
( ~ product(X1,e_3,e_2)
| ~ product(e_2,e_3,e_3)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_33,c_0_60]) ).
cnf(c_0_66,plain,
( ~ product(e_1,e_3,e_3)
| ~ product(e_1,e_2,e_3)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_67,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,e_3,X2)
| product(X1,e_2,X2)
| product(X1,e_1,X2) ),
c_0_63 ).
cnf(c_0_68,negated_conjecture,
( ~ product(e_3,X1,e_2)
| ~ product(e_2,e_3,e_3)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_49,c_0_60]) ).
cnf(c_0_69,negated_conjecture,
( ~ product(e_3,e_3,X1)
| ~ product(e_2,e_3,e_3)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_20,c_0_60]) ).
cnf(c_0_70,negated_conjecture,
( ~ product(e_1,e_3,e_2)
| ~ product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_71,plain,
( ~ product(e_1,e_2,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_66,c_0_24]),c_0_28])]) ).
cnf(c_0_72,negated_conjecture,
( ~ group_element(X1)
| ~ group_element(X2)
| ~ product(X1,X2,X3)
| product(X2,e_1,X3)
| product(X1,e_3,X2)
| product(X1,e_2,X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_67]) ).
cnf(c_0_73,negated_conjecture,
( ~ product(e_3,e_1,e_2)
| ~ product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_64,c_0_68]) ).
cnf(c_0_74,negated_conjecture,
( ~ product(e_3,e_3,e_3)
| ~ product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_61,c_0_69]) ).
cnf(c_0_75,negated_conjecture,
( ~ product(e_1,e_2,e_3)
| product(e_3,e_3,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_58]),c_0_71]) ).
cnf(c_0_76,negated_conjecture,
( ~ product(e_2,e_3,e_3)
| product(e_3,e_2,e_3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_60]),c_0_28])]),c_0_73]),c_0_74]) ).
cnf(c_0_77,negated_conjecture,
( product(e_3,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_75,c_0_24]),c_0_28]),c_0_32])]) ).
cnf(c_0_78,negated_conjecture,
( ~ product(X1,e_2,e_3)
| ~ product(e_2,e_3,e_3)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_33,c_0_76]) ).
cnf(c_0_79,negated_conjecture,
( ~ product(e_2,e_3,e_3)
| product(e_2,e_2,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_77]),c_0_51]) ).
cnf(c_0_80,negated_conjecture,
~ product(e_2,e_3,e_3),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_78]),c_0_79]) ).
cnf(c_0_81,plain,
( product(e_3,e_3,e_3)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[c_0_50,c_0_80]) ).
cnf(c_0_82,negated_conjecture,
( ~ product(e_1,e_3,X1)
| product(e_3,e_3,X1)
| product(e_1,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_37,c_0_81]) ).
cnf(c_0_83,negated_conjecture,
( product(e_3,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_82,c_0_81]) ).
cnf(c_0_84,negated_conjecture,
( ~ product(e_1,e_3,X1)
| product(e_3,e_3,e_3)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_20,c_0_83]) ).
cnf(c_0_85,negated_conjecture,
( ~ product(e_1,e_3,e_3)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_61,c_0_84]) ).
cnf(c_0_86,negated_conjecture,
product(e_3,e_3,e_3),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_24]),c_0_28])]),c_0_80]) ).
cnf(c_0_87,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_49,c_0_21]) ).
cnf(c_0_88,negated_conjecture,
( ~ product(e_3,e_3,X1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_20,c_0_86]) ).
cnf(c_0_89,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X2,X1,e_2)
| product(X2,X1,e_3)
| product(X2,e_3,e_1)
| product(X2,e_2,e_1)
| equalish(e_1,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_67]),c_0_25])]) ).
cnf(c_0_90,negated_conjecture,
( ~ product(e_3,X1,e_3)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_49,c_0_86]) ).
cnf(c_0_91,negated_conjecture,
~ product(e_3,e_3,e_1),
inference(spm,[status(thm)],[c_0_64,c_0_88]) ).
cnf(c_0_92,plain,
( ~ group_element(X1)
| product(X1,e_2,e_1)
| product(X1,e_3,e_1)
| product(X1,e_2,e_3)
| product(X1,e_2,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_32]),c_0_40]) ).
cnf(c_0_93,negated_conjecture,
~ product(e_3,e_2,e_3),
inference(spm,[status(thm)],[c_0_53,c_0_90]) ).
cnf(c_0_94,negated_conjecture,
( product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_28])]),c_0_93]) ).
cnf(c_0_95,negated_conjecture,
~ product(e_3,e_3,e_2),
inference(spm,[status(thm)],[c_0_53,c_0_88]) ).
cnf(c_0_96,negated_conjecture,
( product(e_3,e_2,e_2)
| product(e_2,e_1,e_1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_94]),c_0_32]),c_0_28])]),c_0_95]) ).
cnf(c_0_97,negated_conjecture,
( ~ product(X1,e_2,e_2)
| product(e_2,e_1,e_1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_33,c_0_96]) ).
cnf(c_0_98,negated_conjecture,
( ~ product(e_3,X1,e_1)
| product(e_3,e_2,e_2)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_49,c_0_94]) ).
cnf(c_0_99,negated_conjecture,
( ~ product(e_2,e_2,e_2)
| product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_53,c_0_97]) ).
cnf(c_0_100,negated_conjecture,
( ~ product(e_3,e_1,e_1)
| product(e_3,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_40,c_0_98]) ).
cnf(c_0_101,negated_conjecture,
~ product(e_3,e_1,e_3),
inference(spm,[status(thm)],[c_0_64,c_0_90]) ).
cnf(c_0_102,negated_conjecture,
( ~ product(X3,X2,X4)
| ~ product(X1,X2,X3)
| product(X1,X3,X4) ),
inference(fof_simplification,[status(thm)],[qg3]) ).
cnf(c_0_103,negated_conjecture,
( ~ product(e_2,X1,e_1)
| ~ product(e_2,e_2,e_2)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_49,c_0_99]) ).
cnf(c_0_104,negated_conjecture,
( product(e_3,e_2,e_2)
| product(e_3,e_1,e_2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_21]),c_0_25]),c_0_28])]),c_0_101]) ).
cnf(c_0_105,negated_conjecture,
( ~ product(X3,X2,X4)
| ~ product(X1,X2,X3)
| product(X1,X3,X4) ),
c_0_102 ).
cnf(c_0_106,plain,
( ~ product(e_3,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_3,e_3,e_2)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_45,c_0_36]) ).
cnf(c_0_107,negated_conjecture,
( ~ product(e_2,e_3,e_1)
| ~ product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_45,c_0_103]) ).
cnf(c_0_108,negated_conjecture,
( ~ product(X1,e_1,e_2)
| product(e_3,e_2,e_2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_33,c_0_104]) ).
cnf(c_0_109,negated_conjecture,
( ~ product(X1,e_2,e_1)
| product(e_3,e_2,e_2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_33,c_0_94]) ).
cnf(c_0_110,negated_conjecture,
( ~ group_element(X1)
| ~ group_element(X2)
| ~ product(X3,X2,X1)
| product(X3,X1,e_1)
| product(X1,X2,e_3)
| product(X1,X2,e_2) ),
inference(spm,[status(thm)],[c_0_105,c_0_21]) ).
cnf(c_0_111,plain,
( product(e_2,e_3,e_2)
| product(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_86])]),c_0_95]) ).
cnf(c_0_112,negated_conjecture,
( ~ product(e_2,e_2,e_2)
| 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_107,c_0_21]),c_0_28]),c_0_32])]),c_0_80]) ).
cnf(c_0_113,negated_conjecture,
( ~ product(e_2,e_1,e_2)
| product(e_3,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_53,c_0_108]) ).
cnf(c_0_114,negated_conjecture,
( ~ product(e_1,e_2,e_1)
| product(e_3,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_64,c_0_109]) ).
cnf(c_0_115,negated_conjecture,
( product(e_2,e_3,e_2)
| product(e_1,e_2,e_1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_28]),c_0_32])]),c_0_80]) ).
cnf(c_0_116,negated_conjecture,
( ~ product(e_2,X1,e_2)
| ~ product(e_2,e_2,e_2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_49,c_0_112]) ).
cnf(c_0_117,negated_conjecture,
( ~ product(e_3,X1,e_2)
| ~ product(e_2,e_1,e_2)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_49,c_0_113]) ).
cnf(c_0_118,negated_conjecture,
( ~ group_element(X1)
| ~ group_element(X2)
| ~ product(X3,X1,X2)
| product(X3,e_1,X1)
| product(X1,e_3,X2)
| product(X1,e_2,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_67]) ).
cnf(c_0_119,negated_conjecture,
( product(e_3,e_2,e_2)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_120,negated_conjecture,
~ product(e_2,e_2,e_2),
inference(spm,[status(thm)],[c_0_53,c_0_116]) ).
cnf(c_0_121,negated_conjecture,
( ~ product(e_3,e_1,e_2)
| ~ product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_40,c_0_117]) ).
cnf(c_0_122,negated_conjecture,
( product(e_2,e_3,e_2)
| product(e_3,e_1,e_2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_32])]),c_0_120]) ).
cnf(c_0_123,negated_conjecture,
( ~ product(e_2,e_1,e_2)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_124,negated_conjecture,
product(e_2,e_3,e_2),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_67]),c_0_32])]),c_0_120]) ).
cnf(c_0_125,negated_conjecture,
( ~ product(X1,e_3,e_2)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_33,c_0_124]) ).
cnf(c_0_126,negated_conjecture,
~ product(e_1,e_3,e_2),
inference(spm,[status(thm)],[c_0_40,c_0_125]) ).
cnf(c_0_127,negated_conjecture,
( ~ product(X1,e_2,e_2)
| product(X1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_51,c_0_124]) ).
cnf(c_0_128,negated_conjecture,
~ product(e_1,e_2,e_2),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_129,negated_conjecture,
~ product(e_3,e_2,e_2),
inference(spm,[status(thm)],[c_0_95,c_0_127]) ).
cnf(c_0_130,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_24]),c_0_32])]),c_0_129]),c_0_120]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP128-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 20 20:00:18 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.46 Running first-order theorem proving
% 0.16/0.46 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
% 0.21/0.53 % Version: 3.5.1
% 0.21/0.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.53 % Starting new_bool_3 with 300s (1) cores
% 0.21/0.53 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.53 % Starting sh5l with 300s (1) cores
% 0.21/0.53 % new_bool_1 with pid 1635062 completed with status 0
% 0.21/0.53 % Result found by new_bool_1
% 0.21/0.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.53 % Starting new_bool_3 with 300s (1) cores
% 0.21/0.53 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.53 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.53 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.53 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.21/0.53 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.53 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.53 % SubtermCWHack with pid 1635065 completed with status 0
% 0.21/0.53 % Result found by SubtermCWHack
% 0.21/0.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.53 % Starting new_bool_3 with 300s (1) cores
% 0.21/0.53 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.53 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.53 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.53 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.21/0.53 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.53 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.53 % Preprocessing time : 0.001 s
% 0.21/0.53
% 0.21/0.53 % Proof found!
% 0.21/0.53 % SZS status Unsatisfiable
% 0.21/0.53 % SZS output start CNFRefutation
% See solution above
% 0.21/0.53 % Parsed axioms : 18
% 0.21/0.53 % Removed by relevancy pruning/SinE : 0
% 0.21/0.53 % Initial clauses : 18
% 0.21/0.53 % Removed in clause preprocessing : 0
% 0.21/0.53 % Initial clauses in saturation : 18
% 0.21/0.53 % Processed clauses : 482
% 0.21/0.53 % ...of these trivial : 0
% 0.21/0.53 % ...subsumed : 143
% 0.21/0.53 % ...remaining for further processing : 339
% 0.21/0.53 % Other redundant clauses eliminated : 0
% 0.21/0.53 % Clauses deleted for lack of memory : 0
% 0.21/0.53 % Backward-subsumed : 153
% 0.21/0.53 % Backward-rewritten : 30
% 0.21/0.53 % Generated clauses : 1648
% 0.21/0.53 % ...of the previous two non-redundant : 1561
% 0.21/0.53 % ...aggressively subsumed : 0
% 0.21/0.53 % Contextual simplify-reflections : 10
% 0.21/0.53 % Paramodulations : 1613
% 0.21/0.53 % Factorizations : 0
% 0.21/0.53 % NegExts : 0
% 0.21/0.53 % Equation resolutions : 0
% 0.21/0.53 % Disequality decompositions : 0
% 0.21/0.53 % Total rewrite steps : 1209
% 0.21/0.53 % ...of those cached : 1203
% 0.21/0.53 % Propositional unsat checks : 0
% 0.21/0.53 % Propositional check models : 0
% 0.21/0.53 % Propositional check unsatisfiable : 0
% 0.21/0.53 % Propositional clauses : 0
% 0.21/0.53 % Propositional clauses after purity: 0
% 0.21/0.53 % Propositional unsat core size : 0
% 0.21/0.53 % Propositional preprocessing time : 0.000
% 0.21/0.53 % Propositional encoding time : 0.000
% 0.21/0.53 % Propositional solver time : 0.000
% 0.21/0.53 % Success case prop preproc time : 0.000
% 0.21/0.53 % Success case prop encoding time : 0.000
% 0.21/0.53 % Success case prop solver time : 0.000
% 0.21/0.53 % Current number of processed clauses : 121
% 0.21/0.53 % Positive orientable unit clauses : 6
% 0.21/0.53 % Positive unorientable unit clauses: 0
% 0.21/0.53 % Negative unit clauses : 18
% 0.21/0.53 % Non-unit-clauses : 97
% 0.21/0.53 % Current number of unprocessed clauses: 1017
% 0.21/0.53 % ...number of literals in the above : 5289
% 0.21/0.53 % Current number of archived formulas : 0
% 0.21/0.53 % Current number of archived clauses : 218
% 0.21/0.53 % Clause-clause subsumption calls (NU) : 5558
% 0.21/0.53 % Rec. Clause-clause subsumption calls : 2258
% 0.21/0.53 % Non-unit clause-clause subsumptions : 230
% 0.21/0.53 % Unit Clause-clause subsumption calls : 246
% 0.21/0.53 % Rewrite failures with RHS unbound : 0
% 0.21/0.53 % BW rewrite match attempts : 9
% 0.21/0.53 % BW rewrite match successes : 3
% 0.21/0.53 % Condensation attempts : 0
% 0.21/0.53 % Condensation successes : 0
% 0.21/0.53 % Termbank termtop insertions : 28308
% 0.21/0.53 % Search garbage collected termcells : 48
% 0.21/0.53
% 0.21/0.53 % -------------------------------------------------
% 0.21/0.53 % User time : 0.040 s
% 0.21/0.53 % System time : 0.004 s
% 0.21/0.53 % Total time : 0.044 s
% 0.21/0.53 % Maximum resident set size: 3640 pages
% 0.21/0.53
% 0.21/0.53 % -------------------------------------------------
% 0.21/0.53 % User time : 0.043 s
% 0.21/0.53 % System time : 0.010 s
% 0.21/0.53 % Total time : 0.053 s
% 0.21/0.53 % Maximum resident set size: 4864 pages
% 0.21/0.53 % E exiting
%------------------------------------------------------------------------------