%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP127-4.004 : 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 : n016.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 12:38:14 PM UTC 2026
% Result : Unsatisfiable 0.15s 5.47s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 21
% Syntax : Number of clauses : 137 ( 53 unt; 36 nHn; 135 RR)
% Number of literals : 306 ( 0 equ; 146 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 104 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_total_function1,axiom,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_4)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
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_4,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
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(product_idempotence,axiom,
product(X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
cnf(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
cnf(e_1_is_not_e_4,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
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(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_3_is_not_e_4,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
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(qg3,negated_conjecture,
( ~ product(X3,X1,X4)
| ~ product(X1,X2,X3)
| product(X4,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
cnf(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
cnf(row_surjectivity,axiom,
( ~ group_element(X2)
| ~ group_element(X1)
| product(e_4,X1,X2)
| 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(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_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(qg3_2,negated_conjecture,
( ~ product(X2,X4,X1)
| ~ product(X3,X2,X4)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3_2) ).
cnf(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
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(c_0_21,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_4)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
inference(fof_simplification,[status(thm)],[product_total_function1]) ).
cnf(c_0_22,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
inference(fof_simplification,[status(thm)],[product_right_cancellation]) ).
cnf(c_0_23,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_4)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
c_0_21 ).
cnf(c_0_24,axiom,
group_element(e_4),
element_4 ).
cnf(c_0_25,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
inference(fof_simplification,[status(thm)],[product_left_cancellation]) ).
cnf(c_0_26,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_22 ).
cnf(c_0_27,axiom,
product(X1,X1,X1),
product_idempotence ).
cnf(c_0_28,plain,
( ~ group_element(X1)
| product(X1,e_4,e_4)
| product(X1,e_4,e_3)
| product(X1,e_4,e_2)
| product(X1,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_30,plain,
~ equalish(e_4,e_1),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_1]) ).
cnf(c_0_31,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_25 ).
cnf(c_0_32,plain,
( ~ product(X2,X1,X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
~ equalish(e_4,e_1),
c_0_30 ).
cnf(c_0_35,plain,
~ equalish(e_1,e_4),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_4]) ).
cnf(c_0_36,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_37,plain,
( ~ product(X1,X2,X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_27]) ).
cnf(c_0_38,plain,
( product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_39,plain,
~ equalish(e_1,e_4),
c_0_35 ).
cnf(c_0_40,plain,
( ~ group_element(X1)
| product(X1,e_3,e_4)
| product(X1,e_3,e_3)
| product(X1,e_3,e_2)
| product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_23,c_0_36]) ).
cnf(c_0_41,plain,
~ equalish(e_3,e_1),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_1]) ).
cnf(c_0_42,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_43,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_40,c_0_29]) ).
cnf(c_0_44,plain,
~ equalish(e_3,e_1),
c_0_41 ).
cnf(c_0_45,plain,
( ~ product(X1,e_4,e_3)
| product(e_1,e_4,e_2)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_31,c_0_42]) ).
cnf(c_0_46,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_43]),c_0_44]) ).
cnf(c_0_47,plain,
~ equalish(e_2,e_1),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_1]) ).
cnf(c_0_48,plain,
~ equalish(e_3,e_4),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_4]) ).
cnf(c_0_49,plain,
( ~ product(e_4,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_34,c_0_45]) ).
cnf(c_0_50,plain,
( ~ product(X1,e_3,e_4)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_31,c_0_46]) ).
cnf(c_0_51,plain,
~ equalish(e_1,e_3),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_3]) ).
cnf(c_0_52,negated_conjecture,
( ~ product(X3,X1,X4)
| ~ product(X1,X2,X3)
| product(X4,X1,X2) ),
inference(fof_simplification,[status(thm)],[qg3]) ).
cnf(c_0_53,plain,
~ equalish(e_2,e_1),
c_0_47 ).
cnf(c_0_54,plain,
~ equalish(e_3,e_4),
c_0_48 ).
cnf(c_0_55,plain,
( ~ product(e_1,X1,e_2)
| ~ product(e_4,e_4,e_3)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_26,c_0_49]) ).
cnf(c_0_56,plain,
( ~ product(e_4,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_34,c_0_50]) ).
cnf(c_0_57,plain,
~ equalish(e_1,e_3),
c_0_51 ).
cnf(c_0_58,negated_conjecture,
( ~ product(X3,X1,X4)
| ~ product(X1,X2,X3)
| product(X4,X1,X2) ),
c_0_52 ).
cnf(c_0_59,plain,
( ~ product(e_3,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_60,plain,
( ~ product(e_2,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_53,c_0_50]) ).
cnf(c_0_61,plain,
( ~ product(e_1,e_3,e_2)
| ~ product(e_4,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_62,plain,
( ~ product(e_4,e_3,e_4)
| product(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_56]),c_0_57]) ).
cnf(c_0_63,negated_conjecture,
( ~ product(X1,X2,X1)
| product(X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_58,c_0_27]) ).
cnf(c_0_64,plain,
( ~ product(e_1,X1,e_2)
| ~ product(e_3,e_4,e_3)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_26,c_0_59]) ).
cnf(c_0_65,plain,
( ~ product(e_3,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_44,c_0_50]) ).
cnf(c_0_66,plain,
~ equalish(e_4,e_3),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_3]) ).
cnf(c_0_67,plain,
( ~ product(e_2,e_3,e_4)
| product(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_60]),c_0_57]) ).
cnf(c_0_68,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_40,c_0_24]) ).
cnf(c_0_69,plain,
~ product(e_4,e_3,e_4),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).
cnf(c_0_70,plain,
( ~ product(e_1,e_3,e_2)
| ~ product(e_3,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_54,c_0_64]) ).
cnf(c_0_71,plain,
( ~ product(e_3,e_3,e_4)
| product(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_65]),c_0_57]) ).
cnf(c_0_72,plain,
~ equalish(e_4,e_3),
c_0_66 ).
cnf(c_0_73,plain,
( ~ product(e_1,X1,e_2)
| ~ product(e_2,e_3,e_4)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_26,c_0_67]) ).
cnf(c_0_74,negated_conjecture,
( ~ product(e_4,X1,e_1)
| product(e_3,e_4,X1)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_58,c_0_42]) ).
cnf(c_0_75,plain,
( product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(sr,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_76,plain,
~ product(e_3,e_4,e_3),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_63]) ).
cnf(c_0_77,plain,
( ~ product(X1,e_3,e_2)
| ~ product(e_2,e_3,e_4)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_31,c_0_67]) ).
cnf(c_0_78,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(e_4,X1,X2)
| 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_79,plain,
( ~ product(e_1,e_4,e_2)
| ~ product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_80,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]) ).
cnf(c_0_81,plain,
( ~ product(e_4,e_3,e_2)
| ~ product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_34,c_0_77]) ).
cnf(c_0_82,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(e_4,X1,X2)
| product(e_3,X1,X2)
| product(e_2,X1,X2)
| product(e_1,X1,X2) ),
c_0_78 ).
cnf(c_0_83,negated_conjecture,
( ~ product(e_2,e_3,e_4)
| product(e_4,e_3,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]) ).
cnf(c_0_84,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
inference(fof_simplification,[status(thm)],[product_total_function2]) ).
cnf(c_0_85,plain,
( ~ group_element(X1)
| product(e_4,X1,e_4)
| product(e_3,X1,e_4)
| product(e_2,X1,e_4)
| product(e_1,X1,e_4) ),
inference(spm,[status(thm)],[c_0_82,c_0_24]) ).
cnf(c_0_86,negated_conjecture,
~ product(e_2,e_3,e_4),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_83]),c_0_72]) ).
cnf(c_0_87,plain,
~ equalish(e_1,e_2),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_2]) ).
cnf(c_0_88,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
c_0_84 ).
cnf(c_0_89,negated_conjecture,
( ~ product(X2,X4,X1)
| ~ product(X3,X2,X4)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[qg3_2]) ).
cnf(c_0_90,plain,
( product(e_1,e_3,e_4)
| product(e_3,e_3,e_4) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_36]),c_0_86]),c_0_69]) ).
cnf(c_0_91,plain,
~ equalish(e_1,e_2),
c_0_87 ).
cnf(c_0_92,plain,
( ~ product(e_1,e_3,X1)
| ~ product(e_3,e_3,e_4)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_88,c_0_71]) ).
cnf(c_0_93,negated_conjecture,
( ~ product(X2,X4,X1)
| ~ product(X3,X2,X4)
| product(X1,X2,X3) ),
c_0_89 ).
cnf(c_0_94,plain,
( product(e_3,e_4,e_1)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_28,c_0_36]) ).
cnf(c_0_95,plain,
( ~ product(e_1,e_3,X1)
| product(e_3,e_3,e_4)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_88,c_0_90]) ).
cnf(c_0_96,plain,
( ~ product(e_1,e_3,e_1)
| ~ product(e_3,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_97,negated_conjecture,
( ~ product(e_3,e_4,X1)
| product(X1,e_3,e_1)
| product(e_3,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_93,c_0_90]) ).
cnf(c_0_98,plain,
( product(e_3,e_4,e_4)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(sr,[status(thm)],[c_0_94,c_0_76]) ).
cnf(c_0_99,plain,
~ product(e_1,e_3,e_1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_95]),c_0_96]) ).
cnf(c_0_100,negated_conjecture,
( product(e_3,e_3,e_4)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_99]) ).
cnf(c_0_101,negated_conjecture,
( product(e_3,e_4,e_2)
| product(e_3,e_3,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_100]),c_0_54]) ).
cnf(c_0_102,plain,
( ~ product(X2,X2,X1)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_88,c_0_27]) ).
cnf(c_0_103,negated_conjecture,
( product(e_3,e_3,e_4)
| product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_97,c_0_101]) ).
cnf(c_0_104,plain,
~ equalish(e_4,e_2),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_2]) ).
cnf(c_0_105,negated_conjecture,
product(e_2,e_3,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_72]) ).
cnf(c_0_106,plain,
~ equalish(e_4,e_2),
c_0_104 ).
cnf(c_0_107,negated_conjecture,
( ~ product(X1,e_3,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_31,c_0_105]) ).
cnf(c_0_108,plain,
( ~ product(e_2,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_53,c_0_45]) ).
cnf(c_0_109,negated_conjecture,
~ product(e_4,e_3,e_1),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_110,plain,
( ~ product(e_1,X1,e_2)
| ~ product(e_2,e_4,e_3)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_26,c_0_108]) ).
cnf(c_0_111,plain,
( ~ product(X1,e_3,e_2)
| ~ product(e_3,e_3,e_4)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_31,c_0_71]) ).
cnf(c_0_112,plain,
( product(e_4,e_3,e_2)
| product(e_4,e_3,e_3) ),
inference(sr,[status(thm)],[c_0_75,c_0_109]) ).
cnf(c_0_113,plain,
( ~ product(X1,e_4,e_2)
| ~ product(e_2,e_4,e_3)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_31,c_0_108]) ).
cnf(c_0_114,plain,
( ~ product(e_1,e_3,e_2)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_54,c_0_110]) ).
cnf(c_0_115,plain,
( ~ product(e_4,e_3,e_2)
| ~ product(e_3,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_34,c_0_111]) ).
cnf(c_0_116,plain,
product(e_4,e_3,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_112]),c_0_72]) ).
cnf(c_0_117,negated_conjecture,
( ~ product(e_2,X1,e_1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_26,c_0_105]) ).
cnf(c_0_118,plain,
( ~ group_element(X1)
| product(e_4,X1,e_3)
| product(e_3,X1,e_3)
| product(e_2,X1,e_3)
| product(e_1,X1,e_3) ),
inference(spm,[status(thm)],[c_0_82,c_0_36]) ).
cnf(c_0_119,plain,
( ~ product(e_3,e_4,e_2)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_44,c_0_113]) ).
cnf(c_0_120,plain,
( ~ product(e_3,e_3,e_4)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_114,c_0_71]) ).
cnf(c_0_121,plain,
( ~ product(X1,e_4,e_2)
| ~ product(e_4,e_4,e_3)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_31,c_0_49]) ).
cnf(c_0_122,plain,
~ product(e_3,e_3,e_4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_115,c_0_116])]) ).
cnf(c_0_123,negated_conjecture,
( ~ product(e_4,e_3,X1)
| product(X1,e_4,e_1)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_93,c_0_42]) ).
cnf(c_0_124,negated_conjecture,
~ product(e_2,e_4,e_1),
inference(spm,[status(thm)],[c_0_72,c_0_117]) ).
cnf(c_0_125,plain,
( product(e_1,e_4,e_3)
| product(e_2,e_4,e_3)
| product(e_4,e_4,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_24]),c_0_76]) ).
cnf(c_0_126,negated_conjecture,
~ product(e_2,e_4,e_3),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_101]),c_0_120]) ).
cnf(c_0_127,plain,
( ~ product(e_3,e_4,e_2)
| ~ product(e_4,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_44,c_0_121]) ).
cnf(c_0_128,negated_conjecture,
product(e_3,e_4,e_2),
inference(sr,[status(thm)],[c_0_101,c_0_122]) ).
cnf(c_0_129,plain,
~ equalish(e_3,e_2),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_2]) ).
cnf(c_0_130,negated_conjecture,
product(e_1,e_4,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_116]),c_0_124]) ).
cnf(c_0_131,plain,
( product(e_4,e_4,e_3)
| product(e_1,e_4,e_3) ),
inference(sr,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_132,plain,
~ product(e_4,e_4,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_127,c_0_128])]) ).
cnf(c_0_133,plain,
~ equalish(e_3,e_2),
c_0_129 ).
cnf(c_0_134,negated_conjecture,
( ~ product(e_1,e_4,X1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_88,c_0_130]) ).
cnf(c_0_135,plain,
product(e_1,e_4,e_3),
inference(sr,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_136,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_135])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP127-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/5.38 % Computer : n016.cluster.edu
% 0.14/5.38 % Model : x86_64 x86_64
% 0.14/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.38 % Memory : 8046.5625MB
% 0.14/5.38 % OS : Linux 6.8.0-71-generic
% 0.14/5.38 % CPULimit : 300
% 0.14/5.38 % WCLimit : 300
% 0.14/5.38 % DateTime : Sun Sep 20 20:04:42 UTC 2026
% 0.14/5.38 % CPUTime :
% 0.14/5.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/5.43 Running first-order theorem proving
% 0.15/5.43 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
% 0.15/5.46 % Version: 3.5.1
% 0.15/5.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.46 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.46 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.46 % Starting sh5l with 300s (1) cores
% 0.15/5.46 % new_bool_3 with pid 673233 completed with status 0
% 0.15/5.46 % Result found by new_bool_3
% 0.15/5.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.46 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/5.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/5.46 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.15/5.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/5.46 % Starting SubtermCWHack with 31s (1) cores
% 0.15/5.46 % SubtermCWHack with pid 673239 completed with status 0
% 0.15/5.46 % Result found by SubtermCWHack
% 0.15/5.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.47 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/5.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/5.47 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.15/5.47 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/5.47 % Starting SubtermCWHack with 31s (1) cores
% 0.15/5.47 % Preprocessing time : 0.001 s
% 0.15/5.47
% 0.15/5.47 % Proof found!
% 0.15/5.47 % SZS status Unsatisfiable
% 0.15/5.47 % SZS output start CNFRefutation
% See solution above
% 0.15/5.47 % Parsed axioms : 26
% 0.15/5.47 % Removed by relevancy pruning/SinE : 0
% 0.15/5.47 % Initial clauses : 26
% 0.15/5.47 % Removed in clause preprocessing : 0
% 0.15/5.47 % Initial clauses in saturation : 26
% 0.15/5.47 % Processed clauses : 402
% 0.15/5.47 % ...of these trivial : 2
% 0.15/5.47 % ...subsumed : 56
% 0.15/5.47 % ...remaining for further processing : 344
% 0.15/5.47 % Other redundant clauses eliminated : 0
% 0.15/5.47 % Clauses deleted for lack of memory : 0
% 0.15/5.47 % Backward-subsumed : 178
% 0.15/5.47 % Backward-rewritten : 26
% 0.15/5.47 % Generated clauses : 909
% 0.15/5.47 % ...of the previous two non-redundant : 852
% 0.15/5.47 % ...aggressively subsumed : 0
% 0.15/5.47 % Contextual simplify-reflections : 8
% 0.15/5.47 % Paramodulations : 893
% 0.15/5.47 % Factorizations : 0
% 0.15/5.47 % NegExts : 0
% 0.15/5.47 % Equation resolutions : 0
% 0.15/5.47 % Disequality decompositions : 0
% 0.15/5.47 % Total rewrite steps : 49
% 0.15/5.47 % ...of those cached : 36
% 0.15/5.47 % Propositional unsat checks : 0
% 0.15/5.47 % Propositional check models : 0
% 0.15/5.47 % Propositional check unsatisfiable : 0
% 0.15/5.47 % Propositional clauses : 0
% 0.15/5.47 % Propositional clauses after purity: 0
% 0.15/5.47 % Propositional unsat core size : 0
% 0.15/5.47 % Propositional preprocessing time : 0.000
% 0.15/5.47 % Propositional encoding time : 0.000
% 0.15/5.47 % Propositional solver time : 0.000
% 0.15/5.47 % Success case prop preproc time : 0.000
% 0.15/5.47 % Success case prop encoding time : 0.000
% 0.15/5.47 % Success case prop solver time : 0.000
% 0.15/5.47 % Current number of processed clauses : 124
% 0.15/5.47 % Positive orientable unit clauses : 13
% 0.15/5.47 % Positive unorientable unit clauses: 0
% 0.15/5.47 % Negative unit clauses : 46
% 0.15/5.47 % Non-unit-clauses : 65
% 0.15/5.47 % Current number of unprocessed clauses: 405
% 0.15/5.47 % ...number of literals in the above : 1593
% 0.15/5.47 % Current number of archived formulas : 0
% 0.15/5.47 % Current number of archived clauses : 220
% 0.15/5.47 % Clause-clause subsumption calls (NU) : 6455
% 0.15/5.47 % Rec. Clause-clause subsumption calls : 4867
% 0.15/5.47 % Non-unit clause-clause subsumptions : 64
% 0.15/5.47 % Unit Clause-clause subsumption calls : 1025
% 0.15/5.47 % Rewrite failures with RHS unbound : 0
% 0.15/5.47 % BW rewrite match attempts : 46
% 0.15/5.47 % BW rewrite match successes : 6
% 0.15/5.47 % Condensation attempts : 0
% 0.15/5.47 % Condensation successes : 0
% 0.15/5.47 % Termbank termtop insertions : 10493
% 0.15/5.47 % Search garbage collected termcells : 60
% 0.15/5.47
% 0.15/5.47 % -------------------------------------------------
% 0.15/5.47 % User time : 0.017 s
% 0.15/5.47 % System time : 0.005 s
% 0.15/5.47 % Total time : 0.021 s
% 0.15/5.47 % Maximum resident set size: 3648 pages
% 0.15/5.47
% 0.15/5.47 % -------------------------------------------------
% 0.15/5.47 % User time : 0.017 s
% 0.15/5.47 % System time : 0.009 s
% 0.15/5.47 % Total time : 0.027 s
% 0.15/5.47 % Maximum resident set size: 4608 pages
% 0.15/5.47 % E exiting
%------------------------------------------------------------------------------