%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP124-1.004 : 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 : n003.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 12:41:53 PM UTC 2026
% Result : Unsatisfiable 0.24s 0.60s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 19
% Syntax : Number of clauses : 133 ( 49 unt; 34 nHn; 131 RR)
% Number of literals : 306 ( 0 equ; 153 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 : 76 ( 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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
cnf(element_4,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
cnf(product_idempotence,axiom,
product(X1,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
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(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(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
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(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(qg2_2,negated_conjecture,
( ~ product(X6,X4,X5)
| ~ product(X6,X1,X2)
| ~ product(X4,X5,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2_2) ).
cnf(e_2_is_not_e_4,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
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_2,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
cnf(e_3_is_not_e_4,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
cnf(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
cnf(c_0_19,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_20,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
inference(fof_simplification,[status(thm)],[product_right_cancellation]) ).
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) ),
c_0_19 ).
cnf(c_0_22,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_23,axiom,
group_element(e_4),
element_4 ).
cnf(c_0_24,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_20 ).
cnf(c_0_25,axiom,
product(X1,X1,X1),
product_idempotence ).
cnf(c_0_26,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_21,c_0_22]) ).
cnf(c_0_27,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_28,plain,
~ equalish(e_3,e_1),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_1]) ).
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,
( ~ 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_21,c_0_23]) ).
cnf(c_0_31,plain,
~ equalish(e_4,e_1),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_1]) ).
cnf(c_0_32,plain,
( ~ product(X2,X1,X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_33,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_26,c_0_27]) ).
cnf(c_0_34,plain,
~ equalish(e_3,e_1),
c_0_28 ).
cnf(c_0_35,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_29 ).
cnf(c_0_36,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_30,c_0_27]) ).
cnf(c_0_37,plain,
~ equalish(e_4,e_1),
c_0_31 ).
cnf(c_0_38,plain,
~ equalish(e_1,e_4),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_4]) ).
cnf(c_0_39,plain,
~ equalish(e_2,e_3),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_3]) ).
cnf(c_0_40,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_33]),c_0_34]) ).
cnf(c_0_41,plain,
( ~ product(X1,X2,X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_25]) ).
cnf(c_0_42,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_36]),c_0_37]) ).
cnf(c_0_43,plain,
~ equalish(e_1,e_4),
c_0_38 ).
cnf(c_0_44,plain,
~ equalish(e_2,e_3),
c_0_39 ).
cnf(c_0_45,plain,
( ~ product(e_1,X1,e_4)
| equalish(X1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_24,c_0_40]) ).
cnf(c_0_46,plain,
~ equalish(e_1,e_3),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_3]) ).
cnf(c_0_47,negated_conjecture,
( ~ product(X6,X4,X5)
| ~ product(X6,X1,X2)
| ~ product(X4,X5,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X5) ),
inference(fof_simplification,[status(thm)],[qg2_2]) ).
cnf(c_0_48,plain,
~ equalish(e_2,e_4),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_4]) ).
cnf(c_0_49,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_41,c_0_42]),c_0_43]) ).
cnf(c_0_50,plain,
( ~ product(e_1,e_2,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_45]) ).
cnf(c_0_51,plain,
~ equalish(e_1,e_3),
c_0_46 ).
cnf(c_0_52,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_53,negated_conjecture,
( ~ product(X6,X4,X5)
| ~ product(X6,X1,X2)
| ~ product(X4,X5,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X5) ),
c_0_47 ).
cnf(c_0_54,plain,
~ equalish(e_2,e_4),
c_0_48 ).
cnf(c_0_55,plain,
( ~ product(e_1,X1,e_3)
| equalish(X1,e_4)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_24,c_0_49]) ).
cnf(c_0_56,plain,
( ~ product(e_1,e_2,e_4)
| product(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_50]),c_0_51]) ).
cnf(c_0_57,plain,
( ~ group_element(X1)
| product(X1,e_2,e_4)
| product(X1,e_2,e_3)
| product(X1,e_2,e_2)
| product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_21,c_0_52]) ).
cnf(c_0_58,plain,
~ equalish(e_2,e_1),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_1]) ).
cnf(c_0_59,negated_conjecture,
( ~ product(X3,X1,X4)
| ~ product(X2,X2,X4)
| ~ product(X2,X3,X1)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_53,c_0_25]) ).
cnf(c_0_60,plain,
( ~ product(e_1,e_2,e_3)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_61,plain,
( ~ product(X1,e_3,e_2)
| ~ product(e_1,e_2,e_4)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_35,c_0_56]) ).
cnf(c_0_62,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_57,c_0_27]) ).
cnf(c_0_63,plain,
~ equalish(e_2,e_1),
c_0_58 ).
cnf(c_0_64,negated_conjecture,
( ~ product(e_4,e_3,X1)
| ~ product(e_1,e_1,X1)
| product(e_1,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_49]),c_0_34]) ).
cnf(c_0_65,plain,
( ~ product(X1,e_4,e_2)
| ~ product(e_1,e_2,e_3)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_35,c_0_60]) ).
cnf(c_0_66,plain,
( ~ product(e_4,e_3,e_2)
| ~ product(e_1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_37,c_0_61]) ).
cnf(c_0_67,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_62]),c_0_63]) ).
cnf(c_0_68,negated_conjecture,
( ~ product(e_4,e_3,e_1)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_64,c_0_25]) ).
cnf(c_0_69,plain,
( ~ product(e_3,e_4,e_2)
| ~ product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_34,c_0_65]) ).
cnf(c_0_70,plain,
( ~ product(e_4,e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_71,plain,
~ equalish(e_1,e_2),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_2]) ).
cnf(c_0_72,plain,
( ~ group_element(X1)
| product(X1,e_1,e_4)
| product(X1,e_1,e_3)
| product(X1,e_1,e_2)
| product(X1,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_21,c_0_27]) ).
cnf(c_0_73,negated_conjecture,
( ~ product(X1,e_4,e_2)
| ~ product(e_4,e_3,e_1)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_35,c_0_68]) ).
cnf(c_0_74,plain,
( ~ product(e_4,e_3,e_2)
| ~ product(e_3,e_4,e_2)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_75,plain,
~ equalish(e_1,e_2),
c_0_71 ).
cnf(c_0_76,plain,
( product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_72,c_0_23]) ).
cnf(c_0_77,plain,
( ~ product(X1,e_4,e_3)
| equalish(X1,e_1)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_35,c_0_49]) ).
cnf(c_0_78,plain,
( ~ product(e_2,e_4,e_2)
| ~ product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_63,c_0_65]) ).
cnf(c_0_79,negated_conjecture,
( ~ product(e_3,e_4,e_2)
| ~ product(e_4,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_34,c_0_73]) ).
cnf(c_0_80,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_26,c_0_23]) ).
cnf(c_0_81,plain,
( ~ product(e_4,e_3,e_2)
| ~ product(e_3,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_74]),c_0_75]) ).
cnf(c_0_82,plain,
~ equalish(e_3,e_4),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_4]) ).
cnf(c_0_83,plain,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_76]),c_0_37]) ).
cnf(c_0_84,plain,
( ~ product(e_2,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_63,c_0_77]) ).
cnf(c_0_85,plain,
( ~ product(e_4,e_3,e_2)
| ~ product(e_2,e_4,e_2)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_78,c_0_70]) ).
cnf(c_0_86,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_30,c_0_22]) ).
cnf(c_0_87,negated_conjecture,
( ~ product(e_3,e_4,e_2)
| product(e_4,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_88,plain,
~ equalish(e_3,e_4),
c_0_82 ).
cnf(c_0_89,plain,
~ equalish(e_4,e_3),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_3]) ).
cnf(c_0_90,plain,
( product(e_4,e_1,e_2)
| product(e_4,e_1,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_83]),c_0_43]) ).
cnf(c_0_91,negated_conjecture,
( ~ product(e_4,e_2,X1)
| ~ product(e_1,e_1,X1)
| ~ product(e_1,e_2,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_63]) ).
cnf(c_0_92,plain,
( ~ product(e_1,X1,e_2)
| ~ product(e_2,e_4,e_3)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_24,c_0_84]) ).
cnf(c_0_93,negated_conjecture,
( ~ product(e_2,e_4,e_2)
| ~ product(e_4,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_63,c_0_73]) ).
cnf(c_0_94,plain,
( ~ product(e_4,e_3,e_2)
| ~ product(e_2,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_85]),c_0_75]) ).
cnf(c_0_95,plain,
( ~ product(X1,e_4,e_1)
| equalish(X1,e_3)
| product(e_3,e_4,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_35,c_0_86]) ).
cnf(c_0_96,negated_conjecture,
( ~ product(e_3,e_4,e_2)
| product(e_4,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_87]),c_0_88]) ).
cnf(c_0_97,plain,
~ equalish(e_4,e_3),
c_0_89 ).
cnf(c_0_98,negated_conjecture,
( ~ product(e_1,e_3,X1)
| ~ product(e_4,e_4,X1)
| product(e_4,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_90]),c_0_88]) ).
cnf(c_0_99,negated_conjecture,
( ~ product(e_4,e_2,e_1)
| ~ product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_91,c_0_25]) ).
cnf(c_0_100,plain,
( ~ product(e_1,e_3,e_2)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_88,c_0_92]) ).
cnf(c_0_101,negated_conjecture,
( ~ product(e_2,e_4,e_2)
| product(e_4,e_3,e_4)
| product(e_4,e_3,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_80]),c_0_94]) ).
cnf(c_0_102,plain,
( ~ product(e_2,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_44,c_0_95]) ).
cnf(c_0_103,negated_conjecture,
~ product(e_3,e_4,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_96]),c_0_97]) ).
cnf(c_0_104,negated_conjecture,
( product(e_4,e_1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_40]),c_0_25])]) ).
cnf(c_0_105,negated_conjecture,
( ~ product(e_4,e_2,X1)
| ~ product(e_1,e_1,X1)
| ~ product(e_4,e_3,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_68]),c_0_63]) ).
cnf(c_0_106,negated_conjecture,
( ~ product(e_4,e_3,e_2)
| ~ product(e_4,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_99,c_0_70]) ).
cnf(c_0_107,plain,
( ~ product(e_1,e_2,e_4)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_100,c_0_56]) ).
cnf(c_0_108,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_54,c_0_92]) ).
cnf(c_0_109,negated_conjecture,
( ~ product(e_2,e_4,e_2)
| product(e_4,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_101]),c_0_88]) ).
cnf(c_0_110,plain,
( ~ product(e_2,e_4,e_1)
| product(e_3,e_4,e_3) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_102]),c_0_88]),c_0_103]) ).
cnf(c_0_111,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_4,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_104]),c_0_51]) ).
cnf(c_0_112,negated_conjecture,
( ~ product(e_4,e_2,e_1)
| ~ product(e_4,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_105,c_0_25]) ).
cnf(c_0_113,negated_conjecture,
( ~ product(e_4,e_3,e_2)
| ~ product(e_4,e_2,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_106]),c_0_75]) ).
cnf(c_0_114,plain,
( ~ product(e_2,e_4,e_3)
| product(e_1,e_2,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_67]),c_0_108]) ).
cnf(c_0_115,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_30,c_0_52]) ).
cnf(c_0_116,negated_conjecture,
~ product(e_2,e_4,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_109]),c_0_97]) ).
cnf(c_0_117,plain,
~ product(e_2,e_4,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_110]),c_0_97]) ).
cnf(c_0_118,negated_conjecture,
( ~ product(e_2,e_4,e_3)
| product(e_4,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_100,c_0_111]) ).
cnf(c_0_119,negated_conjecture,
( ~ product(e_4,e_2,e_1)
| product(e_4,e_3,e_4)
| product(e_4,e_3,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_80]),c_0_113]) ).
cnf(c_0_120,plain,
( ~ product(X1,e_2,e_3)
| ~ product(e_2,e_4,e_3)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_35,c_0_114]) ).
cnf(c_0_121,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_4,e_3) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_115,c_0_116]),c_0_117]) ).
cnf(c_0_122,negated_conjecture,
( ~ product(e_4,X1,e_2)
| ~ product(e_2,e_4,e_3)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_24,c_0_118]) ).
cnf(c_0_123,negated_conjecture,
( ~ product(e_4,e_2,e_1)
| product(e_4,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_119]),c_0_88]) ).
cnf(c_0_124,plain,
( ~ product(e_4,e_2,e_3)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_37,c_0_120]) ).
cnf(c_0_125,plain,
product(e_2,e_4,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_121]),c_0_54]) ).
cnf(c_0_126,negated_conjecture,
( ~ product(e_4,e_2,e_2)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_63,c_0_122]) ).
cnf(c_0_127,plain,
( product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_57,c_0_23]) ).
cnf(c_0_128,negated_conjecture,
~ product(e_4,e_2,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_123]),c_0_97]) ).
cnf(c_0_129,plain,
~ product(e_4,e_2,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_124,c_0_125])]) ).
cnf(c_0_130,negated_conjecture,
~ product(e_4,e_2,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_125])]) ).
cnf(c_0_131,plain,
product(e_4,e_2,e_4),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_127,c_0_128]),c_0_129]),c_0_130]) ).
cnf(c_0_132,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_131]),c_0_54]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP124-1.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.45 % Computer : n003.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sun Sep 20 20:00:15 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.52 Running first-order theorem proving
% 0.20/0.52 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
% 0.24/0.60 % Version: 3.5.1
% 0.24/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.60 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.60 % Starting sh5l with 300s (1) cores
% 0.24/0.60 % new_bool_3 with pid 2448877 completed with status 0
% 0.24/0.60 % Result found by new_bool_3
% 0.24/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.60 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/0.60 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/0.60 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.24/0.60 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.60 % Starting SubtermCWHack with 31s (1) cores
% 0.24/0.60 % SubtermCWHack with pid 2448882 completed with status 0
% 0.24/0.60 % Result found by SubtermCWHack
% 0.24/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.60 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/0.60 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/0.60 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.24/0.60 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.60 % Starting SubtermCWHack with 31s (1) cores
% 0.24/0.60 % Preprocessing time : 0.001 s
% 0.24/0.60
% 0.24/0.60 % Proof found!
% 0.24/0.60 % SZS status Unsatisfiable
% 0.24/0.60 % SZS output start CNFRefutation
% See solution above
% 0.24/0.61 % Parsed axioms : 23
% 0.24/0.61 % Removed by relevancy pruning/SinE : 0
% 0.24/0.61 % Initial clauses : 23
% 0.24/0.61 % Removed in clause preprocessing : 0
% 0.24/0.61 % Initial clauses in saturation : 23
% 0.24/0.61 % Processed clauses : 825
% 0.24/0.61 % ...of these trivial : 3
% 0.24/0.61 % ...subsumed : 203
% 0.24/0.61 % ...remaining for further processing : 619
% 0.24/0.61 % Other redundant clauses eliminated : 0
% 0.24/0.61 % Clauses deleted for lack of memory : 0
% 0.24/0.61 % Backward-subsumed : 405
% 0.24/0.61 % Backward-rewritten : 78
% 0.24/0.61 % Generated clauses : 1720
% 0.24/0.61 % ...of the previous two non-redundant : 1714
% 0.24/0.61 % ...aggressively subsumed : 0
% 0.24/0.61 % Contextual simplify-reflections : 10
% 0.24/0.61 % Paramodulations : 1707
% 0.24/0.61 % Factorizations : 0
% 0.24/0.61 % NegExts : 0
% 0.24/0.61 % Equation resolutions : 0
% 0.24/0.61 % Disequality decompositions : 0
% 0.24/0.61 % Total rewrite steps : 121
% 0.24/0.61 % ...of those cached : 109
% 0.24/0.61 % Propositional unsat checks : 0
% 0.24/0.61 % Propositional check models : 0
% 0.24/0.61 % Propositional check unsatisfiable : 0
% 0.24/0.61 % Propositional clauses : 0
% 0.24/0.61 % Propositional clauses after purity: 0
% 0.24/0.61 % Propositional unsat core size : 0
% 0.24/0.61 % Propositional preprocessing time : 0.000
% 0.24/0.61 % Propositional encoding time : 0.000
% 0.24/0.61 % Propositional solver time : 0.000
% 0.24/0.61 % Success case prop preproc time : 0.000
% 0.24/0.61 % Success case prop encoding time : 0.000
% 0.24/0.61 % Success case prop solver time : 0.000
% 0.24/0.61 % Current number of processed clauses : 123
% 0.24/0.61 % Positive orientable unit clauses : 11
% 0.24/0.61 % Positive unorientable unit clauses: 0
% 0.24/0.61 % Negative unit clauses : 49
% 0.24/0.61 % Non-unit-clauses : 63
% 0.24/0.61 % Current number of unprocessed clauses: 220
% 0.24/0.61 % ...number of literals in the above : 923
% 0.24/0.61 % Current number of archived formulas : 0
% 0.24/0.61 % Current number of archived clauses : 496
% 0.24/0.61 % Clause-clause subsumption calls (NU) : 11209
% 0.24/0.61 % Rec. Clause-clause subsumption calls : 6256
% 0.24/0.61 % Non-unit clause-clause subsumptions : 244
% 0.24/0.61 % Unit Clause-clause subsumption calls : 3051
% 0.24/0.61 % Rewrite failures with RHS unbound : 0
% 0.24/0.61 % BW rewrite match attempts : 38
% 0.24/0.61 % BW rewrite match successes : 4
% 0.24/0.61 % Condensation attempts : 0
% 0.24/0.61 % Condensation successes : 0
% 0.24/0.61 % Termbank termtop insertions : 20244
% 0.24/0.61 % Search garbage collected termcells : 57
% 0.24/0.61
% 0.24/0.61 % -------------------------------------------------
% 0.24/0.61 % User time : 0.051 s
% 0.24/0.61 % System time : 0.006 s
% 0.24/0.61 % Total time : 0.057 s
% 0.24/0.61 % Maximum resident set size: 3644 pages
% 0.24/0.61
% 0.24/0.61 % -------------------------------------------------
% 0.24/0.61 % User time : 0.053 s
% 0.24/0.61 % System time : 0.012 s
% 0.24/0.61 % Total time : 0.065 s
% 0.24/0.61 % Maximum resident set size: 4864 pages
% 0.24/0.61 % E exiting
%------------------------------------------------------------------------------