%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP133-1.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 12:42:37 PM UTC 2026
% Result : Unsatisfiable 0.49s 0.49s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 14
% Syntax : Number of clauses : 140 ( 34 unt; 90 nHn; 140 RR)
% Number of literals : 403 ( 0 equ; 96 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 96 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_total_function1,axiom,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
cnf(qg3,negated_conjecture,
( ~ product(X2,X1,X4)
| ~ product(X1,X2,X3)
| product(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).
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(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
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_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
cnf(e_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_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
cnf(e_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_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_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
cnf(product_total_function2,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).
cnf(c_0_14,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
inference(fof_simplification,[status(thm)],[product_total_function1]) ).
cnf(c_0_15,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
c_0_14 ).
cnf(c_0_16,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_17,negated_conjecture,
( ~ product(X2,X1,X4)
| ~ product(X1,X2,X3)
| product(X3,X4,X1) ),
inference(fof_simplification,[status(thm)],[qg3]) ).
cnf(c_0_18,plain,
( ~ group_element(X1)
| product(X1,e_3,e_1)
| product(X1,e_3,e_2)
| product(X1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
( ~ product(X2,X1,X4)
| ~ product(X1,X2,X3)
| product(X3,X4,X1) ),
c_0_17 ).
cnf(c_0_20,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_21,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
inference(fof_simplification,[status(thm)],[product_left_cancellation]) ).
cnf(c_0_22,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_23,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
inference(fof_simplification,[status(thm)],[product_right_cancellation]) ).
cnf(c_0_24,negated_conjecture,
( ~ product(e_3,e_3,X1)
| product(X1,e_1,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_21 ).
cnf(c_0_26,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_27,plain,
~ equalish(e_1,e_3),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_3]) ).
cnf(c_0_28,plain,
( ~ group_element(X1)
| product(X1,e_2,e_1)
| product(X1,e_2,e_2)
| product(X1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_29,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_23 ).
cnf(c_0_30,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_31,plain,
~ equalish(e_2,e_3),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_3]) ).
cnf(c_0_32,negated_conjecture,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_24,c_0_20]) ).
cnf(c_0_33,plain,
( ~ product(X1,e_3,e_1)
| equalish(X1,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_34,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_18,c_0_26]) ).
cnf(c_0_35,plain,
~ equalish(e_1,e_3),
c_0_27 ).
cnf(c_0_36,plain,
~ equalish(e_3,e_1),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_1]) ).
cnf(c_0_37,plain,
( ~ group_element(X1)
| product(X1,e_1,e_1)
| product(X1,e_1,e_2)
| product(X1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_15,c_0_26]) ).
cnf(c_0_38,plain,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_28,c_0_22]) ).
cnf(c_0_39,plain,
( ~ product(e_2,X1,e_1)
| equalish(X1,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_40,plain,
~ equalish(e_2,e_3),
c_0_31 ).
cnf(c_0_41,plain,
~ equalish(e_1,e_2),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_2]) ).
cnf(c_0_42,negated_conjecture,
( ~ product(e_1,X1,e_3)
| equalish(X1,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_29,c_0_32]) ).
cnf(c_0_43,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_44,plain,
~ equalish(e_3,e_1),
c_0_36 ).
cnf(c_0_45,plain,
( ~ product(e_3,X1,e_1)
| equalish(X1,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_29,c_0_20]) ).
cnf(c_0_46,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_37,c_0_16]) ).
cnf(c_0_47,negated_conjecture,
( ~ product(e_2,e_2,X1)
| product(X1,e_1,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_19,c_0_38]) ).
cnf(c_0_48,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_38]),c_0_40]) ).
cnf(c_0_49,plain,
( ~ product(e_2,X1,e_1)
| equalish(X1,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_29,c_0_38]) ).
cnf(c_0_50,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_37,c_0_22]) ).
cnf(c_0_51,plain,
~ equalish(e_1,e_2),
c_0_41 ).
cnf(c_0_52,negated_conjecture,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_53,negated_conjecture,
( ~ product(X1,e_1,e_3)
| equalish(X1,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_32]) ).
cnf(c_0_54,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_35]) ).
cnf(c_0_55,negated_conjecture,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_47,c_0_38]) ).
cnf(c_0_56,plain,
( ~ product(e_2,X1,e_3)
| equalish(X1,e_3)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_29,c_0_48]) ).
cnf(c_0_57,plain,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
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(e_3,e_1,X1)
| product(X1,e_2,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_19,c_0_52]) ).
cnf(c_0_60,negated_conjecture,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_44]) ).
cnf(c_0_61,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_28,c_0_16]) ).
cnf(c_0_62,negated_conjecture,
( ~ product(X1,e_1,e_2)
| equalish(X1,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_55]) ).
cnf(c_0_63,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_35]) ).
cnf(c_0_64,plain,
~ equalish(e_2,e_1),
c_0_58 ).
cnf(c_0_65,negated_conjecture,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_66,plain,
( ~ product(X1,e_2,e_1)
| equalish(X1,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_61]) ).
cnf(c_0_67,negated_conjecture,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]) ).
cnf(c_0_68,negated_conjecture,
( ~ product(e_3,X1,e_3)
| equalish(X1,e_3)
| product(e_2,e_2,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_29,c_0_65]) ).
cnf(c_0_69,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_38]),c_0_40]) ).
cnf(c_0_70,plain,
~ equalish(e_3,e_2),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_2]) ).
cnf(c_0_71,negated_conjecture,
( ~ product(X1,e_3,e_2)
| equalish(X1,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_67]) ).
cnf(c_0_72,negated_conjecture,
( product(e_3,e_3,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_3,e_2,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_40]) ).
cnf(c_0_73,plain,
~ equalish(e_3,e_2),
c_0_70 ).
cnf(c_0_74,negated_conjecture,
( ~ product(e_3,e_2,X1)
| product(X1,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_19,c_0_67]) ).
cnf(c_0_75,negated_conjecture,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_3,e_2,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_76,negated_conjecture,
( ~ product(e_1,e_2,X1)
| product(X1,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_19,c_0_50]) ).
cnf(c_0_77,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_28,c_0_26]) ).
cnf(c_0_78,negated_conjecture,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_79,plain,
( ~ product(X1,e_1,e_1)
| equalish(X1,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_50]) ).
cnf(c_0_80,negated_conjecture,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_81,plain,
( ~ product(X1,e_1,e_1)
| equalish(X1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_46]) ).
cnf(c_0_82,negated_conjecture,
( ~ product(X1,e_2,e_3)
| equalish(X1,e_2)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_78]) ).
cnf(c_0_83,negated_conjecture,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_51]) ).
cnf(c_0_84,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_50]),c_0_40]) ).
cnf(c_0_85,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_37,c_0_26]) ).
cnf(c_0_86,plain,
( ~ product(e_1,X1,e_1)
| equalish(X1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_29,c_0_34]) ).
cnf(c_0_87,negated_conjecture,
( ~ product(e_2,e_2,X1)
| product(X1,e_3,e_2)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_19,c_0_78]) ).
cnf(c_0_88,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_1,e_2,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_51]) ).
cnf(c_0_89,plain,
( ~ product(X1,e_1,e_3)
| equalish(X1,e_3)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_84]) ).
cnf(c_0_90,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_85]),c_0_51]) ).
cnf(c_0_91,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_77]),c_0_40]) ).
cnf(c_0_92,plain,
( ~ product(e_1,X1,e_1)
| equalish(X1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_29,c_0_77]) ).
cnf(c_0_93,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_87,c_0_78]) ).
cnf(c_0_94,negated_conjecture,
( ~ product(e_1,X1,e_2)
| equalish(X1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_29,c_0_88]) ).
cnf(c_0_95,plain,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_1,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_35]) ).
cnf(c_0_96,plain,
( ~ product(e_1,X1,e_3)
| equalish(X1,e_3)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_29,c_0_91]) ).
cnf(c_0_97,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_85]),c_0_51]) ).
cnf(c_0_98,negated_conjecture,
( ~ product(e_3,X1,e_2)
| equalish(X1,e_3)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_29,c_0_93]) ).
cnf(c_0_99,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_3,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_51]) ).
cnf(c_0_100,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_35]) ).
cnf(c_0_101,negated_conjecture,
( ~ product(e_2,X1,e_3)
| equalish(X1,e_2)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_29,c_0_78]) ).
cnf(c_0_102,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_35]) ).
cnf(c_0_103,plain,
( ~ product(X1,e_1,e_2)
| equalish(X1,e_1)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_100]) ).
cnf(c_0_104,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_2,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_51]) ).
cnf(c_0_105,negated_conjecture,
( ~ product(X1,e_3,e_2)
| equalish(X1,e_3)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_93]) ).
cnf(c_0_106,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_64]) ).
cnf(c_0_107,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
inference(fof_simplification,[status(thm)],[product_total_function2]) ).
cnf(c_0_108,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_35]) ).
cnf(c_0_109,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
c_0_107 ).
cnf(c_0_110,negated_conjecture,
( ~ product(e_1,e_2,X1)
| product(X1,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_19,c_0_104]) ).
cnf(c_0_111,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_1,e_2,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_108]),c_0_51]) ).
cnf(c_0_112,negated_conjecture,
( ~ product(e_2,e_2,X1)
| equalish(X1,e_3)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_109,c_0_78]) ).
cnf(c_0_113,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_114,negated_conjecture,
product(e_2,e_2,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_35]) ).
cnf(c_0_115,negated_conjecture,
( ~ product(X1,e_2,e_2)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_114]) ).
cnf(c_0_116,negated_conjecture,
( ~ product(e_2,X1,e_2)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_29,c_0_114]) ).
cnf(c_0_117,negated_conjecture,
~ product(e_1,e_2,e_2),
inference(spm,[status(thm)],[c_0_51,c_0_115]) ).
cnf(c_0_118,negated_conjecture,
~ product(e_2,e_1,e_2),
inference(spm,[status(thm)],[c_0_51,c_0_116]) ).
cnf(c_0_119,negated_conjecture,
( ~ product(e_1,e_2,X1)
| equalish(X1,e_3)
| product(e_1,e_2,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_109,c_0_83]) ).
cnf(c_0_120,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_3) ),
inference(sr,[status(thm)],[c_0_77,c_0_117]) ).
cnf(c_0_121,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_3) ),
inference(sr,[status(thm)],[c_0_50,c_0_118]) ).
cnf(c_0_122,negated_conjecture,
( product(e_2,e_1,e_3)
| product(e_1,e_2,e_3) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_118]),c_0_117]),c_0_35]) ).
cnf(c_0_123,negated_conjecture,
( ~ product(e_3,e_2,X1)
| product(X1,e_1,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_19,c_0_30]) ).
cnf(c_0_124,plain,
( ~ product(X1,e_1,e_1)
| equalish(X1,e_2)
| product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_121]) ).
cnf(c_0_125,negated_conjecture,
( product(e_2,e_1,e_3)
| product(e_3,e_1,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_122]),c_0_118]) ).
cnf(c_0_126,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_50]),c_0_35]) ).
cnf(c_0_127,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_1,e_1,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_123,c_0_61]) ).
cnf(c_0_128,negated_conjecture,
~ product(e_2,e_3,e_2),
inference(spm,[status(thm)],[c_0_73,c_0_116]) ).
cnf(c_0_129,negated_conjecture,
~ product(e_3,e_2,e_2),
inference(spm,[status(thm)],[c_0_73,c_0_115]) ).
cnf(c_0_130,negated_conjecture,
product(e_2,e_1,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_73]) ).
cnf(c_0_131,plain,
( ~ product(X1,e_1,e_3)
| equalish(X1,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_126]) ).
cnf(c_0_132,negated_conjecture,
( product(e_3,e_2,e_3)
| product(e_1,e_1,e_3)
| product(e_2,e_3,e_3) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_127,c_0_128]),c_0_129]) ).
cnf(c_0_133,negated_conjecture,
( ~ product(e_2,X1,e_3)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_29,c_0_130]) ).
cnf(c_0_134,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_3,e_2,e_3) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_128]),c_0_118]),c_0_51]) ).
cnf(c_0_135,negated_conjecture,
~ product(e_2,e_3,e_3),
inference(spm,[status(thm)],[c_0_44,c_0_133]) ).
cnf(c_0_136,negated_conjecture,
( ~ product(X1,e_1,e_3)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_130]) ).
cnf(c_0_137,negated_conjecture,
product(e_3,e_2,e_3),
inference(sr,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_138,negated_conjecture,
~ product(e_3,e_1,e_3),
inference(spm,[status(thm)],[c_0_73,c_0_136]) ).
cnf(c_0_139,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_137]),c_0_135]),c_0_128]),c_0_138]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP133-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 20:04:50 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.49/0.49 % Version: 3.5.1
% 0.49/0.49 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.49/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.49/0.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.49/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.49/0.49 % Starting new_bool_1 with 300s (1) cores
% 0.49/0.49 % Starting sh5l with 300s (1) cores
% 0.49/0.49 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3808115 completed with status 0
% 0.49/0.49 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.49/0.49 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.49/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.49/0.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.49/0.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.49/0.49 % No SInE strategy applied
% 0.49/0.49 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.49/0.49 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.49/0.49 % Starting SubtermCWHack with 136s (1) cores
% 0.49/0.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.49/0.49 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.49/0.49 % Starting new_bool_3 with 136s (1) cores
% 0.49/0.49 % Starting new_bool_1 with 136s (1) cores
% 0.49/0.49 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3808120 completed with status 0
% 0.49/0.49 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.49/0.49 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.49/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.49/0.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.49/0.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.49/0.49 % No SInE strategy applied
% 0.49/0.49 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.49/0.49 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.49/0.49 % Starting SubtermCWHack with 136s (1) cores
% 0.49/0.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.49/0.49 % Preprocessing time : 0.001 s
% 0.49/0.49 % Presaturation interreduction done
% 0.49/0.49
% 0.49/0.49 % Proof found!
% 0.49/0.49 % SZS status Unsatisfiable
% 0.49/0.49 % SZS output start CNFRefutation
% See solution above
% 0.49/0.49 % Parsed axioms : 14
% 0.49/0.49 % Removed by relevancy pruning/SinE : 0
% 0.49/0.49 % Initial clauses : 14
% 0.49/0.49 % Removed in clause preprocessing : 0
% 0.49/0.49 % Initial clauses in saturation : 14
% 0.49/0.49 % Processed clauses : 661
% 0.49/0.49 % ...of these trivial : 1
% 0.49/0.49 % ...subsumed : 321
% 0.49/0.49 % ...remaining for further processing : 339
% 0.49/0.49 % Other redundant clauses eliminated : 0
% 0.49/0.49 % Clauses deleted for lack of memory : 0
% 0.49/0.49 % Backward-subsumed : 117
% 0.49/0.49 % Backward-rewritten : 56
% 0.49/0.49 % Generated clauses : 1762
% 0.49/0.49 % ...of the previous two non-redundant : 1757
% 0.49/0.49 % ...aggressively subsumed : 0
% 0.49/0.49 % Contextual simplify-reflections : 0
% 0.49/0.49 % Paramodulations : 1705
% 0.49/0.49 % Factorizations : 0
% 0.49/0.49 % NegExts : 0
% 0.49/0.49 % Equation resolutions : 0
% 0.49/0.49 % Disequality decompositions : 0
% 0.49/0.49 % Total rewrite steps : 61
% 0.49/0.49 % ...of those cached : 55
% 0.49/0.49 % Propositional unsat checks : 0
% 0.49/0.49 % Propositional check models : 0
% 0.49/0.49 % Propositional check unsatisfiable : 0
% 0.49/0.49 % Propositional clauses : 0
% 0.49/0.49 % Propositional clauses after purity: 0
% 0.49/0.49 % Propositional unsat core size : 0
% 0.49/0.49 % Propositional preprocessing time : 0.000
% 0.49/0.49 % Propositional encoding time : 0.000
% 0.49/0.49 % Propositional solver time : 0.000
% 0.49/0.49 % Success case prop preproc time : 0.000
% 0.49/0.49 % Success case prop encoding time : 0.000
% 0.49/0.49 % Success case prop solver time : 0.000
% 0.49/0.49 % Current number of processed clauses : 95
% 0.49/0.49 % Positive orientable unit clauses : 10
% 0.49/0.49 % Positive unorientable unit clauses: 0
% 0.49/0.49 % Negative unit clauses : 16
% 0.49/0.49 % Non-unit-clauses : 69
% 0.49/0.49 % Current number of unprocessed clauses: 1047
% 0.49/0.49 % ...number of literals in the above : 5351
% 0.49/0.49 % Current number of archived formulas : 0
% 0.49/0.49 % Current number of archived clauses : 244
% 0.49/0.49 % Clause-clause subsumption calls (NU) : 7421
% 0.49/0.49 % Rec. Clause-clause subsumption calls : 1924
% 0.49/0.49 % Non-unit clause-clause subsumptions : 424
% 0.49/0.49 % Unit Clause-clause subsumption calls : 449
% 0.49/0.49 % Rewrite failures with RHS unbound : 0
% 0.49/0.49 % BW rewrite match attempts : 18
% 0.49/0.49 % BW rewrite match successes : 6
% 0.49/0.49 % Condensation attempts : 0
% 0.49/0.49 % Condensation successes : 0
% 0.49/0.49 % Termbank termtop insertions : 32119
% 0.49/0.49 % Search garbage collected termcells : 36
% 0.49/0.49
% 0.49/0.49 % -------------------------------------------------
% 0.49/0.49 % User time : 0.052 s
% 0.49/0.49 % System time : 0.004 s
% 0.49/0.49 % Total time : 0.057 s
% 0.49/0.49 % Maximum resident set size: 3636 pages
% 0.49/0.49
% 0.49/0.49 % -------------------------------------------------
% 0.49/0.49 % User time : 0.209 s
% 0.49/0.49 % System time : 0.018 s
% 0.49/0.49 % Total time : 0.226 s
% 0.49/0.49 % Maximum resident set size: 4864 pages
% 0.49/0.49 % E exiting
%------------------------------------------------------------------------------