%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP129-4.004 : TPTP v9.2.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:24:27 PM UTC 2026
% Result : Unsatisfiable 1.74s 1.85s
% Output : CNFRefutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 24
% Syntax : Number of clauses : 167 ( 42 unt; 108 nHn; 167 RR)
% Number of literals : 460 ( 0 equ; 114 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 : 108 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_total_function1,axiom,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| product(X1,X2,e_3)
| product(X1,X2,e_4)
| ~ group_element(X1)
| ~ group_element(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
cnf(qg3_1,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X3,X1,X4)
| ~ product(X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3_1) ).
cnf(column_surjectivity,axiom,
( product(X1,e_1,X2)
| product(X1,e_2,X2)
| product(X1,e_3,X2)
| product(X1,e_4,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',column_surjectivity) ).
cnf(product_left_cancellation,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_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(row_surjectivity,axiom,
( product(e_1,X1,X2)
| product(e_2,X1,X2)
| product(e_3,X1,X2)
| product(e_4,X1,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',row_surjectivity) ).
cnf(product_right_cancellation,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(product_total_function2,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).
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(qg3,negated_conjecture,
( product(X3,X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).
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(qg3_2,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X2,X4,X3)
| ~ product(X4,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3_2) ).
cnf(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
cnf(element_4,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
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(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_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_1,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
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(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(c_0_24,axiom,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| product(X1,X2,e_3)
| product(X1,X2,e_4)
| ~ group_element(X1)
| ~ group_element(X2) ),
product_total_function1 ).
cnf(c_0_25,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_26,plain,
( product(X1,e_2,e_4)
| product(X1,e_2,e_3)
| product(X1,e_2,e_2)
| product(X1,e_2,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X3,X1,X4)
| ~ product(X2,X3,X4) ),
qg3_1 ).
cnf(c_0_28,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( product(e_2,e_2,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,X1,e_2)
| ~ product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_30,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,X1,e_2)
| ~ product(X1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_27,c_0_30]) ).
cnf(c_0_32,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_2,X1,e_2)
| ~ product(X1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_27,c_0_32]) ).
cnf(c_0_34,axiom,
( product(X1,e_1,X2)
| product(X1,e_2,X2)
| product(X1,e_3,X2)
| product(X1,e_4,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
column_surjectivity ).
cnf(c_0_35,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
product_left_cancellation ).
cnf(c_0_36,negated_conjecture,
product(e_2,e_2,e_2),
inference(spm,[status(thm)],[c_0_33,c_0_32]) ).
cnf(c_0_37,plain,
( product(X1,e_4,e_2)
| product(X1,e_3,e_2)
| product(X1,e_2,e_2)
| product(X1,e_1,e_2)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_25]) ).
cnf(c_0_38,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_39,axiom,
~ equalish(e_1,e_2),
e_1_is_not_e_2 ).
cnf(c_0_40,negated_conjecture,
( equalish(X1,e_2)
| ~ product(X1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,axiom,
( product(e_1,X1,X2)
| product(e_2,X1,X2)
| product(e_3,X1,X2)
| product(e_4,X1,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
row_surjectivity ).
cnf(c_0_42,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_right_cancellation ).
cnf(c_0_43,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,negated_conjecture,
~ product(e_1,e_2,e_2),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,plain,
( product(e_4,X1,e_2)
| product(e_3,X1,e_2)
| product(e_2,X1,e_2)
| product(e_1,X1,e_2)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_25]) ).
cnf(c_0_46,negated_conjecture,
( equalish(X1,e_2)
| ~ product(e_2,X1,e_2) ),
inference(spm,[status(thm)],[c_0_42,c_0_36]) ).
cnf(c_0_47,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_1,e_2) ),
inference(sr,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_4,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_45,c_0_38]) ).
cnf(c_0_49,negated_conjecture,
~ product(e_2,e_1,e_2),
inference(spm,[status(thm)],[c_0_39,c_0_46]) ).
cnf(c_0_50,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
product_total_function2 ).
cnf(c_0_51,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_1,e_4,e_2)
| product(e_1,X1,e_1)
| ~ product(X1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_27,c_0_47]) ).
cnf(c_0_52,plain,
( product(e_4,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_1,e_1,e_2) ),
inference(sr,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,plain,
( equalish(X1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_4,e_2)
| ~ product(e_1,e_1,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_47]) ).
cnf(c_0_54,negated_conjecture,
( product(e_1,e_1,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_51,c_0_47]) ).
cnf(c_0_55,plain,
( equalish(X1,e_1)
| product(e_3,e_1,e_2)
| product(e_4,e_1,e_2)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_42,c_0_52]) ).
cnf(c_0_56,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_39]) ).
cnf(c_0_57,axiom,
~ equalish(e_4,e_1),
e_4_is_not_e_1 ).
cnf(c_0_58,negated_conjecture,
( product(X3,X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X2,X3,X4) ),
qg3 ).
cnf(c_0_59,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_26,c_0_38]) ).
cnf(c_0_60,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_4,e_1,e_2)
| product(e_3,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]) ).
cnf(c_0_61,axiom,
~ equalish(e_3,e_1),
e_3_is_not_e_1 ).
cnf(c_0_62,negated_conjecture,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| ~ product(X1,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_58]) ).
cnf(c_0_63,negated_conjecture,
( product(e_4,e_1,e_2)
| product(e_3,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_60]),c_0_61]) ).
cnf(c_0_64,negated_conjecture,
( product(X1,X2,X3)
| ~ product(X2,X4,X3)
| ~ product(X4,X1,X2) ),
qg3_2 ).
cnf(c_0_65,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_44]) ).
cnf(c_0_66,axiom,
~ equalish(e_4,e_2),
e_4_is_not_e_2 ).
cnf(c_0_67,axiom,
group_element(e_4),
element_4 ).
cnf(c_0_68,negated_conjecture,
( product(e_1,e_2,e_3)
| product(e_3,e_1,e_2)
| product(e_2,e_4,X1)
| ~ product(e_4,e_1,X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_69,negated_conjecture,
~ product(e_2,e_4,e_2),
inference(spm,[status(thm)],[c_0_66,c_0_46]) ).
cnf(c_0_70,plain,
( product(e_4,e_1,e_2)
| product(e_4,e_2,e_2)
| product(e_4,e_3,e_2)
| product(e_4,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_37,c_0_67]) ).
cnf(c_0_71,negated_conjecture,
~ product(e_4,e_2,e_2),
inference(spm,[status(thm)],[c_0_66,c_0_40]) ).
cnf(c_0_72,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_1,e_2,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_63]),c_0_69]) ).
cnf(c_0_73,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_4,X1,e_1)
| ~ product(X1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_27,c_0_56]) ).
cnf(c_0_74,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_75,plain,
( product(e_4,e_4,e_2)
| product(e_4,e_3,e_2)
| product(e_4,e_1,e_2) ),
inference(sr,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_76,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_2,X1,e_3)
| ~ product(X1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_58,c_0_72]) ).
cnf(c_0_77,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_4,e_4,e_1)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_73,c_0_63]) ).
cnf(c_0_78,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_1,X1,e_4)
| ~ product(X1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_27,c_0_63]) ).
cnf(c_0_79,plain,
( product(X1,e_4,e_3)
| product(X1,e_3,e_3)
| product(X1,e_2,e_3)
| product(X1,e_1,e_3)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_74]) ).
cnf(c_0_80,axiom,
~ equalish(e_3,e_2),
e_3_is_not_e_2 ).
cnf(c_0_81,negated_conjecture,
( equalish(X1,e_2)
| ~ product(e_2,e_2,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_36]) ).
cnf(c_0_82,plain,
( equalish(X1,e_4)
| product(e_4,e_3,e_2)
| product(e_4,e_4,e_2)
| ~ product(X1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_35,c_0_75]) ).
cnf(c_0_83,negated_conjecture,
( product(e_2,e_4,e_3)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_76,c_0_63]) ).
cnf(c_0_84,axiom,
~ equalish(e_3,e_4),
e_3_is_not_e_4 ).
cnf(c_0_85,negated_conjecture,
( product(e_4,e_4,e_1)
| product(e_3,e_1,e_2)
| product(e_3,X1,e_1)
| ~ product(X1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_27,c_0_77]) ).
cnf(c_0_86,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_1,e_1,e_4)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_78,c_0_56]) ).
cnf(c_0_87,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_2,e_3)
| product(e_2,e_3,e_3)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_79,c_0_25]) ).
cnf(c_0_88,negated_conjecture,
~ product(e_2,e_2,e_3),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_89,negated_conjecture,
( equalish(X1,e_1)
| product(e_1,e_3,e_2)
| ~ product(X1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_35,c_0_56]) ).
cnf(c_0_90,negated_conjecture,
( product(e_2,e_4,e_3)
| product(e_4,e_4,e_2)
| product(e_4,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84]) ).
cnf(c_0_91,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_1,X1,e_2)
| ~ product(X1,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_58,c_0_63]) ).
cnf(c_0_92,negated_conjecture,
( product(e_3,e_4,e_1)
| product(e_3,e_1,e_2)
| product(e_4,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_85,c_0_63]) ).
cnf(c_0_93,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,X1,e_1)
| ~ product(X1,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_27,c_0_86]) ).
cnf(c_0_94,plain,
( product(e_1,e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_3,e_4,e_2)
| product(e_4,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_45,c_0_67]) ).
cnf(c_0_95,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_3,e_3)
| product(e_2,e_1,e_3) ),
inference(sr,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_96,negated_conjecture,
( product(e_2,e_4,e_3)
| product(e_1,X1,e_3)
| ~ product(X1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_27,c_0_83]) ).
cnf(c_0_97,negated_conjecture,
( product(e_4,e_3,e_2)
| product(e_2,e_4,e_3)
| product(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_57]) ).
cnf(c_0_98,negated_conjecture,
( product(e_3,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_99,negated_conjecture,
( equalish(X1,e_4)
| product(e_3,e_1,e_2)
| product(e_1,e_3,e_2)
| ~ product(e_1,e_1,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_86]) ).
cnf(c_0_100,negated_conjecture,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_93,c_0_86]) ).
cnf(c_0_101,axiom,
~ equalish(e_1,e_4),
e_1_is_not_e_4 ).
cnf(c_0_102,plain,
( product(e_4,e_4,e_2)
| product(e_3,e_4,e_2)
| product(e_1,e_4,e_2) ),
inference(sr,[status(thm)],[c_0_94,c_0_69]) ).
cnf(c_0_103,plain,
( equalish(X1,e_2)
| product(e_2,e_3,e_3)
| product(e_2,e_4,e_3)
| ~ product(X1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_35,c_0_95]) ).
cnf(c_0_104,negated_conjecture,
( product(e_4,e_3,e_2)
| product(e_1,e_1,e_3)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_105,negated_conjecture,
( equalish(X1,e_4)
| product(e_3,e_1,e_2)
| product(e_3,e_4,e_1)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_42,c_0_98]) ).
cnf(c_0_106,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_3,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101]) ).
cnf(c_0_107,plain,
( product(X1,e_3,e_4)
| product(X1,e_3,e_3)
| product(X1,e_3,e_2)
| product(X1,e_3,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_74]) ).
cnf(c_0_108,plain,
( equalish(X1,e_4)
| product(e_3,e_4,e_2)
| product(e_4,e_4,e_2)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_42,c_0_102]) ).
cnf(c_0_109,negated_conjecture,
( product(e_4,e_3,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_39]) ).
cnf(c_0_110,negated_conjecture,
( product(e_3,e_4,e_1)
| product(e_3,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_84]) ).
cnf(c_0_111,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_107,c_0_25]) ).
cnf(c_0_112,negated_conjecture,
~ product(e_2,e_3,e_2),
inference(spm,[status(thm)],[c_0_80,c_0_46]) ).
cnf(c_0_113,negated_conjecture,
( equalish(X1,e_1)
| product(e_3,e_1,e_2)
| ~ product(e_4,X1,e_2) ),
inference(spm,[status(thm)],[c_0_42,c_0_63]) ).
cnf(c_0_114,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_4,e_4,e_2)
| product(e_3,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_106]),c_0_84]) ).
cnf(c_0_115,plain,
( product(e_4,X1,e_3)
| product(e_3,X1,e_3)
| product(e_2,X1,e_3)
| product(e_1,X1,e_3)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_74]) ).
cnf(c_0_116,negated_conjecture,
( equalish(X1,e_2)
| product(e_1,e_3,e_2)
| ~ product(e_1,e_4,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_56]) ).
cnf(c_0_117,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_1,e_4,e_3)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_96,c_0_109]) ).
cnf(c_0_118,negated_conjecture,
( product(e_3,e_4,e_1)
| product(e_1,X1,e_2)
| ~ product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_58,c_0_110]) ).
cnf(c_0_119,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_1) ),
inference(sr,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_120,negated_conjecture,
( product(e_3,e_4,e_2)
| product(e_3,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_57]) ).
cnf(c_0_121,plain,
( product(e_1,e_2,e_3)
| product(e_2,e_2,e_3)
| product(e_3,e_2,e_3)
| product(e_4,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_115,c_0_25]) ).
cnf(c_0_122,negated_conjecture,
( product(e_2,e_4,e_3)
| product(e_2,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_80]) ).
cnf(c_0_123,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_4)
| product(e_3,e_4,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_44]) ).
cnf(c_0_124,negated_conjecture,
( product(e_3,e_4,e_2)
| product(e_1,X1,e_2)
| ~ product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_58,c_0_120]) ).
cnf(c_0_125,plain,
( product(e_4,e_2,e_3)
| product(e_3,e_2,e_3)
| product(e_1,e_2,e_3) ),
inference(sr,[status(thm)],[c_0_121,c_0_88]) ).
cnf(c_0_126,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_1,e_1,e_3)
| product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_96,c_0_122]) ).
cnf(c_0_127,negated_conjecture,
( equalish(X1,e_1)
| product(e_2,e_3,e_4)
| product(e_2,e_3,e_3)
| ~ product(e_3,e_4,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_123]) ).
cnf(c_0_128,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_4)
| product(e_3,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_119]),c_0_44]) ).
cnf(c_0_129,axiom,
~ equalish(e_2,e_1),
e_2_is_not_e_1 ).
cnf(c_0_130,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_107,c_0_74]) ).
cnf(c_0_131,negated_conjecture,
( product(e_3,e_2,e_3)
| product(e_4,e_2,e_3)
| product(e_2,e_3,X1)
| ~ product(e_3,e_1,X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_125]) ).
cnf(c_0_132,negated_conjecture,
( product(e_2,e_4,e_3)
| product(e_2,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_126]),c_0_39]) ).
cnf(c_0_133,negated_conjecture,
( product(e_3,e_4,e_1)
| product(e_1,e_2,X1)
| ~ product(e_2,e_3,X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_110]) ).
cnf(c_0_134,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_129]) ).
cnf(c_0_135,negated_conjecture,
( product(e_3,e_3,e_4)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,X1,e_3)
| ~ product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_27,c_0_130]) ).
cnf(c_0_136,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_26,c_0_74]) ).
cnf(c_0_137,negated_conjecture,
~ product(e_3,e_2,e_2),
inference(spm,[status(thm)],[c_0_80,c_0_40]) ).
cnf(c_0_138,negated_conjecture,
( product(e_3,e_4,e_1)
| product(e_4,e_2,e_3)
| product(e_3,e_2,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_110]),c_0_112]) ).
cnf(c_0_139,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_4,X1,e_3)
| ~ product(X1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_58,c_0_132]) ).
cnf(c_0_140,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_1,e_2,e_4)
| product(e_3,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_141,negated_conjecture,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_135,c_0_130]) ).
cnf(c_0_142,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_1) ),
inference(sr,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_143,negated_conjecture,
( equalish(X1,e_2)
| product(e_3,e_2,e_3)
| product(e_3,e_4,e_1)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_42,c_0_138]) ).
cnf(c_0_144,negated_conjecture,
( product(e_3,e_4,e_1)
| product(e_4,e_1,e_3)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_145,negated_conjecture,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,X1,e_3)
| ~ product(X1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_27,c_0_141]) ).
cnf(c_0_146,plain,
( equalish(X1,e_2)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_4)
| ~ product(e_3,X1,e_1) ),
inference(spm,[status(thm)],[c_0_42,c_0_142]) ).
cnf(c_0_147,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_3,e_4,e_1)
| product(e_3,e_2,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_39]) ).
cnf(c_0_148,negated_conjecture,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_145,c_0_141]) ).
cnf(c_0_149,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_3,e_2,e_4)
| product(e_3,e_2,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_66]) ).
cnf(c_0_150,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_4,e_3,X1)
| ~ product(e_3,e_2,X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_132]) ).
cnf(c_0_151,negated_conjecture,
( equalish(X1,e_3)
| product(e_3,e_3,e_2)
| ~ product(X1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_35,c_0_148]) ).
cnf(c_0_152,negated_conjecture,
( product(e_4,e_3,e_3)
| product(e_2,e_3,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_149]),c_0_150]) ).
cnf(c_0_153,axiom,
~ equalish(e_4,e_3),
e_4_is_not_e_3 ).
cnf(c_0_154,negated_conjecture,
( equalish(X1,e_1)
| product(e_3,e_4,e_2)
| ~ product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_42,c_0_120]) ).
cnf(c_0_155,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_153]) ).
cnf(c_0_156,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_3,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_61]) ).
cnf(c_0_157,negated_conjecture,
( equalish(X1,e_3)
| product(e_2,e_3,e_3)
| ~ product(X1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_35,c_0_155]) ).
cnf(c_0_158,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_156]),c_0_61]) ).
cnf(c_0_159,axiom,
~ equalish(e_1,e_3),
e_1_is_not_e_3 ).
cnf(c_0_160,negated_conjecture,
product(e_2,e_3,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_159]) ).
cnf(c_0_161,axiom,
~ equalish(e_2,e_3),
e_2_is_not_e_3 ).
cnf(c_0_162,negated_conjecture,
product(e_3,e_3,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_160]),c_0_161]) ).
cnf(c_0_163,negated_conjecture,
( equalish(X1,e_2)
| ~ product(X1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_35,c_0_160]) ).
cnf(c_0_164,negated_conjecture,
( product(e_3,X1,e_3)
| ~ product(X1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_27,c_0_162]) ).
cnf(c_0_165,negated_conjecture,
~ product(e_3,e_3,e_3),
inference(spm,[status(thm)],[c_0_80,c_0_163]) ).
cnf(c_0_166,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_162]),c_0_165]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP129-4.004 : TPTP v9.2.1. Bugfixed v1.2.1.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n022.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:24:06 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.74/1.85 % Version : CSE_E---1.7
% 1.74/1.85 % Problem : theBenchmark.p
% 1.74/1.85 % SZS status Unsatisfiable for theBenchmark.p
% 1.74/1.85 % SZS output start CNFRefutation
% See solution above
% 1.74/1.86 % Total time : 1.367s
%------------------------------------------------------------------------------