%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP129-1.003 : TPTP v9.2.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n026.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 04:24:16 PM UTC 2026
% Result : Unsatisfiable 1.43s 1.78s
% Output : CNFRefutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 14
% Syntax : Number of clauses : 125 ( 24 unt; 91 nHn; 125 RR)
% Number of literals : 365 ( 0 equ; 77 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 : 78 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_total_function1,axiom,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| product(X1,X2,e_3)
| ~ group_element(X1)
| ~ group_element(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
cnf(product_right_cancellation,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
cnf(qg3,negated_conjecture,
( product(X3,X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
cnf(e_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(product_left_cancellation,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
cnf(product_total_function2,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
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(c_0_14,axiom,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| product(X1,X2,e_3)
| ~ group_element(X1)
| ~ group_element(X2) ),
product_total_function1 ).
cnf(c_0_15,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_16,plain,
( 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_14,c_0_15]) ).
cnf(c_0_17,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_18,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_19,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_right_cancellation ).
cnf(c_0_20,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
( 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_14,c_0_18]) ).
cnf(c_0_22,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| equalish(X1,e_3)
| ~ product(e_1,X1,e_1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_21,c_0_17]) ).
cnf(c_0_24,axiom,
~ equalish(e_2,e_3),
e_2_is_not_e_3 ).
cnf(c_0_25,plain,
( product(X1,e_1,e_3)
| product(X1,e_1,e_2)
| product(X1,e_1,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_26,negated_conjecture,
( product(X3,X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X2,X3,X4) ),
qg3 ).
cnf(c_0_27,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,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_22,c_0_23]),c_0_24]) ).
cnf(c_0_28,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| equalish(X1,e_2)
| ~ product(e_1,X1,e_1) ),
inference(spm,[status(thm)],[c_0_19,c_0_23]) ).
cnf(c_0_29,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_30,axiom,
~ equalish(e_1,e_2),
e_1_is_not_e_2 ).
cnf(c_0_31,negated_conjecture,
( 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_26,c_0_23]),c_0_26]) ).
cnf(c_0_32,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| equalish(X1,e_3)
| ~ product(e_1,X1,e_3) ),
inference(spm,[status(thm)],[c_0_19,c_0_27]) ).
cnf(c_0_33,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31]) ).
cnf(c_0_34,axiom,
~ equalish(e_1,e_3),
e_1_is_not_e_3 ).
cnf(c_0_35,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| 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_36,negated_conjecture,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_3,X1,e_2)
| ~ product(X1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_26,c_0_35]) ).
cnf(c_0_37,negated_conjecture,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_33]),c_0_31]) ).
cnf(c_0_38,negated_conjecture,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| ~ product(X1,e_1,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_20]),c_0_26]) ).
cnf(c_0_39,negated_conjecture,
( product(e_1,e_2,e_2)
| product(e_2,X1,e_3)
| ~ product(X1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_26,c_0_37]) ).
cnf(c_0_40,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_29]),c_0_34]),c_0_38]) ).
cnf(c_0_41,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
product_left_cancellation ).
cnf(c_0_42,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_15]) ).
cnf(c_0_43,negated_conjecture,
( product(e_1,e_2,e_2)
| equalish(X1,e_2)
| ~ product(e_1,X1,e_3) ),
inference(spm,[status(thm)],[c_0_19,c_0_37]) ).
cnf(c_0_44,negated_conjecture,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_2,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_38]) ).
cnf(c_0_45,axiom,
~ equalish(e_3,e_2),
e_3_is_not_e_2 ).
cnf(c_0_46,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| equalish(X1,e_3)
| ~ product(X1,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_1,e_2,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
cnf(c_0_48,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_1,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_46,c_0_29]),c_0_34]) ).
cnf(c_0_49,negated_conjecture,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,X1,e_2)
| ~ product(X1,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_26,c_0_40]) ).
cnf(c_0_50,negated_conjecture,
( product(e_1,e_2,e_2)
| equalish(X1,e_3)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_19,c_0_47]) ).
cnf(c_0_51,negated_conjecture,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_2,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_48]),c_0_30]) ).
cnf(c_0_52,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_42]),c_0_38]) ).
cnf(c_0_53,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_1,e_2,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_34]) ).
cnf(c_0_54,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_3,e_1,e_2)
| equalish(X1,e_3)
| ~ product(e_1,X1,e_3) ),
inference(spm,[status(thm)],[c_0_19,c_0_52]) ).
cnf(c_0_55,negated_conjecture,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| equalish(X1,e_2)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_19,c_0_53]) ).
cnf(c_0_56,negated_conjecture,
( product(e_3,e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_48]),c_0_34]) ).
cnf(c_0_57,negated_conjecture,
( product(e_1,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_55,c_0_56]),c_0_30]) ).
cnf(c_0_58,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_3,e_1,e_2)
| product(e_3,X1,e_3)
| ~ product(X1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_26,c_0_52]) ).
cnf(c_0_59,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_57]),c_0_45]) ).
cnf(c_0_60,negated_conjecture,
( product(e_3,e_3,e_3)
| product(e_3,e_1,e_2)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_61,negated_conjecture,
( product(e_1,e_2,e_2)
| product(e_3,X1,e_2)
| ~ product(X1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_26,c_0_47]) ).
cnf(c_0_62,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_3,e_3,e_3)
| equalish(X1,e_3)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_19,c_0_60]) ).
cnf(c_0_63,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_3,e_3,e_2)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_61,c_0_59]) ).
cnf(c_0_64,negated_conjecture,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_3)
| product(e_3,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_24]) ).
cnf(c_0_65,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_66,negated_conjecture,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_1,X1,e_2)
| ~ product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_26,c_0_64]) ).
cnf(c_0_67,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| equalish(X1,e_3)
| ~ product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_41,c_0_65]) ).
cnf(c_0_68,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_69,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_66,c_0_65]) ).
cnf(c_0_70,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_24]) ).
cnf(c_0_71,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| equalish(X1,e_2)
| ~ product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_41,c_0_68]) ).
cnf(c_0_72,negated_conjecture,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| equalish(X1,e_3)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_19,c_0_69]) ).
cnf(c_0_73,negated_conjecture,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_2,e_3,e_3)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_39,c_0_64]) ).
cnf(c_0_74,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_75,plain,
( product(e_3,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3)
| equalish(X1,e_3)
| ~ product(X1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_41,c_0_70]) ).
cnf(c_0_76,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_20]),c_0_30]) ).
cnf(c_0_77,negated_conjecture,
( product(e_3,e_1,e_2)
| equalish(X1,e_1)
| ~ product(e_3,X1,e_3) ),
inference(spm,[status(thm)],[c_0_19,c_0_59]) ).
cnf(c_0_78,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_24]) ).
cnf(c_0_79,axiom,
~ equalish(e_3,e_1),
e_3_is_not_e_1 ).
cnf(c_0_80,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| equalish(X1,e_2)
| ~ product(X1,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_41,c_0_74]) ).
cnf(c_0_81,plain,
( product(e_1,e_3,e_2)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_3,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_34]) ).
cnf(c_0_82,negated_conjecture,
( product(e_3,e_3,e_2)
| product(e_2,e_3,e_3)
| product(e_3,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]) ).
cnf(c_0_83,plain,
( product(e_1,e_1,e_3)
| product(e_1,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_80,c_0_29]),c_0_30]) ).
cnf(c_0_84,plain,
( product(e_3,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3)
| equalish(X1,e_3)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_19,c_0_81]) ).
cnf(c_0_85,negated_conjecture,
( product(e_3,e_3,e_2)
| product(e_2,e_3,e_3)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_39,c_0_82]) ).
cnf(c_0_86,negated_conjecture,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_1,e_2,e_2) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_83]),c_0_30]),c_0_39]) ).
cnf(c_0_87,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_1,e_1,e_2)
| equalish(X1,e_1)
| ~ product(X1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_41,c_0_83]) ).
cnf(c_0_88,negated_conjecture,
( product(e_1,e_2,e_2)
| equalish(X1,e_1)
| ~ product(X1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_41,c_0_47]) ).
cnf(c_0_89,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_3,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_24]) ).
cnf(c_0_90,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,X1,e_2)
| ~ product(X1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_26,c_0_86]) ).
cnf(c_0_91,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_1,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_87,c_0_59]),c_0_79]) ).
cnf(c_0_92,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
product_total_function2 ).
cnf(c_0_93,negated_conjecture,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_3)
| product(e_1,e_2,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_79]) ).
cnf(c_0_94,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_1,X1,e_3)
| ~ product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_26,c_0_59]) ).
cnf(c_0_95,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_96,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| equalish(X1,e_2)
| ~ product(e_1,e_2,X1) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_97,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_1,e_2,e_3)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_94,c_0_68]) ).
cnf(c_0_98,negated_conjecture,
( product(e_2,e_3,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_90,c_0_95]) ).
cnf(c_0_99,negated_conjecture,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_3)
| equalish(X1,e_3)
| ~ product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_19,c_0_89]) ).
cnf(c_0_100,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_45]) ).
cnf(c_0_101,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_2,e_3,e_2)
| equalish(X1,e_1)
| ~ product(e_2,X1,e_3) ),
inference(spm,[status(thm)],[c_0_19,c_0_98]) ).
cnf(c_0_102,negated_conjecture,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_34]) ).
cnf(c_0_103,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| equalish(X1,e_1)
| ~ product(X1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_41,c_0_40]) ).
cnf(c_0_104,negated_conjecture,
( product(e_2,e_3,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_79]) ).
cnf(c_0_105,axiom,
~ equalish(e_2,e_1),
e_2_is_not_e_1 ).
cnf(c_0_106,negated_conjecture,
( product(e_2,e_3,e_2)
| equalish(X1,e_2)
| ~ product(X1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_41,c_0_102]) ).
cnf(c_0_107,negated_conjecture,
( product(e_2,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_103,c_0_104]),c_0_105]) ).
cnf(c_0_108,negated_conjecture,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| equalish(X1,e_3)
| ~ product(X1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_41,c_0_64]) ).
cnf(c_0_109,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_2,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_30]) ).
cnf(c_0_110,negated_conjecture,
( product(e_2,e_3,e_2)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_104]),c_0_24]) ).
cnf(c_0_111,negated_conjecture,
( product(e_2,e_3,e_2)
| equalish(X1,e_1)
| ~ product(X1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_41,c_0_109]) ).
cnf(c_0_112,negated_conjecture,
( product(e_3,e_3,e_2)
| product(e_2,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_110]),c_0_45]) ).
cnf(c_0_113,negated_conjecture,
product(e_2,e_3,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_79]) ).
cnf(c_0_114,negated_conjecture,
( equalish(X1,e_2)
| ~ product(X1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_41,c_0_113]) ).
cnf(c_0_115,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| equalish(X1,e_1)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_19,c_0_40]) ).
cnf(c_0_116,negated_conjecture,
~ product(e_3,e_3,e_2),
inference(spm,[status(thm)],[c_0_45,c_0_114]) ).
cnf(c_0_117,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_86]),c_0_105]),c_0_38]) ).
cnf(c_0_118,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_1) ),
inference(sr,[status(thm)],[c_0_65,c_0_116]) ).
cnf(c_0_119,negated_conjecture,
~ product(e_1,e_3,e_2),
inference(spm,[status(thm)],[c_0_30,c_0_114]) ).
cnf(c_0_120,negated_conjecture,
( equalish(X1,e_3)
| ~ product(e_2,X1,e_2) ),
inference(spm,[status(thm)],[c_0_19,c_0_113]) ).
cnf(c_0_121,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_2,e_1,e_2)
| equalish(X1,e_1)
| ~ product(X1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_41,c_0_117]) ).
cnf(c_0_122,negated_conjecture,
product(e_3,e_3,e_3),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_118]),c_0_116]),c_0_119]) ).
cnf(c_0_123,negated_conjecture,
~ product(e_2,e_1,e_2),
inference(spm,[status(thm)],[c_0_34,c_0_120]) ).
cnf(c_0_124,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_119]),c_0_123]),c_0_79]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP129-1.003 : TPTP v9.2.1. Released v1.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.34 % Computer : n026.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon May 4 18:24:38 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.43/1.78 % Version : CSE_E---1.7
% 1.43/1.78 % Problem : theBenchmark.p
% 1.43/1.78 % SZS status Unsatisfiable for theBenchmark.p
% 1.43/1.78 % SZS output start CNFRefutation
% See solution above
% 1.43/1.78 % Total time : 1.371s
%------------------------------------------------------------------------------