%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP123-9.003 : TPTP v9.2.1. Bugfixed v1.2.1.
% 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 04:23:56 PM UTC 2026
% Result : Unsatisfiable 0.27s 1.62s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 22
% Syntax : Number of clauses : 135 ( 75 unt; 19 nHn; 109 RR)
% Number of literals : 280 ( 0 equ; 148 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 217 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(qg1a,negated_conjecture,
( product2(X4,X1,X2)
| ~ product1(X1,X2,X3)
| ~ product1(X3,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1a) ).
cnf(product2_left_cancellation,axiom,
( equalish(X1,X4)
| ~ product2(X1,X2,X3)
| ~ product2(X4,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_left_cancellation) ).
cnf(product1_left_cancellation,axiom,
( equalish(X1,X4)
| ~ product1(X1,X2,X3)
| ~ product1(X4,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_left_cancellation) ).
cnf(product2_right_cancellation,axiom,
( equalish(X2,X4)
| ~ product2(X1,X2,X3)
| ~ product2(X1,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_right_cancellation) ).
cnf(product1_right_cancellation,axiom,
( equalish(X2,X4)
| ~ product1(X1,X2,X3)
| ~ product1(X1,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_right_cancellation) ).
cnf(product2_total_function2,axiom,
( equalish(X3,X4)
| ~ product2(X1,X2,X3)
| ~ product2(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_total_function2) ).
cnf(product1_total_function2,axiom,
( equalish(X3,X4)
| ~ product1(X1,X2,X3)
| ~ product1(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_total_function2) ).
cnf(row_surjectivity,axiom,
( product(e_1,X1,X2)
| product(e_2,X1,X2)
| product(e_3,X1,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',row_surjectivity) ).
cnf(column_surjectivity,axiom,
( product(X1,e_1,X2)
| product(X1,e_2,X2)
| product(X1,e_3,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',column_surjectivity) ).
cnf(product2_total_function1,axiom,
( product2(X1,X2,e_1)
| product2(X1,X2,e_2)
| product2(X1,X2,e_3)
| ~ group_element(X1)
| ~ group_element(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_total_function1) ).
cnf(product1_total_function1,axiom,
( product1(X1,X2,e_1)
| product1(X1,X2,e_2)
| product1(X1,X2,e_3)
| ~ group_element(X1)
| ~ group_element(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_total_function1) ).
cnf(product2_idempotence,axiom,
product2(X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_idempotence) ).
cnf(product1_idempotence,axiom,
product1(X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_idempotence) ).
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(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(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
cnf(e_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(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(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
cnf(i_0_22,negated_conjecture,
( product2(X4,X1,X2)
| ~ product1(X1,X2,X3)
| ~ product1(X3,X2,X4) ),
qg1a,
[final] ).
cnf(i_0_23,axiom,
( equalish(X1,X4)
| ~ product2(X1,X2,X3)
| ~ product2(X4,X2,X3) ),
product2_left_cancellation,
[final] ).
cnf(i_0_24,axiom,
( equalish(X1,X4)
| ~ product1(X1,X2,X3)
| ~ product1(X4,X2,X3) ),
product1_left_cancellation,
[final] ).
cnf(i_0_25,axiom,
( equalish(X2,X4)
| ~ product2(X1,X2,X3)
| ~ product2(X1,X4,X3) ),
product2_right_cancellation,
[final] ).
cnf(i_0_26,axiom,
( equalish(X2,X4)
| ~ product1(X1,X2,X3)
| ~ product1(X1,X4,X3) ),
product1_right_cancellation,
[final] ).
cnf(i_0_27,axiom,
( equalish(X3,X4)
| ~ product2(X1,X2,X3)
| ~ product2(X1,X2,X4) ),
product2_total_function2,
[final] ).
cnf(i_0_28,axiom,
( equalish(X3,X4)
| ~ product1(X1,X2,X3)
| ~ product1(X1,X2,X4) ),
product1_total_function2,
[final] ).
cnf(i_0_29,axiom,
( product(e_1,X1,X2)
| product(e_2,X1,X2)
| product(e_3,X1,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
row_surjectivity,
[final] ).
cnf(i_0_30,axiom,
( product(X1,e_1,X2)
| product(X1,e_2,X2)
| product(X1,e_3,X2)
| ~ group_element(X1)
| ~ group_element(X2) ),
column_surjectivity,
[final] ).
cnf(i_0_31,axiom,
( product2(X1,X2,e_1)
| product2(X1,X2,e_2)
| product2(X1,X2,e_3)
| ~ group_element(X1)
| ~ group_element(X2) ),
product2_total_function1,
[final] ).
cnf(i_0_32,axiom,
( product1(X1,X2,e_1)
| product1(X1,X2,e_2)
| product1(X1,X2,e_3)
| ~ group_element(X1)
| ~ group_element(X2) ),
product1_total_function1,
[final] ).
cnf(i_0_33,axiom,
product2(X1,X1,X1),
product2_idempotence,
[final] ).
cnf(i_0_34,axiom,
product1(X1,X1,X1),
product1_idempotence,
[final] ).
cnf(i_0_35,axiom,
~ equalish(e_3,e_2),
e_3_is_not_e_2,
[final] ).
cnf(i_0_36,axiom,
~ equalish(e_3,e_1),
e_3_is_not_e_1,
[final] ).
cnf(i_0_37,axiom,
~ equalish(e_2,e_3),
e_2_is_not_e_3,
[final] ).
cnf(i_0_38,axiom,
~ equalish(e_2,e_1),
e_2_is_not_e_1,
[final] ).
cnf(i_0_39,axiom,
~ equalish(e_1,e_3),
e_1_is_not_e_3,
[final] ).
cnf(i_0_40,axiom,
~ equalish(e_1,e_2),
e_1_is_not_e_2,
[final] ).
cnf(i_0_41,axiom,
group_element(e_3),
element_3,
[final] ).
cnf(i_0_42,axiom,
group_element(e_2),
element_2,
[final] ).
cnf(i_0_43,axiom,
group_element(e_1),
element_1,
[final] ).
cnf(i_0_44,plain,
~ product2(e_3,e_2,e_2),
inference(scs_inference,[],[i_0_33,i_0_35,i_0_23]) ).
cnf(i_0_45,plain,
product2(X1,X1,X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_46,plain,
( ~ product2(X1,X2,X3)
| equalish(X4,X1)
| ~ product2(X4,X2,X3) ),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_47,plain,
~ product2(e_2,e_3,e_2),
inference(scs_inference,[],[i_0_33,i_0_45,i_0_35,i_0_23,i_0_25]) ).
cnf(i_0_48,plain,
product2(X1,X1,X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_49,plain,
( ~ product2(X1,X2,X3)
| equalish(X4,X2)
| ~ product2(X1,X4,X3) ),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_50,plain,
~ product2(e_2,e_2,e_3),
inference(scs_inference,[],[i_0_33,i_0_45,i_0_48,i_0_35,i_0_23,i_0_25,i_0_27]) ).
cnf(i_0_51,plain,
product2(X1,X1,X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_52,plain,
( ~ product2(X1,X2,X3)
| equalish(X4,X3)
| ~ product2(X1,X2,X4) ),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_53,plain,
~ product1(e_3,e_2,e_2),
inference(scs_inference,[],[i_0_33,i_0_45,i_0_48,i_0_34,i_0_35,i_0_23,i_0_25,i_0_27,i_0_24]) ).
cnf(i_0_54,plain,
product1(X1,X1,X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_55,plain,
( ~ product1(X1,X2,X3)
| equalish(X4,X1)
| ~ product1(X4,X2,X3) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_56,plain,
~ product1(e_2,e_3,e_2),
inference(scs_inference,[],[i_0_33,i_0_45,i_0_48,i_0_34,i_0_54,i_0_35,i_0_23,i_0_25,i_0_27,i_0_24,i_0_26]) ).
cnf(i_0_57,plain,
product1(X1,X1,X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_58,plain,
( ~ product1(X1,X2,X3)
| equalish(X4,X2)
| ~ product1(X1,X4,X3) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_59,plain,
~ product1(e_2,e_2,e_3),
inference(scs_inference,[],[i_0_33,i_0_45,i_0_48,i_0_34,i_0_54,i_0_57,i_0_35,i_0_23,i_0_25,i_0_27,i_0_24,i_0_26,i_0_28]) ).
cnf(i_0_60,plain,
product1(X1,X1,X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_61,plain,
( ~ product1(X1,X2,X3)
| equalish(X4,X3)
| ~ product1(X1,X2,X4) ),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_62,plain,
( product1(e_3,e_2,e_3)
| product1(e_3,e_2,e_1) ),
inference(scs_inference,[],[i_0_33,i_0_45,i_0_48,i_0_34,i_0_54,i_0_57,i_0_35,i_0_41,i_0_42,i_0_23,i_0_25,i_0_27,i_0_24,i_0_26,i_0_28,i_0_32]) ).
cnf(i_0_63,plain,
( product1(X1,X2,e_2)
| product1(X1,X2,e_3)
| product1(X1,X2,e_1)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_64,plain,
( product2(e_3,e_2,e_3)
| product2(e_3,e_2,e_1) ),
inference(scs_inference,[],[i_0_33,i_0_45,i_0_48,i_0_34,i_0_54,i_0_57,i_0_35,i_0_41,i_0_42,i_0_23,i_0_25,i_0_27,i_0_24,i_0_26,i_0_28,i_0_32,i_0_31]) ).
cnf(i_0_65,plain,
( product2(X1,X2,e_2)
| product2(X1,X2,e_3)
| product2(X1,X2,e_1)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_66,plain,
~ product2(e_3,e_1,e_1),
inference(scs_inference,[],[i_0_33,i_0_36,i_0_23]) ).
cnf(i_0_67,plain,
product2(X1,X1,X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_68,plain,
( ~ product2(X1,X2,X3)
| equalish(X4,X1)
| ~ product2(X4,X2,X3) ),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_69,plain,
~ product2(e_1,e_3,e_1),
inference(scs_inference,[],[i_0_33,i_0_67,i_0_36,i_0_23,i_0_25]) ).
cnf(i_0_70,plain,
product2(X1,X1,X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_71,plain,
( ~ product2(X1,X2,X3)
| equalish(X4,X2)
| ~ product2(X1,X4,X3) ),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_72,plain,
~ product2(e_1,e_1,e_3),
inference(scs_inference,[],[i_0_33,i_0_67,i_0_70,i_0_36,i_0_23,i_0_25,i_0_27]) ).
cnf(i_0_73,plain,
product2(X1,X1,X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_74,plain,
( ~ product2(X1,X2,X3)
| equalish(X4,X3)
| ~ product2(X1,X2,X4) ),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_75,plain,
~ product1(e_3,e_1,e_1),
inference(scs_inference,[],[i_0_33,i_0_67,i_0_70,i_0_36,i_0_34,i_0_23,i_0_25,i_0_27,i_0_24]) ).
cnf(i_0_76,plain,
product1(X1,X1,X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_77,plain,
( ~ product1(X1,X2,X3)
| equalish(X4,X1)
| ~ product1(X4,X2,X3) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_78,plain,
~ product1(e_1,e_3,e_1),
inference(scs_inference,[],[i_0_33,i_0_67,i_0_70,i_0_36,i_0_34,i_0_76,i_0_23,i_0_25,i_0_27,i_0_24,i_0_26]) ).
cnf(i_0_79,plain,
product1(X1,X1,X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_80,plain,
( ~ product1(X1,X2,X3)
| equalish(X4,X2)
| ~ product1(X1,X4,X3) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_81,plain,
~ product1(e_1,e_1,e_3),
inference(scs_inference,[],[i_0_33,i_0_67,i_0_70,i_0_36,i_0_34,i_0_76,i_0_79,i_0_23,i_0_25,i_0_27,i_0_24,i_0_26,i_0_28]) ).
cnf(i_0_82,plain,
product1(X1,X1,X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_83,plain,
( ~ product1(X1,X2,X3)
| equalish(X4,X3)
| ~ product1(X1,X2,X4) ),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_84,plain,
( product2(e_2,e_3,e_3)
| product2(e_2,e_3,e_1) ),
inference(scs_inference,[],[i_0_33,i_0_67,i_0_70,i_0_47,i_0_36,i_0_34,i_0_76,i_0_79,i_0_41,i_0_42,i_0_23,i_0_25,i_0_27,i_0_24,i_0_26,i_0_28,i_0_31]) ).
cnf(i_0_85,plain,
( product2(X1,X2,e_2)
| product2(X1,X2,e_3)
| product2(X1,X2,e_1)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_86,plain,
( product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_1) ),
inference(scs_inference,[],[i_0_33,i_0_67,i_0_70,i_0_47,i_0_36,i_0_56,i_0_34,i_0_76,i_0_79,i_0_41,i_0_42,i_0_23,i_0_25,i_0_27,i_0_24,i_0_26,i_0_28,i_0_31,i_0_32]) ).
cnf(i_0_87,plain,
( product1(X1,X2,e_2)
| product1(X1,X2,e_3)
| product1(X1,X2,e_1)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_88,plain,
~ product2(e_2,e_3,e_3),
inference(scs_inference,[],[i_0_33,i_0_37,i_0_23]) ).
cnf(i_0_89,plain,
product2(X1,X1,X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_90,plain,
( ~ product2(X1,X2,X3)
| equalish(X4,X1)
| ~ product2(X4,X2,X3) ),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_91,plain,
~ product2(e_3,e_2,e_3),
inference(scs_inference,[],[i_0_33,i_0_89,i_0_37,i_0_23,i_0_25]) ).
cnf(i_0_92,plain,
product2(X1,X1,X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_93,plain,
( ~ product2(X1,X2,X3)
| equalish(X4,X2)
| ~ product2(X1,X4,X3) ),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_94,plain,
~ product2(e_3,e_3,e_2),
inference(scs_inference,[],[i_0_33,i_0_89,i_0_92,i_0_37,i_0_23,i_0_25,i_0_27]) ).
cnf(i_0_95,plain,
product2(X1,X1,X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_96,plain,
( ~ product2(X1,X2,X3)
| equalish(X4,X3)
| ~ product2(X1,X2,X4) ),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_97,plain,
~ product1(e_2,e_3,e_3),
inference(scs_inference,[],[i_0_33,i_0_89,i_0_92,i_0_37,i_0_34,i_0_23,i_0_25,i_0_27,i_0_24]) ).
cnf(i_0_98,plain,
product1(X1,X1,X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_99,plain,
( ~ product1(X1,X2,X3)
| equalish(X4,X1)
| ~ product1(X4,X2,X3) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_100,plain,
~ product1(e_3,e_2,e_3),
inference(scs_inference,[],[i_0_33,i_0_89,i_0_92,i_0_37,i_0_34,i_0_98,i_0_23,i_0_25,i_0_27,i_0_24,i_0_26]) ).
cnf(i_0_101,plain,
product1(X1,X1,X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_102,plain,
( ~ product1(X1,X2,X3)
| equalish(X4,X2)
| ~ product1(X1,X4,X3) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_103,plain,
~ product1(e_3,e_3,e_2),
inference(scs_inference,[],[i_0_33,i_0_89,i_0_92,i_0_37,i_0_34,i_0_98,i_0_101,i_0_23,i_0_25,i_0_27,i_0_24,i_0_26,i_0_28]) ).
cnf(i_0_104,plain,
product1(X1,X1,X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_105,plain,
( ~ product1(X1,X2,X3)
| equalish(X4,X3)
| ~ product1(X1,X2,X4) ),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_106,plain,
product2(e_3,e_2,e_1),
inference(scs_inference,[],[i_0_33,i_0_89,i_0_92,i_0_44,i_0_37,i_0_34,i_0_98,i_0_101,i_0_41,i_0_42,i_0_23,i_0_25,i_0_27,i_0_24,i_0_26,i_0_28,i_0_31]) ).
cnf(i_0_107,plain,
( product2(X1,X2,e_2)
| product2(X1,X2,e_3)
| product2(X1,X2,e_1)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_108,plain,
product1(e_3,e_2,e_1),
inference(scs_inference,[],[i_0_33,i_0_89,i_0_92,i_0_44,i_0_53,i_0_37,i_0_34,i_0_98,i_0_101,i_0_41,i_0_42,i_0_23,i_0_25,i_0_27,i_0_24,i_0_26,i_0_28,i_0_31,i_0_32]) ).
cnf(i_0_109,plain,
( product1(X1,X2,e_2)
| product1(X1,X2,e_3)
| product1(X1,X2,e_1)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_110,plain,
product1(e_2,e_3,e_1),
inference(scs_inference,[],[i_0_33,i_0_89,i_0_92,i_0_44,i_0_53,i_0_37,i_0_34,i_0_98,i_0_101,i_0_41,i_0_42,i_0_23,i_0_25,i_0_27,i_0_24,i_0_26,i_0_28,i_0_31,i_0_32,i_0_86]) ).
cnf(i_0_111,plain,
product2(e_2,e_3,e_1),
inference(scs_inference,[],[i_0_33,i_0_89,i_0_92,i_0_44,i_0_53,i_0_37,i_0_34,i_0_98,i_0_101,i_0_41,i_0_42,i_0_23,i_0_25,i_0_27,i_0_24,i_0_26,i_0_28,i_0_31,i_0_32,i_0_86,i_0_84]) ).
cnf(i_0_112,plain,
( product2(e_1,X1,e_2)
| ~ product1(X1,e_2,e_3) ),
inference(scs_inference,[],[i_0_33,i_0_89,i_0_92,i_0_44,i_0_53,i_0_37,i_0_34,i_0_98,i_0_101,i_0_41,i_0_42,i_0_23,i_0_25,i_0_27,i_0_24,i_0_26,i_0_28,i_0_31,i_0_32,i_0_86,i_0_84,i_0_22]) ).
cnf(i_0_113,plain,
( ~ product1(X1,X2,X3)
| product2(X3,X4,X2)
| ~ product1(X4,X2,X1) ),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_114,plain,
~ product1(e_1,e_3,e_2),
inference(scs_inference,[],[i_0_110,i_0_72,i_0_22]) ).
cnf(i_0_115,plain,
( ~ product1(X1,X2,X3)
| product2(X3,X4,X2)
| ~ product1(X4,X2,X1) ),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_116,plain,
~ product2(e_2,e_1,e_1),
inference(scs_inference,[],[i_0_33,i_0_110,i_0_72,i_0_38,i_0_22,i_0_23]) ).
cnf(i_0_117,plain,
product2(X1,X1,X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_118,plain,
( ~ product2(X1,X2,X3)
| equalish(X4,X1)
| ~ product2(X4,X2,X3) ),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_119,plain,
~ product2(e_1,e_1,e_2),
inference(scs_inference,[],[i_0_33,i_0_117,i_0_110,i_0_72,i_0_38,i_0_22,i_0_23,i_0_27]) ).
cnf(i_0_120,plain,
product2(X1,X1,X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_121,plain,
( ~ product2(X1,X2,X3)
| equalish(X4,X3)
| ~ product2(X1,X2,X4) ),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_122,plain,
~ product1(e_1,e_2,e_1),
inference(scs_inference,[],[i_0_33,i_0_117,i_0_108,i_0_110,i_0_72,i_0_38,i_0_39,i_0_22,i_0_23,i_0_27,i_0_24]) ).
cnf(i_0_123,plain,
( ~ product1(X1,X2,X3)
| equalish(X4,X1)
| ~ product1(X4,X2,X3) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_124,plain,
~ product1(e_1,e_1,e_2),
inference(scs_inference,[],[i_0_33,i_0_117,i_0_108,i_0_110,i_0_72,i_0_38,i_0_39,i_0_34,i_0_22,i_0_23,i_0_27,i_0_24,i_0_28]) ).
cnf(i_0_125,plain,
product1(X1,X1,X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_126,plain,
( ~ product1(X1,X2,X3)
| equalish(X4,X3)
| ~ product1(X1,X2,X4) ),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_127,plain,
~ product2(e_1,e_2,e_1),
inference(scs_inference,[],[i_0_33,i_0_117,i_0_120,i_0_108,i_0_110,i_0_72,i_0_38,i_0_39,i_0_34,i_0_22,i_0_23,i_0_27,i_0_24,i_0_28,i_0_25]) ).
cnf(i_0_128,plain,
product2(X1,X1,X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_129,plain,
( ~ product2(X1,X2,X3)
| equalish(X4,X2)
| ~ product2(X1,X4,X3) ),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_130,plain,
~ product1(e_2,e_1,e_1),
inference(scs_inference,[],[i_0_33,i_0_117,i_0_120,i_0_108,i_0_110,i_0_72,i_0_38,i_0_39,i_0_34,i_0_22,i_0_23,i_0_27,i_0_24,i_0_28,i_0_25,i_0_26]) ).
cnf(i_0_131,plain,
( ~ product1(X1,X2,X3)
| equalish(X4,X2)
| ~ product1(X1,X4,X3) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_132,plain,
product1(e_1,e_3,e_3),
inference(scs_inference,[],[i_0_33,i_0_117,i_0_120,i_0_108,i_0_110,i_0_72,i_0_38,i_0_39,i_0_43,i_0_78,i_0_34,i_0_41,i_0_22,i_0_23,i_0_27,i_0_24,i_0_28,i_0_25,i_0_26,i_0_32]) ).
cnf(i_0_133,plain,
( product1(X1,X2,e_2)
| product1(X1,X2,e_3)
| product1(X1,X2,e_1)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_134,plain,
$false,
inference(scs_inference,[],[i_0_132,i_0_91,i_0_110,i_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP123-9.003 : TPTP v9.2.1. Bugfixed v1.2.1.
% 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
% 0.15/0.33 % Computer : n026.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 18:22:53 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.27/1.62 % Version : CSE_E---1.7
% 0.27/1.62 % Problem : theBenchmark.p
% 0.27/1.62 % SZS status Unsatisfiable for theBenchmark.p
% 0.27/1.62 % SZS output start CNFRefutation
% See solution above
% 0.47/1.82 % Total time : 1.272s
%------------------------------------------------------------------------------