%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP130-1.003 : TPTP v9.2.1. Released v1.2.0.
% 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 : n005.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 04:24:28 PM UTC 2026
% Result : Unsatisfiable 1.40s 1.77s
% Output : CNFRefutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 14
% Syntax : Number of clauses : 90 ( 23 unt; 56 nHn; 90 RR)
% Number of literals : 244 ( 0 equ; 60 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 : 62 ( 0 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/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(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
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(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(qg3,negated_conjecture,
( product(X4,X2,X1)
| ~ product(X1,X2,X3)
| ~ product(X1,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).
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_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(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_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_1,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
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(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(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(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_23,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_24,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_25,axiom,
~ equalish(e_2,e_3),
e_2_is_not_e_3 ).
cnf(c_0_26,negated_conjecture,
( product(X4,X2,X1)
| ~ product(X1,X2,X3)
| ~ product(X1,X3,X4) ),
qg3 ).
cnf(c_0_27,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_22,c_0_17]) ).
cnf(c_0_28,axiom,
~ equalish(e_1,e_3),
e_1_is_not_e_3 ).
cnf(c_0_29,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_23,c_0_24]),c_0_25]) ).
cnf(c_0_30,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_24]) ).
cnf(c_0_31,axiom,
~ equalish(e_1,e_2),
e_1_is_not_e_2 ).
cnf(c_0_32,negated_conjecture,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,X1,e_1)
| ~ product(e_1,X1,e_3) ),
inference(spm,[status(thm)],[c_0_26,c_0_20]) ).
cnf(c_0_33,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_1,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_23,c_0_27]),c_0_28]) ).
cnf(c_0_34,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_29]) ).
cnf(c_0_35,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_1,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_30,c_0_27]),c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,X1,e_1)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_38,plain,
( product(e_1,e_1,e_2)
| 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_34,c_0_35]),c_0_28]) ).
cnf(c_0_39,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_22,c_0_15]) ).
cnf(c_0_40,negated_conjecture,
( product(e_1,e_1,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_23,c_0_36]),c_0_28]) ).
cnf(c_0_41,negated_conjecture,
( product(e_1,e_3,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_37,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_1,X1,e_3)
| ~ product(e_3,X1,e_1) ),
inference(spm,[status(thm)],[c_0_26,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_2,X1,e_1)
| ~ product(e_1,X1,e_1) ),
inference(spm,[status(thm)],[c_0_26,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
( 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_30,c_0_41]),c_0_31]) ).
cnf(c_0_45,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
product_total_function2 ).
cnf(c_0_46,negated_conjecture,
( product(e_1,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_42,c_0_39]) ).
cnf(c_0_47,negated_conjecture,
( product(e_2,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_43,c_0_20]) ).
cnf(c_0_48,negated_conjecture,
( product(e_1,e_3,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_37,c_0_44]) ).
cnf(c_0_49,axiom,
~ equalish(e_3,e_2),
e_3_is_not_e_2 ).
cnf(c_0_50,negated_conjecture,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| equalish(X1,e_3)
| ~ product(e_1,e_1,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,X1,e_1)
| ~ product(e_1,X1,e_3) ),
inference(spm,[status(thm)],[c_0_26,c_0_47]) ).
cnf(c_0_52,negated_conjecture,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_48]),c_0_49]) ).
cnf(c_0_53,negated_conjecture,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| equalish(X1,e_1)
| ~ product(e_1,X1,e_3) ),
inference(spm,[status(thm)],[c_0_19,c_0_46]) ).
cnf(c_0_54,negated_conjecture,
( product(e_1,e_3,e_3)
| 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_50,c_0_40]),c_0_25]) ).
cnf(c_0_55,axiom,
~ equalish(e_3,e_1),
e_3_is_not_e_1 ).
cnf(c_0_56,negated_conjecture,
( product(e_3,e_3,e_1)
| product(e_2,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_51,c_0_47]) ).
cnf(c_0_57,negated_conjecture,
( product(e_1,e_2,e_2)
| product(e_3,X1,e_1)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_26,c_0_52]) ).
cnf(c_0_58,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_53,c_0_54]),c_0_55]) ).
cnf(c_0_59,axiom,
~ equalish(e_2,e_1),
e_2_is_not_e_1 ).
cnf(c_0_60,negated_conjecture,
( product(e_2,e_3,e_1)
| product(e_3,e_3,e_1)
| equalish(X1,e_3)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_19,c_0_56]) ).
cnf(c_0_61,negated_conjecture,
( product(e_2,e_3,e_1)
| product(e_3,e_3,e_1)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_57,c_0_56]) ).
cnf(c_0_62,negated_conjecture,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| equalish(X1,e_3)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_19,c_0_58]) ).
cnf(c_0_63,negated_conjecture,
( product(e_1,e_2,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_53,c_0_52]),c_0_59]) ).
cnf(c_0_64,negated_conjecture,
( product(e_3,e_3,e_1)
| product(e_2,e_3,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_25]) ).
cnf(c_0_65,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_66,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
product_left_cancellation ).
cnf(c_0_67,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_62,c_0_63]),c_0_25]) ).
cnf(c_0_68,negated_conjecture,
( product(e_2,e_3,e_1)
| product(e_1,X1,e_3)
| ~ product(e_3,X1,e_3) ),
inference(spm,[status(thm)],[c_0_26,c_0_64]) ).
cnf(c_0_69,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| equalish(X1,e_2)
| ~ product(e_3,X1,e_1) ),
inference(spm,[status(thm)],[c_0_19,c_0_65]) ).
cnf(c_0_70,negated_conjecture,
( product(e_3,e_1,e_2)
| equalish(X1,e_3)
| ~ product(X1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_71,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_1,e_1,e_3)
| product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_68,c_0_67]) ).
cnf(c_0_72,negated_conjecture,
( product(e_2,e_3,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_64]),c_0_49]) ).
cnf(c_0_73,negated_conjecture,
( product(e_2,e_3,e_1)
| product(e_3,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_28]) ).
cnf(c_0_74,negated_conjecture,
( product(e_3,e_2,e_2)
| product(e_2,e_3,e_1)
| equalish(X1,e_3)
| ~ product(X1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_66,c_0_72]) ).
cnf(c_0_75,negated_conjecture,
( product(e_3,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_68,c_0_72]) ).
cnf(c_0_76,negated_conjecture,
( product(e_2,e_3,e_1)
| equalish(X1,e_1)
| ~ product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_19,c_0_73]) ).
cnf(c_0_77,negated_conjecture,
( product(e_2,e_3,e_1)
| product(e_3,e_2,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_28]) ).
cnf(c_0_78,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| equalish(X1,e_1)
| ~ product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_66,c_0_20]) ).
cnf(c_0_79,negated_conjecture,
product(e_2,e_3,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_59]) ).
cnf(c_0_80,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_52]) ).
cnf(c_0_81,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_59]) ).
cnf(c_0_82,negated_conjecture,
( equalish(X1,e_2)
| ~ product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_66,c_0_79]) ).
cnf(c_0_83,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_80,c_0_81]),c_0_49]) ).
cnf(c_0_84,negated_conjecture,
~ product(e_3,e_3,e_1),
inference(spm,[status(thm)],[c_0_49,c_0_82]) ).
cnf(c_0_85,negated_conjecture,
product(e_1,e_2,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_83]),c_0_84]) ).
cnf(c_0_86,negated_conjecture,
( equalish(X1,e_3)
| ~ product(e_2,X1,e_1) ),
inference(spm,[status(thm)],[c_0_19,c_0_79]) ).
cnf(c_0_87,negated_conjecture,
( product(e_2,X1,e_1)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_26,c_0_85]) ).
cnf(c_0_88,negated_conjecture,
~ product(e_2,e_2,e_1),
inference(spm,[status(thm)],[c_0_25,c_0_86]) ).
cnf(c_0_89,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_85]),c_0_88]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP130-1.003 : TPTP v9.2.1. Released v1.2.0.
% 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 : n005.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 18:24:00 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.40/1.77 % Version : CSE_E---1.7
% 1.40/1.77 % Problem : theBenchmark.p
% 1.40/1.77 % SZS status Unsatisfiable for theBenchmark.p
% 1.40/1.77 % SZS output start CNFRefutation
% See solution above
% 1.40/1.77 % Total time : 1.373s
%------------------------------------------------------------------------------