TSTP Solution File: GRP126-4.004 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : GRP126-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n012.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 : Thu Aug 31 00:57:59 EDT 2023
% Result : Unsatisfiable 3.03s 1.18s
% Output : CNFRefutation 3.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 20
% Syntax : Number of clauses : 118 ( 16 unt; 34 nHn; 117 RR)
% Number of literals : 442 ( 0 equ; 207 neg)
% Maximal clause size : 14 ( 3 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 : 133 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c_49,plain,
( ~ group_element(X0)
| ~ group_element(X1)
| product(e_1,X0,X1)
| product(e_2,X0,X1)
| product(e_3,X0,X1)
| product(e_4,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',row_surjectivity) ).
cnf(c_50,plain,
( ~ group_element(X0)
| ~ group_element(X1)
| product(X0,e_1,X1)
| product(X0,e_2,X1)
| product(X0,e_3,X1)
| product(X0,e_4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',column_surjectivity) ).
cnf(c_51,negated_conjecture,
( ~ product(X0,X1,X2)
| ~ product(X3,X2,X0)
| product(X1,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg4_1) ).
cnf(c_52,negated_conjecture,
( ~ product(X0,X1,X2)
| ~ product(X2,X3,X1)
| product(X1,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg4_2) ).
cnf(c_53,plain,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
cnf(c_54,plain,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
cnf(c_55,plain,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
cnf(c_56,plain,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
cnf(c_57,plain,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
cnf(c_58,plain,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
cnf(c_59,plain,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
cnf(c_61,plain,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
cnf(c_65,plain,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
cnf(c_68,plain,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
cnf(c_69,plain,
( ~ group_element(X0)
| ~ group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2)
| product(X0,X1,e_3)
| product(X0,X1,e_4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
cnf(c_70,plain,
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| equalish(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
cnf(c_71,plain,
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| equalish(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(c_72,plain,
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X2)
| equalish(X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(c_73,plain,
product(X0,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
cnf(c_74,negated_conjecture,
( ~ product(X0,X1,X2)
| ~ product(X1,X0,X3)
| product(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg4) ).
cnf(c_75,plain,
product(e_1,e_1,e_1),
inference(instantiation,[status(thm)],[c_73]) ).
cnf(c_183,plain,
( ~ product(X0,X1,e_1)
| ~ product(X0,X1,e_2) ),
inference(resolution,[status(thm)],[c_57,c_70]) ).
cnf(c_184,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_183]) ).
cnf(c_191,plain,
( ~ product(X0,e_1,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[status(thm)],[c_57,c_71]) ).
cnf(c_192,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_191]) ).
cnf(c_199,plain,
( ~ product(e_1,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[c_57,c_72]) ).
cnf(c_200,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_2,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_199]) ).
cnf(c_207,plain,
( ~ product(X0,X1,e_1)
| ~ product(X0,X1,e_3) ),
inference(resolution,[status(thm)],[c_58,c_70]) ).
cnf(c_208,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_207]) ).
cnf(c_215,plain,
( ~ product(X0,e_1,X1)
| ~ product(X0,e_3,X1) ),
inference(resolution,[status(thm)],[c_58,c_71]) ).
cnf(c_216,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_215]) ).
cnf(c_223,plain,
( ~ product(e_1,X0,X1)
| ~ product(e_3,X0,X1) ),
inference(resolution,[status(thm)],[c_58,c_72]) ).
cnf(c_224,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_3,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_223]) ).
cnf(c_231,plain,
( ~ product(X0,X1,e_1)
| ~ product(X0,X1,e_4) ),
inference(resolution,[status(thm)],[c_59,c_70]) ).
cnf(c_232,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_1,e_4) ),
inference(instantiation,[status(thm)],[c_231]) ).
cnf(c_382,plain,
( ~ product(X0,e_1,X1)
| ~ product(X0,e_2,X1)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[c_71]) ).
cnf(c_383,plain,
( ~ product(e_1,X0,X1)
| ~ product(e_2,X0,X1)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[c_72]) ).
cnf(c_384,plain,
( ~ product(X0,X1,e_1)
| ~ product(X0,X1,e_3)
| equalish(e_1,e_3) ),
inference(instantiation,[status(thm)],[c_70]) ).
cnf(c_385,plain,
( ~ product(X0,e_1,X1)
| ~ product(X0,e_3,X1)
| equalish(e_1,e_3) ),
inference(instantiation,[status(thm)],[c_71]) ).
cnf(c_386,plain,
( ~ product(e_1,X0,X1)
| ~ product(e_3,X0,X1)
| equalish(e_1,e_3) ),
inference(instantiation,[status(thm)],[c_72]) ).
cnf(c_388,plain,
( ~ product(X0,e_1,X1)
| ~ product(X0,e_4,X1)
| equalish(e_1,e_4) ),
inference(instantiation,[status(thm)],[c_71]) ).
cnf(c_389,plain,
( ~ product(e_1,X0,X1)
| ~ product(e_4,X0,X1)
| equalish(e_1,e_4) ),
inference(instantiation,[status(thm)],[c_72]) ).
cnf(c_393,plain,
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_3)
| equalish(e_2,e_3) ),
inference(instantiation,[status(thm)],[c_70]) ).
cnf(c_395,plain,
( ~ product(e_2,X0,X1)
| ~ product(e_3,X0,X1)
| equalish(e_2,e_3) ),
inference(instantiation,[status(thm)],[c_72]) ).
cnf(c_405,plain,
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_4)
| equalish(e_3,e_4) ),
inference(instantiation,[status(thm)],[c_70]) ).
cnf(c_406,plain,
( ~ product(X0,e_3,X1)
| ~ product(X0,e_4,X1)
| equalish(e_3,e_4) ),
inference(instantiation,[status(thm)],[c_71]) ).
cnf(c_414,plain,
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_4)
| equalish(e_4,e_3) ),
inference(instantiation,[status(thm)],[c_70]) ).
cnf(c_421,plain,
( ~ group_element(X0)
| ~ group_element(e_2)
| product(X0,e_1,e_2)
| product(X0,e_2,e_2)
| product(X0,e_3,e_2)
| product(X0,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_422,plain,
( ~ group_element(e_1)
| ~ group_element(e_2)
| 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(instantiation,[status(thm)],[c_421]) ).
cnf(c_430,plain,
product(e_2,e_2,e_2),
inference(instantiation,[status(thm)],[c_73]) ).
cnf(c_436,plain,
( ~ product(X0,X1,e_2)
| ~ product(e_2,X2,X1)
| product(X2,e_2,X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_448,plain,
( ~ product(X0,e_2,X1)
| ~ product(X1,X2,e_2)
| product(e_2,X0,X2) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_452,plain,
( ~ group_element(X0)
| ~ group_element(e_2)
| product(e_2,X0,e_1)
| product(e_2,X0,e_2)
| product(e_2,X0,e_3)
| product(e_2,X0,e_4) ),
inference(instantiation,[status(thm)],[c_69]) ).
cnf(c_453,plain,
( ~ group_element(e_1)
| ~ group_element(e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_4) ),
inference(instantiation,[status(thm)],[c_452]) ).
cnf(c_460,plain,
( ~ group_element(X0)
| ~ group_element(e_3)
| product(X0,e_1,e_3)
| product(X0,e_2,e_3)
| product(X0,e_3,e_3)
| product(X0,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_461,plain,
( ~ group_element(e_1)
| ~ group_element(e_3)
| product(e_1,e_1,e_3)
| product(e_1,e_2,e_3)
| product(e_1,e_3,e_3)
| product(e_1,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_460]) ).
cnf(c_468,plain,
( ~ product(e_3,e_3,e_1)
| ~ product(e_3,e_3,e_3)
| equalish(e_1,e_3) ),
inference(instantiation,[status(thm)],[c_384]) ).
cnf(c_469,plain,
product(e_3,e_3,e_3),
inference(instantiation,[status(thm)],[c_73]) ).
cnf(c_475,plain,
( ~ product(X0,X1,e_3)
| ~ product(e_3,X2,X1)
| product(X2,e_3,X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_479,plain,
( ~ group_element(X0)
| ~ group_element(e_3)
| product(X0,e_3,e_1)
| product(X0,e_3,e_2)
| product(X0,e_3,e_3)
| product(X0,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_69]) ).
cnf(c_480,plain,
( ~ group_element(e_1)
| ~ group_element(e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_479]) ).
cnf(c_484,plain,
( ~ group_element(X0)
| ~ group_element(e_3)
| product(e_3,e_1,X0)
| product(e_3,e_2,X0)
| product(e_3,e_3,X0)
| product(e_3,e_4,X0) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_485,plain,
( ~ group_element(e_1)
| ~ group_element(e_3)
| product(e_3,e_1,e_1)
| product(e_3,e_2,e_1)
| product(e_3,e_3,e_1)
| product(e_3,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_484]) ).
cnf(c_486,plain,
( ~ product(X0,X1,X2)
| ~ product(X1,X0,e_3)
| product(e_3,X2,X0) ),
inference(instantiation,[status(thm)],[c_74]) ).
cnf(c_487,plain,
( ~ product(X0,e_3,X1)
| ~ product(X1,X2,e_3)
| product(e_3,X0,X2) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_496,plain,
( ~ group_element(X0)
| ~ group_element(e_4)
| product(e_1,X0,e_4)
| product(e_2,X0,e_4)
| product(e_3,X0,e_4)
| product(e_4,X0,e_4) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_497,plain,
( ~ group_element(e_1)
| ~ group_element(e_4)
| product(e_1,e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_3,e_1,e_4)
| product(e_4,e_1,e_4) ),
inference(instantiation,[status(thm)],[c_496]) ).
cnf(c_501,plain,
( ~ product(X0,e_4,X1)
| ~ product(e_4,X0,X2)
| product(X1,X2,e_4) ),
inference(instantiation,[status(thm)],[c_74]) ).
cnf(c_508,plain,
product(e_4,e_4,e_4),
inference(instantiation,[status(thm)],[c_73]) ).
cnf(c_530,plain,
( ~ group_element(X0)
| ~ group_element(e_4)
| product(e_4,X0,e_1)
| product(e_4,X0,e_2)
| product(e_4,X0,e_3)
| product(e_4,X0,e_4) ),
inference(instantiation,[status(thm)],[c_69]) ).
cnf(c_576,plain,
( ~ product(X0,X1,e_4)
| ~ group_element(X1)
| ~ group_element(X2)
| product(X2,e_4,X0)
| product(e_1,X2,X1)
| product(e_2,X2,X1)
| product(e_3,X2,X1) ),
inference(superposition,[status(thm)],[c_49,c_51]) ).
cnf(c_612,plain,
( ~ product(X0,X1,e_4)
| ~ group_element(X1)
| ~ group_element(X2)
| product(X2,e_4,X0)
| product(e_1,X2,X1)
| product(e_2,X2,X1)
| product(e_3,X2,X1) ),
inference(superposition,[status(thm)],[c_49,c_51]) ).
cnf(c_1035,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_2,e_2,e_2)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[c_382]) ).
cnf(c_1037,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_2,e_2,e_2)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[c_383]) ).
cnf(c_1055,plain,
( ~ product(e_3,e_3,e_2)
| ~ product(e_3,e_3,e_3)
| equalish(e_2,e_3) ),
inference(instantiation,[status(thm)],[c_393]) ).
cnf(c_1060,plain,
( ~ product(e_3,e_1,e_3)
| ~ product(e_3,e_3,e_3)
| equalish(e_1,e_3) ),
inference(instantiation,[status(thm)],[c_385]) ).
cnf(c_1063,plain,
( ~ product(e_2,e_3,e_3)
| ~ product(e_3,e_3,e_3)
| equalish(e_2,e_3) ),
inference(instantiation,[status(thm)],[c_395]) ).
cnf(c_1064,plain,
( ~ product(e_1,e_3,e_3)
| ~ product(e_3,e_3,e_3)
| equalish(e_1,e_3) ),
inference(instantiation,[status(thm)],[c_386]) ).
cnf(c_1088,plain,
( ~ group_element(X0)
| ~ group_element(X1)
| ~ group_element(e_4)
| product(e_1,X1,X0)
| product(e_2,X1,X0)
| product(e_3,X1,X0)
| product(X1,e_4,e_4)
| product(e_1,X0,e_4)
| product(e_2,X0,e_4)
| product(e_3,X0,e_4) ),
inference(superposition,[status(thm)],[c_49,c_576]) ).
cnf(c_1089,plain,
( ~ group_element(X0)
| ~ group_element(X1)
| product(e_1,X1,X0)
| product(e_2,X1,X0)
| product(e_3,X1,X0)
| product(X1,e_4,e_4)
| product(e_1,X0,e_4)
| product(e_2,X0,e_4)
| product(e_3,X0,e_4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1088,c_56]) ).
cnf(c_1113,plain,
( ~ group_element(X0)
| ~ group_element(X1)
| ~ group_element(e_4)
| product(e_1,X1,X0)
| product(e_2,X1,X0)
| product(e_3,X1,X0)
| product(X1,e_4,e_4)
| product(e_1,X0,e_4)
| product(e_2,X0,e_4)
| product(e_3,X0,e_4) ),
inference(superposition,[status(thm)],[c_49,c_612]) ).
cnf(c_1114,plain,
( ~ group_element(X0)
| ~ group_element(X1)
| product(e_1,X1,X0)
| product(e_2,X1,X0)
| product(e_3,X1,X0)
| product(X1,e_4,e_4)
| product(e_1,X0,e_4)
| product(e_2,X0,e_4)
| product(e_3,X0,e_4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1113,c_56]) ).
cnf(c_1334,plain,
( ~ product(e_4,e_4,e_3)
| ~ product(e_4,e_4,e_4)
| equalish(e_3,e_4) ),
inference(instantiation,[status(thm)],[c_405]) ).
cnf(c_1340,plain,
( ~ product(e_4,e_3,e_4)
| ~ product(e_4,e_4,e_4)
| equalish(e_3,e_4) ),
inference(instantiation,[status(thm)],[c_406]) ).
cnf(c_1342,plain,
( ~ product(e_4,e_1,e_4)
| ~ product(e_4,e_4,e_4)
| equalish(e_1,e_4) ),
inference(instantiation,[status(thm)],[c_388]) ).
cnf(c_1348,plain,
( ~ product(e_1,e_4,e_4)
| ~ product(e_4,e_4,e_4)
| equalish(e_1,e_4) ),
inference(instantiation,[status(thm)],[c_389]) ).
cnf(c_1402,plain,
( ~ group_element(e_3)
| ~ group_element(e_4)
| product(e_1,e_3,e_4)
| product(e_1,e_4,e_4)
| product(e_2,e_3,e_4)
| product(e_2,e_4,e_4)
| product(e_3,e_3,e_4)
| product(e_3,e_4,e_4) ),
inference(equality_factoring,[status(thm)],[c_1089]) ).
cnf(c_1409,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_4,e_4)
| product(e_2,e_3,e_4)
| product(e_2,e_4,e_4)
| product(e_3,e_3,e_4)
| product(e_3,e_4,e_4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1402,c_56,c_55]) ).
cnf(c_1646,plain,
( ~ product(X0,e_3,X1)
| ~ group_element(X0)
| ~ group_element(X2)
| product(e_1,X2,X0)
| product(e_2,X2,X0)
| product(e_3,X2,X0)
| product(X1,e_4,e_3)
| product(X2,e_4,e_4)
| product(e_1,X0,e_4)
| product(e_2,X0,e_4) ),
inference(superposition,[status(thm)],[c_1114,c_74]) ).
cnf(c_2063,plain,
( ~ product(e_1,e_3,e_2)
| ~ product(e_4,e_3,e_2)
| equalish(e_1,e_4) ),
inference(instantiation,[status(thm)],[c_389]) ).
cnf(c_2067,plain,
( ~ product(X0,e_2,X1)
| ~ product(X1,e_3,e_2)
| product(e_2,X0,e_3) ),
inference(instantiation,[status(thm)],[c_448]) ).
cnf(c_2468,plain,
( ~ product(e_2,X0,X1)
| ~ product(X0,e_2,e_3)
| product(e_3,X1,e_2) ),
inference(instantiation,[status(thm)],[c_486]) ).
cnf(c_2751,plain,
( ~ group_element(X0)
| ~ group_element(X1)
| ~ group_element(e_3)
| product(X0,e_4,e_4)
| product(X1,e_4,e_4)
| product(e_1,X0,e_3)
| product(e_1,X1,e_3)
| product(e_2,X0,e_3)
| product(e_2,X1,e_3)
| product(e_3,X0,e_3)
| product(e_3,X1,e_3)
| product(e_1,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_4,e_4,e_3) ),
inference(superposition,[status(thm)],[c_1114,c_1646]) ).
cnf(c_2766,plain,
( ~ group_element(X0)
| ~ group_element(X1)
| product(X0,e_4,e_4)
| product(X1,e_4,e_4)
| product(e_1,X0,e_3)
| product(e_1,X1,e_3)
| product(e_2,X0,e_3)
| product(e_2,X1,e_3)
| product(e_3,X0,e_3)
| product(e_3,X1,e_3)
| product(e_1,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_4,e_4,e_3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2751,c_55]) ).
cnf(c_2797,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_3)
| product(e_1,e_3,e_4)
| product(e_1,e_4,e_4)
| product(e_2,e_1,e_3)
| product(e_2,e_3,e_4)
| product(e_3,e_1,e_3)
| product(e_4,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_2766]) ).
cnf(c_3029,plain,
( ~ product(X0,e_3,e_2)
| ~ product(e_2,X1,e_3)
| product(X1,e_2,X0) ),
inference(instantiation,[status(thm)],[c_436]) ).
cnf(c_3030,plain,
( ~ product(e_1,e_3,e_2)
| ~ product(e_2,e_1,e_3)
| product(e_1,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_3029]) ).
cnf(c_3532,plain,
( ~ product(e_3,e_4,X0)
| ~ product(e_4,e_3,X1)
| product(X0,X1,e_4) ),
inference(instantiation,[status(thm)],[c_501]) ).
cnf(c_3533,plain,
( ~ product(e_3,e_4,e_1)
| ~ product(e_4,e_3,e_1)
| product(e_1,e_1,e_4) ),
inference(instantiation,[status(thm)],[c_3532]) ).
cnf(c_3691,plain,
( ~ product(X0,e_4,e_3)
| ~ product(e_3,X1,e_4)
| product(X1,e_3,X0) ),
inference(instantiation,[status(thm)],[c_475]) ).
cnf(c_3692,plain,
( ~ product(e_1,e_4,e_3)
| ~ product(e_3,e_1,e_4)
| product(e_1,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_3691]) ).
cnf(c_3779,plain,
( ~ product(e_2,X0,e_3)
| ~ product(e_2,X0,e_4)
| equalish(e_4,e_3) ),
inference(instantiation,[status(thm)],[c_414]) ).
cnf(c_3790,plain,
( ~ product(e_2,e_1,e_3)
| ~ product(e_2,e_1,e_4)
| equalish(e_4,e_3) ),
inference(instantiation,[status(thm)],[c_3779]) ).
cnf(c_3805,plain,
( ~ product(X0,e_4,e_2)
| ~ product(e_2,X1,e_4)
| product(X1,e_2,X0) ),
inference(instantiation,[status(thm)],[c_436]) ).
cnf(c_3806,plain,
( ~ product(e_1,e_4,e_2)
| ~ product(e_2,e_1,e_4)
| product(e_1,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_3805]) ).
cnf(c_3840,plain,
( product(e_2,e_3,e_4)
| product(e_1,e_3,e_4) ),
inference(global_subsumption_just,[status(thm)],[c_1409,c_55,c_53,c_75,c_65,c_59,c_58,c_192,c_208,c_216,c_469,c_480,c_508,c_1060,c_1064,c_1334,c_1348,c_2797,c_3030]) ).
cnf(c_3841,plain,
( product(e_1,e_3,e_4)
| product(e_2,e_3,e_4) ),
inference(renaming,[status(thm)],[c_3840]) ).
cnf(c_3852,plain,
( ~ group_element(X0)
| ~ group_element(e_3)
| product(X0,e_4,e_2)
| product(e_1,X0,e_3)
| product(e_2,X0,e_3)
| product(e_3,X0,e_3)
| product(e_1,e_3,e_4) ),
inference(superposition,[status(thm)],[c_3841,c_576]) ).
cnf(c_3862,plain,
( ~ group_element(X0)
| product(X0,e_4,e_2)
| product(e_1,X0,e_3)
| product(e_2,X0,e_3)
| product(e_3,X0,e_3)
| product(e_1,e_3,e_4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3852,c_55]) ).
cnf(c_3900,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_3)
| product(e_1,e_3,e_4)
| product(e_1,e_4,e_2)
| product(e_2,e_1,e_3)
| product(e_3,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_3862]) ).
cnf(c_4447,plain,
( ~ product(X0,e_3,e_4)
| ~ product(e_4,e_3,e_3)
| product(e_3,X0,e_3) ),
inference(instantiation,[status(thm)],[c_487]) ).
cnf(c_4448,plain,
( ~ product(e_1,e_3,e_4)
| ~ product(e_4,e_3,e_3)
| product(e_3,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_4447]) ).
cnf(c_5021,plain,
( ~ product(X0,e_3,e_2)
| ~ product(e_3,e_2,X0)
| product(e_2,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_2067]) ).
cnf(c_5022,plain,
( ~ product(e_1,e_3,e_2)
| ~ product(e_3,e_2,e_1)
| product(e_2,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_5021]) ).
cnf(c_5145,plain,
( ~ group_element(e_3)
| ~ group_element(e_4)
| product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_530]) ).
cnf(c_5181,plain,
( ~ product(X0,e_2,e_3)
| ~ product(e_2,X0,e_3)
| product(e_3,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_2468]) ).
cnf(c_5182,plain,
( ~ product(e_1,e_2,e_3)
| ~ product(e_2,e_1,e_3)
| product(e_3,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_5181]) ).
cnf(c_5352,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5182,c_5145,c_5022,c_4448,c_3900,c_3806,c_3790,c_3692,c_3533,c_2063,c_1340,c_1342,c_1063,c_1064,c_1060,c_1055,c_1037,c_1035,c_508,c_497,c_485,c_469,c_468,c_461,c_453,c_430,c_422,c_232,c_224,c_216,c_208,c_200,c_192,c_184,c_57,c_58,c_59,c_61,c_65,c_68,c_75,c_53,c_54,c_55,c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP126-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 29 02:11:54 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.49 Running first-order theorem proving
% 0.21/0.49 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.03/1.18 % SZS status Started for theBenchmark.p
% 3.03/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 3.03/1.18
% 3.03/1.18 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.03/1.18
% 3.03/1.18 ------ iProver source info
% 3.03/1.18
% 3.03/1.18 git: date: 2023-05-31 18:12:56 +0000
% 3.03/1.18 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.03/1.18 git: non_committed_changes: false
% 3.03/1.18 git: last_make_outside_of_git: false
% 3.03/1.18
% 3.03/1.18 ------ Parsing...successful
% 3.03/1.18
% 3.03/1.18 ------ preprocesses with Option_epr_non_horn_non_eq
% 3.03/1.18
% 3.03/1.18
% 3.03/1.18 ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e
% 3.03/1.18
% 3.03/1.18 ------ Preprocessing...------ preprocesses with Option_epr_non_horn_non_eq
% 3.03/1.18 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.03/1.18 ------ Proving...
% 3.03/1.18 ------ Problem Properties
% 3.03/1.18
% 3.03/1.18
% 3.03/1.18 clauses 26
% 3.03/1.18 conjectures 3
% 3.03/1.18 EPR 26
% 3.03/1.18 Horn 23
% 3.03/1.18 unary 17
% 3.03/1.18 binary 0
% 3.03/1.18 lits 53
% 3.03/1.18 lits eq 0
% 3.03/1.18 fd_pure 0
% 3.03/1.18 fd_pseudo 0
% 3.03/1.18 fd_cond 0
% 3.03/1.18 fd_pseudo_cond 0
% 3.03/1.18 AC symbols 0
% 3.03/1.18
% 3.03/1.18 ------ Schedule EPR non Horn non eq is on
% 3.03/1.18
% 3.03/1.18 ------ no equalities: superposition off
% 3.03/1.18
% 3.03/1.18 ------ Input Options "--resolution_flag false" Time Limit: 70.
% 3.03/1.18
% 3.03/1.18
% 3.03/1.18 ------
% 3.03/1.18 Current options:
% 3.03/1.18 ------
% 3.03/1.18
% 3.03/1.18
% 3.03/1.18
% 3.03/1.18
% 3.03/1.18 ------ Proving...
% 3.03/1.18
% 3.03/1.18
% 3.03/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 3.03/1.18
% 3.03/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.03/1.18
% 3.03/1.18
%------------------------------------------------------------------------------