TSTP Solution File: GRP129-4.004 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : GRP129-4.004 : 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 00:58:06 EDT 2023
% Result : Unsatisfiable 3.38s 1.16s
% Output : CNFRefutation 3.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 21
% Syntax : Number of clauses : 159 ( 13 unt; 18 nHn; 159 RR)
% Number of literals : 486 ( 0 equ; 296 neg)
% Maximal clause size : 6 ( 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 : 179 ( 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(X1,X3,X2)
| product(X3,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3_1) ).
cnf(c_52,negated_conjecture,
( ~ product(X0,X1,X2)
| ~ product(X2,X0,X3)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3_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_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_60,plain,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
cnf(c_61,plain,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
cnf(c_63,plain,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
cnf(c_64,plain,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
cnf(c_66,plain,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
cnf(c_67,plain,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
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,negated_conjecture,
( ~ product(X0,X1,X2)
| ~ product(X3,X0,X1)
| product(X1,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
cnf(c_75,plain,
( ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_4) ),
inference(instantiation,[status(thm)],[c_69]) ).
cnf(c_182,plain,
( ~ product(X0,X1,e_1)
| ~ product(X0,X1,e_2) ),
inference(resolution,[status(thm)],[c_57,c_70]) ).
cnf(c_183,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_182]) ).
cnf(c_190,plain,
( ~ product(X0,e_1,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[status(thm)],[c_57,c_71]) ).
cnf(c_191,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_190]) ).
cnf(c_198,plain,
( ~ product(e_1,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[c_57,c_72]) ).
cnf(c_199,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_2,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_198]) ).
cnf(c_206,plain,
( ~ product(X0,X1,e_1)
| ~ product(X0,X1,e_3) ),
inference(resolution,[status(thm)],[c_58,c_70]) ).
cnf(c_207,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_206]) ).
cnf(c_214,plain,
( ~ product(X0,e_1,X1)
| ~ product(X0,e_3,X1) ),
inference(resolution,[status(thm)],[c_58,c_71]) ).
cnf(c_215,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_214]) ).
cnf(c_222,plain,
( ~ product(e_1,X0,X1)
| ~ product(e_3,X0,X1) ),
inference(resolution,[status(thm)],[c_58,c_72]) ).
cnf(c_223,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_3,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_222]) ).
cnf(c_246,plain,
( ~ product(e_1,X0,X1)
| ~ product(e_4,X0,X1) ),
inference(resolution,[status(thm)],[c_59,c_72]) ).
cnf(c_247,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_4,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_246]) ).
cnf(c_381,plain,
( ~ product(X0,e_1,X1)
| ~ product(X0,e_2,X1)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[c_71]) ).
cnf(c_385,plain,
( ~ product(e_1,X0,X1)
| ~ product(e_3,X0,X1)
| equalish(e_1,e_3) ),
inference(instantiation,[status(thm)],[c_72]) ).
cnf(c_390,plain,
( ~ product(X0,e_1,X1)
| ~ product(X0,e_2,X1)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[c_71]) ).
cnf(c_391,plain,
( ~ product(e_1,X0,X1)
| ~ product(e_2,X0,X1)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[c_72]) ).
cnf(c_393,plain,
( ~ product(X0,e_2,X1)
| ~ product(X0,e_3,X1)
| equalish(e_2,e_3) ),
inference(instantiation,[status(thm)],[c_71]) ).
cnf(c_394,plain,
( ~ product(e_2,X0,X1)
| ~ product(e_3,X0,X1)
| equalish(e_2,e_3) ),
inference(instantiation,[status(thm)],[c_72]) ).
cnf(c_398,plain,
( ~ product(X0,X1,e_1)
| ~ product(X0,X1,e_3)
| equalish(e_3,e_1) ),
inference(instantiation,[status(thm)],[c_70]) ).
cnf(c_401,plain,
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_3)
| equalish(e_3,e_2) ),
inference(instantiation,[status(thm)],[c_70]) ).
cnf(c_403,plain,
( ~ product(e_2,X0,X1)
| ~ product(e_3,X0,X1)
| equalish(e_3,e_2) ),
inference(instantiation,[status(thm)],[c_72]) ).
cnf(c_407,plain,
( ~ product(X0,X1,e_1)
| ~ product(X0,X1,e_4)
| equalish(e_4,e_1) ),
inference(instantiation,[status(thm)],[c_70]) ).
cnf(c_410,plain,
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_4)
| equalish(e_4,e_2) ),
inference(instantiation,[status(thm)],[c_70]) ).
cnf(c_420,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_421,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_420]) ).
cnf(c_422,plain,
( ~ product(X0,X1,X2)
| ~ product(X1,X2,e_2)
| product(X2,X0,e_2) ),
inference(instantiation,[status(thm)],[c_73]) ).
cnf(c_423,plain,
( ~ product(X0,e_2,X1)
| ~ product(e_2,X2,X1)
| product(X2,X0,e_2) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_425,plain,
( ~ product(X0,X1,X2)
| ~ product(X2,X0,e_2)
| product(X1,X2,e_2) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_427,plain,
( ~ group_element(X0)
| ~ group_element(e_2)
| product(e_1,e_2,X0)
| product(e_2,e_2,X0)
| product(e_3,e_2,X0)
| product(e_4,e_2,X0) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_428,plain,
( ~ group_element(e_1)
| ~ group_element(e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_2,e_1)
| product(e_3,e_2,e_1)
| product(e_4,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_427]) ).
cnf(c_429,plain,
( ~ product(X0,X1,X2)
| ~ product(e_2,X0,X1)
| product(X1,e_2,X2) ),
inference(instantiation,[status(thm)],[c_73]) ).
cnf(c_431,plain,
( ~ product(X0,X1,X2)
| ~ product(e_2,X0,X2)
| product(X1,e_2,X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_432,plain,
( ~ product(X0,X1,e_2)
| ~ product(e_2,X0,X2)
| product(X1,e_2,X2) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_435,plain,
( ~ group_element(X0)
| ~ group_element(e_2)
| product(X0,e_2,e_1)
| product(X0,e_2,e_2)
| product(X0,e_2,e_3)
| product(X0,e_2,e_4) ),
inference(instantiation,[status(thm)],[c_69]) ).
cnf(c_436,plain,
( ~ group_element(e_1)
| ~ group_element(e_2)
| 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(instantiation,[status(thm)],[c_435]) ).
cnf(c_438,plain,
( ~ group_element(X0)
| ~ group_element(e_2)
| product(e_2,e_1,X0)
| product(e_2,e_2,X0)
| product(e_2,e_3,X0)
| product(e_2,e_4,X0) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_439,plain,
( ~ group_element(e_1)
| ~ group_element(e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_1)
| product(e_2,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_438]) ).
cnf(c_440,plain,
( ~ product(X0,e_2,X1)
| ~ product(X2,X0,e_2)
| product(e_2,X2,X1) ),
inference(instantiation,[status(thm)],[c_73]) ).
cnf(c_442,plain,
( ~ product(X0,X1,X2)
| ~ product(X1,e_2,X2)
| product(e_2,X0,X1) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_443,plain,
( ~ product(X0,X1,X2)
| ~ product(X1,e_2,X0)
| product(e_2,X0,X2) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_445,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_446,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_445]) ).
cnf(c_453,plain,
( ~ product(X0,X1,X2)
| ~ product(X1,X2,e_3)
| product(X2,X0,e_3) ),
inference(instantiation,[status(thm)],[c_73]) ).
cnf(c_460,plain,
( ~ product(X0,X1,X2)
| ~ product(e_3,X0,X1)
| product(X1,e_3,X2) ),
inference(instantiation,[status(thm)],[c_73]) ).
cnf(c_462,plain,
( ~ product(X0,X1,X2)
| ~ product(e_3,X0,X2)
| product(X1,e_3,X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_463,plain,
( ~ product(X0,X1,e_3)
| ~ product(e_3,X0,X2)
| product(X1,e_3,X2) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_471,plain,
( ~ product(X0,e_3,X1)
| ~ product(X2,X0,e_3)
| product(e_3,X2,X1) ),
inference(instantiation,[status(thm)],[c_73]) ).
cnf(c_476,plain,
( ~ group_element(X0)
| ~ group_element(e_3)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2)
| product(e_3,X0,e_3)
| product(e_3,X0,e_4) ),
inference(instantiation,[status(thm)],[c_69]) ).
cnf(c_477,plain,
( ~ group_element(e_1)
| ~ group_element(e_3)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_4) ),
inference(instantiation,[status(thm)],[c_476]) ).
cnf(c_664,plain,
( ~ product(X0,X1,e_4)
| ~ product(X1,X2,e_4)
| product(X2,X0,X1) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_665,plain,
( ~ product(e_1,e_1,e_4)
| product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_664]) ).
cnf(c_667,plain,
( ~ product(X0,e_4,X1)
| ~ product(X2,X0,e_4)
| product(e_4,X2,X1) ),
inference(instantiation,[status(thm)],[c_73]) ).
cnf(c_1520,plain,
( ~ product(X0,e_2,X1)
| ~ product(e_2,X0,X1)
| product(e_2,e_2,X0) ),
inference(instantiation,[status(thm)],[c_431]) ).
cnf(c_1521,plain,
( ~ product(X0,e_2,X1)
| ~ product(e_2,X0,e_2)
| product(e_2,e_2,X1) ),
inference(instantiation,[status(thm)],[c_429]) ).
cnf(c_1531,plain,
( ~ product(X0,e_2,X1)
| ~ product(e_2,X1,X2)
| product(X1,X0,X2) ),
inference(instantiation,[status(thm)],[c_73]) ).
cnf(c_1556,plain,
( ~ product(e_4,X0,X1)
| ~ product(X0,e_2,e_4)
| product(e_2,e_4,X1) ),
inference(instantiation,[status(thm)],[c_443]) ).
cnf(c_1615,plain,
( ~ product(X0,X1,e_3)
| ~ product(X1,X2,e_3)
| product(X2,X0,X1) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_1616,plain,
( ~ product(e_1,e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_1615]) ).
cnf(c_1720,plain,
( ~ product(X0,e_2,e_3)
| ~ product(e_3,X0,e_2)
| product(e_2,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_453]) ).
cnf(c_1737,plain,
( ~ product(e_1,e_2,e_3)
| ~ product(e_3,e_1,e_2)
| product(e_2,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_1720]) ).
cnf(c_1779,plain,
( ~ product(X0,e_2,X1)
| ~ product(e_3,X0,e_2)
| product(e_2,e_3,X1) ),
inference(instantiation,[status(thm)],[c_460]) ).
cnf(c_1794,plain,
( ~ product(X0,X1,e_3)
| ~ product(e_3,X0,e_2)
| product(X1,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_425]) ).
cnf(c_2112,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_2,e_2,e_2)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[c_391]) ).
cnf(c_2123,plain,
( ~ product(X0,e_2,e_2)
| ~ product(e_2,X0,e_2)
| product(e_2,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_425]) ).
cnf(c_2124,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_2,e_1,e_2)
| product(e_2,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_2123]) ).
cnf(c_2365,plain,
( ~ product(X0,e_4,X1)
| ~ product(e_3,X0,e_4)
| product(e_4,e_3,X1) ),
inference(instantiation,[status(thm)],[c_460]) ).
cnf(c_2712,plain,
( ~ group_element(e_2)
| 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(instantiation,[status(thm)],[c_435]) ).
cnf(c_2720,plain,
( ~ product(e_2,X0,e_2)
| ~ product(e_2,e_2,X0)
| product(X0,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_422]) ).
cnf(c_2731,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_2,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_2720]) ).
cnf(c_2740,plain,
( ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_2,e_3)
| equalish(e_3,e_1) ),
inference(instantiation,[status(thm)],[c_398]) ).
cnf(c_2742,plain,
( ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_2,e_4)
| equalish(e_4,e_1) ),
inference(instantiation,[status(thm)],[c_407]) ).
cnf(c_2756,plain,
( ~ product(X0,e_2,e_2)
| ~ product(e_2,e_2,X1)
| product(e_2,X0,X1) ),
inference(instantiation,[status(thm)],[c_440]) ).
cnf(c_2757,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_2,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_2756]) ).
cnf(c_2759,plain,
( ~ product(e_2,e_2,X0)
| ~ product(e_3,e_2,X0)
| equalish(e_3,e_2) ),
inference(instantiation,[status(thm)],[c_403]) ).
cnf(c_2768,plain,
( ~ product(e_2,X0,e_2)
| ~ product(e_2,e_2,X1)
| product(X0,e_2,X1) ),
inference(instantiation,[status(thm)],[c_432]) ).
cnf(c_2934,plain,
( ~ product(e_2,X0,e_3)
| ~ product(e_3,e_2,e_3)
| product(X0,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_462]) ).
cnf(c_2937,plain,
( ~ product(X0,e_3,e_2)
| ~ product(e_2,X0,e_3)
| product(e_3,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_422]) ).
cnf(c_2948,plain,
( ~ product(e_1,e_3,e_2)
| ~ product(e_2,e_1,e_3)
| product(e_3,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_2937]) ).
cnf(c_2950,plain,
( ~ product(e_2,e_1,e_3)
| ~ product(e_3,e_2,e_3)
| product(e_1,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_2934]) ).
cnf(c_2954,plain,
( ~ product(e_2,X0,e_2)
| ~ product(e_2,X0,e_3)
| equalish(e_3,e_2) ),
inference(instantiation,[status(thm)],[c_401]) ).
cnf(c_2956,plain,
( ~ product(e_2,X0,e_3)
| ~ product(e_3,e_2,X1)
| product(X0,e_3,X1) ),
inference(instantiation,[status(thm)],[c_463]) ).
cnf(c_2957,plain,
( ~ product(e_2,e_1,e_3)
| ~ product(e_3,e_2,e_1)
| product(e_1,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_2956]) ).
cnf(c_2959,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_2,e_1,e_3)
| equalish(e_3,e_2) ),
inference(instantiation,[status(thm)],[c_2954]) ).
cnf(c_2963,plain,
( ~ product(e_2,e_1,e_3)
| ~ product(e_2,e_2,e_3)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[c_390]) ).
cnf(c_2976,plain,
( ~ product(X0,e_2,e_3)
| ~ product(e_2,e_3,e_3)
| product(e_3,X0,e_3) ),
inference(instantiation,[status(thm)],[c_471]) ).
cnf(c_2977,plain,
( ~ product(e_1,e_2,e_3)
| ~ product(e_2,e_3,e_3)
| product(e_3,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_2976]) ).
cnf(c_2988,plain,
( ~ product(X0,e_2,e_3)
| ~ product(e_2,X1,e_3)
| product(X1,X0,e_2) ),
inference(instantiation,[status(thm)],[c_423]) ).
cnf(c_2989,plain,
( ~ product(e_1,e_2,e_3)
| ~ product(e_2,e_1,e_3)
| product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_2988]) ).
cnf(c_3150,plain,
( ~ product(X0,e_2,e_3)
| ~ product(e_3,X0,e_3)
| product(e_2,e_3,X0) ),
inference(instantiation,[status(thm)],[c_462]) ).
cnf(c_3165,plain,
( ~ product(e_1,e_2,e_3)
| ~ product(e_3,e_1,e_3)
| product(e_2,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_3150]) ).
cnf(c_3186,plain,
( ~ product(e_1,e_2,e_3)
| ~ product(e_2,e_2,e_3)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[c_391]) ).
cnf(c_3489,plain,
( ~ product(X0,e_2,e_2)
| ~ product(X0,e_3,e_2)
| equalish(e_2,e_3) ),
inference(instantiation,[status(thm)],[c_393]) ).
cnf(c_3492,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_1,e_3,e_2)
| equalish(e_2,e_3) ),
inference(instantiation,[status(thm)],[c_3489]) ).
cnf(c_3941,plain,
( ~ product(X0,e_2,e_4)
| ~ product(e_2,X0,e_4)
| product(e_2,e_2,X0) ),
inference(instantiation,[status(thm)],[c_442]) ).
cnf(c_3948,plain,
( ~ product(e_1,e_2,e_4)
| ~ product(e_2,e_1,e_4)
| product(e_2,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_3941]) ).
cnf(c_3971,plain,
( ~ product(e_2,e_1,e_4)
| ~ product(e_2,e_2,e_4)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[c_381]) ).
cnf(c_3977,plain,
( ~ product(e_2,X0,e_4)
| ~ product(e_3,X0,e_4)
| equalish(e_2,e_3) ),
inference(instantiation,[status(thm)],[c_394]) ).
cnf(c_3980,plain,
( ~ product(e_2,e_1,e_4)
| ~ product(e_3,e_1,e_4)
| equalish(e_2,e_3) ),
inference(instantiation,[status(thm)],[c_3977]) ).
cnf(c_3982,plain,
( ~ product(X0,e_2,e_4)
| ~ product(e_2,X1,e_4)
| product(X1,X0,e_2) ),
inference(instantiation,[status(thm)],[c_423]) ).
cnf(c_3983,plain,
( ~ product(e_1,e_2,e_4)
| ~ product(e_2,e_1,e_4)
| product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_3982]) ).
cnf(c_4466,plain,
( ~ product(X0,X1,e_2)
| ~ product(X1,e_2,X0)
| product(e_2,X0,e_2) ),
inference(instantiation,[status(thm)],[c_443]) ).
cnf(c_4482,plain,
( ~ product(X0,X1,e_2)
| ~ product(X1,X2,e_2)
| product(X2,X0,X1) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_4483,plain,
( ~ product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_4482]) ).
cnf(c_5422,plain,
( ~ product(X0,e_2,e_2)
| ~ product(X0,e_2,e_4)
| equalish(e_4,e_2) ),
inference(instantiation,[status(thm)],[c_410]) ).
cnf(c_5429,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_1,e_2,e_4)
| equalish(e_4,e_2) ),
inference(instantiation,[status(thm)],[c_5422]) ).
cnf(c_5440,plain,
( ~ group_element(e_2)
| ~ group_element(e_3)
| 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(instantiation,[status(thm)],[c_435]) ).
cnf(c_5442,plain,
( ~ product(e_1,e_2,e_4)
| ~ product(e_3,e_2,e_4)
| equalish(e_1,e_3) ),
inference(instantiation,[status(thm)],[c_385]) ).
cnf(c_5464,plain,
( ~ product(X0,e_2,e_4)
| ~ product(e_2,e_4,X1)
| product(e_4,X0,X1) ),
inference(instantiation,[status(thm)],[c_667]) ).
cnf(c_5465,plain,
( ~ product(e_1,e_2,e_4)
| ~ product(e_2,e_4,e_1)
| product(e_4,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_5464]) ).
cnf(c_5713,plain,
( ~ product(e_4,e_2,X0)
| ~ product(e_4,e_3,X0)
| equalish(e_2,e_3) ),
inference(instantiation,[status(thm)],[c_393]) ).
cnf(c_5716,plain,
( ~ product(e_4,e_2,e_1)
| ~ product(e_4,e_3,e_1)
| equalish(e_2,e_3) ),
inference(instantiation,[status(thm)],[c_5713]) ).
cnf(c_6583,plain,
( ~ product(X0,e_2,e_2)
| ~ product(e_2,e_2,e_3)
| product(e_2,X0,e_3) ),
inference(instantiation,[status(thm)],[c_1531]) ).
cnf(c_6584,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_2,e_2,e_3)
| product(e_2,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_6583]) ).
cnf(c_7692,plain,
( ~ product(X0,e_2,e_4)
| ~ product(e_2,X0,e_2)
| product(e_2,e_2,e_4) ),
inference(instantiation,[status(thm)],[c_1521]) ).
cnf(c_7693,plain,
( ~ product(e_1,e_2,e_4)
| ~ product(e_2,e_1,e_2)
| product(e_2,e_2,e_4) ),
inference(instantiation,[status(thm)],[c_7692]) ).
cnf(c_7722,plain,
( ~ product(e_4,e_2,X0)
| ~ product(e_2,e_2,e_4)
| product(e_2,e_4,X0) ),
inference(instantiation,[status(thm)],[c_1556]) ).
cnf(c_7723,plain,
( ~ product(e_2,e_2,e_4)
| ~ product(e_4,e_2,e_1)
| product(e_2,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_7722]) ).
cnf(c_7845,plain,
( ~ product(e_2,e_2,X0)
| ~ product(e_3,e_2,e_2)
| product(e_2,e_3,X0) ),
inference(instantiation,[status(thm)],[c_1779]) ).
cnf(c_7846,plain,
( ~ product(e_2,e_2,e_1)
| ~ product(e_3,e_2,e_2)
| product(e_2,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_7845]) ).
cnf(c_7858,plain,
( ~ product(e_2,X0,e_3)
| ~ product(e_3,e_2,e_2)
| product(X0,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_1794]) ).
cnf(c_7859,plain,
( ~ product(e_2,e_1,e_3)
| ~ product(e_3,e_2,e_2)
| product(e_1,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_7858]) ).
cnf(c_8105,plain,
( ~ product(e_2,X0,e_2)
| ~ product(e_2,e_2,e_3)
| product(X0,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_2768]) ).
cnf(c_8106,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_2,e_2,e_3)
| product(e_1,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_8105]) ).
cnf(c_8428,plain,
( ~ product(e_2,e_4,X0)
| ~ product(e_3,e_2,e_4)
| product(e_4,e_3,X0) ),
inference(instantiation,[status(thm)],[c_2365]) ).
cnf(c_8435,plain,
( ~ product(e_2,e_4,e_1)
| ~ product(e_3,e_2,e_4)
| product(e_4,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_8428]) ).
cnf(c_8618,plain,
( ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_3,e_1)
| equalish(e_2,e_3) ),
inference(instantiation,[status(thm)],[c_393]) ).
cnf(c_8619,plain,
( ~ product(X0,e_2,e_3)
| ~ product(e_2,e_3,e_1)
| product(e_3,X0,e_1) ),
inference(instantiation,[status(thm)],[c_471]) ).
cnf(c_8620,plain,
( ~ product(e_1,e_2,e_3)
| ~ product(e_2,e_3,e_1)
| product(e_3,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_8619]) ).
cnf(c_8687,plain,
( ~ product(e_1,e_2,e_3)
| ~ product(e_2,e_1,e_2)
| product(e_2,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_1521]) ).
cnf(c_10433,plain,
( ~ product(e_2,e_3,X0)
| ~ product(e_3,e_2,X0)
| product(e_2,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_1520]) ).
cnf(c_10434,plain,
( ~ product(e_2,e_3,e_1)
| ~ product(e_3,e_2,e_1)
| product(e_2,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_10433]) ).
cnf(c_11239,plain,
( ~ product(X0,e_4,e_2)
| ~ product(e_4,e_2,X0)
| product(e_2,X0,e_2) ),
inference(instantiation,[status(thm)],[c_4466]) ).
cnf(c_11240,plain,
( ~ product(e_1,e_4,e_2)
| ~ product(e_4,e_2,e_1)
| product(e_2,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_11239]) ).
cnf(c_14434,plain,
( ~ product(e_2,e_2,e_2)
| ~ product(e_3,e_2,e_2)
| equalish(e_3,e_2) ),
inference(instantiation,[status(thm)],[c_2759]) ).
cnf(c_14696,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_14434,c_11240,c_10434,c_8687,c_8618,c_8620,c_8435,c_8106,c_7859,c_7846,c_7723,c_7693,c_6584,c_5716,c_5465,c_5442,c_5440,c_5429,c_4483,c_3983,c_3980,c_3971,c_3948,c_3492,c_3186,c_3165,c_2989,c_2977,c_2963,c_2959,c_2957,c_2950,c_2948,c_2757,c_2740,c_2742,c_2731,c_2712,c_2124,c_2112,c_1737,c_1616,c_665,c_477,c_446,c_439,c_436,c_428,c_421,c_247,c_223,c_215,c_207,c_199,c_191,c_183,c_75,c_57,c_58,c_60,c_61,c_63,c_64,c_66,c_67,c_53,c_54,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP129-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 20:11:54 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.38/1.16 % SZS status Started for theBenchmark.p
% 3.38/1.16 % SZS status Unsatisfiable for theBenchmark.p
% 3.38/1.16
% 3.38/1.16 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.38/1.16
% 3.38/1.16 ------ iProver source info
% 3.38/1.16
% 3.38/1.16 git: date: 2023-05-31 18:12:56 +0000
% 3.38/1.16 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.38/1.16 git: non_committed_changes: false
% 3.38/1.16 git: last_make_outside_of_git: false
% 3.38/1.16
% 3.38/1.16 ------ Parsing...successful
% 3.38/1.16
% 3.38/1.16 ------ preprocesses with Option_epr_non_horn_non_eq
% 3.38/1.16
% 3.38/1.16
% 3.38/1.16 ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e
% 3.38/1.16
% 3.38/1.16 ------ Preprocessing...------ preprocesses with Option_epr_non_horn_non_eq
% 3.38/1.16 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.38/1.16 ------ Proving...
% 3.38/1.16 ------ Problem Properties
% 3.38/1.16
% 3.38/1.16
% 3.38/1.16 clauses 25
% 3.38/1.16 conjectures 3
% 3.38/1.16 EPR 25
% 3.38/1.16 Horn 22
% 3.38/1.16 unary 16
% 3.38/1.16 binary 0
% 3.38/1.16 lits 52
% 3.38/1.16 lits eq 0
% 3.38/1.16 fd_pure 0
% 3.38/1.16 fd_pseudo 0
% 3.38/1.16 fd_cond 0
% 3.38/1.16 fd_pseudo_cond 0
% 3.38/1.16 AC symbols 0
% 3.38/1.16
% 3.38/1.16 ------ Schedule EPR non Horn non eq is on
% 3.38/1.16
% 3.38/1.16 ------ no equalities: superposition off
% 3.38/1.16
% 3.38/1.16 ------ Input Options "--resolution_flag false" Time Limit: 70.
% 3.38/1.16
% 3.38/1.16
% 3.38/1.16 ------
% 3.38/1.16 Current options:
% 3.38/1.16 ------
% 3.38/1.16
% 3.38/1.16
% 3.38/1.16
% 3.38/1.16
% 3.38/1.16 ------ Proving...
% 3.38/1.16
% 3.38/1.16
% 3.38/1.16 % SZS status Unsatisfiable for theBenchmark.p
% 3.38/1.16
% 3.38/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.38/1.16
% 3.38/1.16
%------------------------------------------------------------------------------