%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : GRP132-2.002 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n025.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 Jul 24 06:26:56 PM UTC 2025
% Result : Unsatisfiable 6.97s 1.22s
% Output : CNFRefutation 6.97s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named qg2_1)
% Comments :
%------------------------------------------------------------------------------
cnf(11,plain,
( ~ product(X0,X1,X2)
| ~ product(X3,X4,X2)
| ~ product(X5,X0,X1)
| ~ product(X5,X3,X4)
| equalish(X0,X3) ),
inference(cnf,[status(esa)],[qg2_1]) ).
cnf(l0,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_1,e_1,e_2)
| ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_1)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(7,plain,
( ~ group_element(X0)
| ~ group_element(X1)
| product(X0,X1,e_2)
| product(X0,X1,e_1) ),
inference(cnf,[status(esa)],[product_total_function1]) ).
cnf(l1,plain,
( ~ group_element(e_1)
| ~ group_element(e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(6,plain,
~ equalish(e_2,e_1),
inference(cnf,[status(esa)],[e_2_is_not_e_1]) ).
cnf(l8,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[6]) ).
cnf(l2,plain,
( ~ group_element(e_2)
| ~ group_element(e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(3,plain,
group_element(e_1),
inference(cnf,[status(esa)],[element_1]) ).
cnf(l6,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l32,plain,
( ~ group_element(e_1)
| ~ group_element(e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(12,plain,
( ~ product(X0,X1,X2)
| ~ product(X3,X4,X2)
| ~ product(X5,X0,X1)
| ~ product(X5,X3,X4)
| equalish(X1,X4) ),
inference(cnf,[status(esa)],[qg2_2]) ).
cnf(l432,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_2,e_2,e_1)
| ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_2,e_2)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(5,plain,
~ equalish(e_1,e_2),
inference(cnf,[status(esa)],[e_1_is_not_e_2]) ).
cnf(l433,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[5]) ).
cnf(l434,plain,
( ~ group_element(e_1)
| ~ group_element(e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l5,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(9,plain,
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| equalish(X1,X3) ),
inference(cnf,[status(esa)],[product_right_cancellation]) ).
cnf(l435,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_2,e_1)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l17,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l436,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[5]) ).
cnf(4,plain,
group_element(e_2),
inference(cnf,[status(esa)],[element_2]) ).
cnf(l12,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l54,plain,
( ~ product(e_1,e_1,e_2)
| ~ product(e_2,e_2,e_2)
| ~ product(e_2,e_1,e_1)
| ~ product(e_2,e_2,e_2)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(l59,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[5]) ).
cnf(l438,plain,
( ~ product(e_2,e_1,e_1)
| ~ product(e_2,e_2,e_1)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l67,plain,
( ~ group_element(e_2)
| ~ group_element(e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l34,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l437,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l41,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l92,plain,
( ~ group_element(e_2)
| ~ group_element(e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l439,plain,
( ~ group_element(e_2)
| ~ group_element(e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l440,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_2,e_2,e_2)
| ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_2,e_2)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(l447,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l458,plain,
( ~ group_element(e_1)
| ~ group_element(e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l3,plain,
( ~ group_element(e_1)
| ~ group_element(e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l459,plain,
( ~ group_element(e_2)
| ~ group_element(e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l446,plain,
( ~ group_element(e_2)
| ~ group_element(e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l460,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l443,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l450,plain,
( ~ group_element(e_1)
| ~ group_element(e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l56,plain,
( ~ group_element(e_2)
| ~ group_element(e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l471,plain,
( ~ product(e_2,e_2,e_2)
| ~ product(e_1,e_1,e_2)
| ~ product(e_2,e_2,e_2)
| ~ product(e_2,e_1,e_1)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l468,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l88,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l296,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l441,plain,
( ~ product(e_1,e_1,e_2)
| ~ product(e_2,e_1,e_2)
| ~ product(e_2,e_1,e_1)
| ~ product(e_2,e_2,e_1)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l449,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[5]) ).
cnf(l510,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[5]) ).
cnf(l43,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l445,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l98,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(10,plain,
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X2)
| equalish(X0,X3) ),
inference(cnf,[status(esa)],[product_left_cancellation]) ).
cnf(l68,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_2,e_2,e_1)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(l142,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l271,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_1,e_1,e_2)
| ~ product(e_1,e_1,e_2)
| ~ product(e_1,e_1,e_1)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(l469,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l457,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l285,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l462,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l560,plain,
( ~ group_element(e_1)
| ~ group_element(e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l475,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l451,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l300,plain,
( ~ group_element(e_1)
| ~ group_element(e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l561,plain,
( ~ product(e_2,e_1,e_1)
| ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_1)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l442,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[5]) ).
cnf(l448,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_1,e_1,e_2)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(l272,plain,
( ~ group_element(e_1)
| ~ group_element(e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l565,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l567,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[6]) ).
cnf(l283,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[5]) ).
cnf(l563,plain,
( ~ product(e_2,e_1,e_1)
| ~ product(e_1,e_1,e_1)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(l464,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[6]) ).
cnf(l568,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l463,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_1)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l511,plain,
( ~ group_element(e_2)
| ~ group_element(e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l558,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l473,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[6]) ).
cnf(l562,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l571,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[6]) ).
cnf(l570,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l321,plain,
( ~ group_element(e_1)
| ~ group_element(e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l444,plain,
( ~ group_element(e_2)
| ~ group_element(e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l590,plain,
( ~ group_element(e_2)
| ~ group_element(e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l591,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l333,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l550,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l594,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l15,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l578,plain,
( ~ group_element(e_1)
| ~ group_element(e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l587,plain,
( ~ product(e_1,e_1,e_2)
| ~ product(e_2,e_1,e_2)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(l559,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l335,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l585,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l477,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[6]) ).
cnf(l600,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_1,e_2,e_2)
| ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_1,e_2)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(l566,plain,
( ~ product(e_2,e_1,e_1)
| ~ product(e_2,e_2,e_1)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l573,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[5]) ).
cnf(l476,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l317,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[6]) ).
cnf(l579,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l601,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[5]) ).
cnf(l454,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_2,e_2,e_2)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(l275,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l324,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_1,e_1,e_2)
| ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_1,e_1)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l597,plain,
( ~ group_element(e_2)
| ~ group_element(e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l274,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l659,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l362,plain,
( ~ group_element(e_2)
| ~ group_element(e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l400,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l533,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l517,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[5]) ).
cnf(l599,plain,
( ~ product(e_2,e_2,e_2)
| ~ product(e_2,e_1,e_2)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l461,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_2,e_1,e_1)
| ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_2,e_1)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l646,plain,
( ~ group_element(e_2)
| ~ group_element(e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l277,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_1,e_1,e_2)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l658,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l467,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[5]) ).
cnf(l470,plain,
( ~ group_element(e_1)
| ~ group_element(e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l82,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l647,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l650,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l626,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l381,plain,
( ~ group_element(e_2)
| ~ group_element(e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l326,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[6]) ).
cnf(l653,plain,
( ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_1,e_1)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l685,plain,
( ~ group_element(e_2)
| ~ group_element(e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l420,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l336,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[6]) ).
cnf(l273,plain,
( ~ group_element(e_1)
| ~ group_element(e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l421,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l686,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l388,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l472,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l634,plain,
( ~ product(e_1,e_1,e_2)
| ~ product(e_2,e_2,e_2)
| ~ product(e_2,e_1,e_1)
| ~ product(e_2,e_2,e_2)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(l680,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[6]) ).
cnf(l651,plain,
( ~ product(e_2,e_2,e_2)
| ~ product(e_1,e_2,e_2)
| ~ product(e_2,e_2,e_2)
| ~ product(e_2,e_1,e_2)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l698,plain,
( ~ group_element(e_2)
| ~ group_element(e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l700,plain,
( ~ product(e_2,e_2,e_2)
| ~ product(e_1,e_1,e_2)
| ~ product(e_2,e_2,e_2)
| ~ product(e_2,e_1,e_1)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(l695,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_1,e_2,e_2)
| ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_1,e_2)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(l688,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l349,plain,
( ~ product(e_2,e_2,e_1)
| ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_2,e_2)
| ~ product(e_1,e_1,e_1)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l678,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[5]) ).
cnf(l654,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[6]) ).
cnf(l327,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l632,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[5]) ).
cnf(l652,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[6]) ).
cnf(l334,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l689,plain,
( ~ group_element(e_2)
| ~ group_element(e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l703,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[5]) ).
cnf(l613,plain,
( ~ group_element(e_2)
| ~ group_element(e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l699,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l586,plain,
( ~ product(e_2,e_2,e_2)
| ~ product(e_1,e_2,e_2)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(l604,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_2,e_2,e_2)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(l701,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[6]) ).
cnf(l614,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l706,plain,
( ~ product(e_2,e_2,e_2)
| ~ product(e_2,e_1,e_2)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l711,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[6]) ).
cnf(l588,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[6]) ).
cnf(l657,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[5]) ).
cnf(l702,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l644,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[6]) ).
cnf(l705,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l630,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l628,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_2,e_2,e_2)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(l707,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l631,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[5]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l8,l2,l6,l32,l432,l433,l434,l5,l435,l17,l436,l12,l54,l59,l438,l67,l34,l437,l41,l92,l439,l440,l447,l458,l3,l459,l446,l460,l443,l450,l56,l471,l468,l88,l296,l441,l449,l510,l43,l445,l98,l68,l142,l271,l469,l457,l285,l462,l560,l475,l451,l300,l561,l442,l448,l272,l565,l567,l283,l563,l464,l568,l463,l511,l558,l473,l562,l571,l570,l321,l444,l590,l591,l333,l550,l594,l15,l578,l587,l559,l335,l585,l477,l600,l566,l573,l476,l317,l579,l601,l454,l275,l324,l597,l274,l659,l362,l400,l533,l517,l599,l461,l646,l277,l658,l467,l470,l82,l647,l650,l626,l381,l326,l653,l685,l420,l336,l273,l421,l686,l388,l472,l634,l680,l651,l698,l700,l695,l688,l349,l678,l654,l327,l632,l652,l334,l689,l703,l613,l699,l586,l604,l701,l614,l706,l711,l588,l657,l702,l644,l705,l630,l628,l707,l631]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP132-2.002 : TPTP v9.0.0. Released v1.2.0.
% 0.10/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Jul 20 14:05:49 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % launching worker at depth: 1
% 0.14/0.35 % launching worker at depth: 2
% 0.14/0.35 % launching worker at depth: 6
% 0.14/0.35 % launching worker at depth: 8
% 0.14/0.35 % launching worker at depth: 5
% 0.14/0.35 % launching worker at depth: 3
% 0.14/0.35 % launching worker at depth: 7
% 0.14/0.35 % launching worker at depth: 4
% 0.14/0.35 % launching worker at depth: 9
% 0.14/0.36 % launching worker at depth: 10
% 0.14/0.40 % launching worker at depth: 11
% 1.96/0.58 % launching worker at depth: 12
% 6.97/1.22 % SZS status Theorem for theBenchmark
% 6.97/1.22 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------