%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : GRP131-1.002 : 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 : n018.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 2.98s 0.77s
% Output : CNFRefutation 2.98s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named qg1_1)
% Comments :
%------------------------------------------------------------------------------
cnf(8,plain,
( ~ product(X0,X1,X2)
| ~ product(X3,X4,X2)
| ~ product(X5,X1,X0)
| ~ product(X5,X4,X3)
| equalish(X0,X3) ),
inference(cnf,[status(esa)],[qg1_1]) ).
cnf(l0,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_2,e_1,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)],[8]) ).
cnf(4,plain,
( ~ group_element(X0)
| ~ group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2) ),
inference(cnf,[status(esa)],[product_total_function1]) ).
cnf(l1,plain,
( ~ group_element(e_2)
| ~ group_element(e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l2,plain,
( ~ group_element(e_1)
| ~ group_element(e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l3,plain,
( ~ group_element(e_2)
| ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l4,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_2,e_1,e_1)
| ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_2)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(0,plain,
group_element(e_1),
inference(cnf,[status(esa)],[element_1]) ).
cnf(l5,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(1,plain,
group_element(e_2),
inference(cnf,[status(esa)],[element_2]) ).
cnf(l6,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(7,plain,
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X2)
| equalish(X0,X3) ),
inference(cnf,[status(esa)],[product_left_cancellation]) ).
cnf(l7,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_2,e_2,e_2)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(2,plain,
~ equalish(e_1,e_2),
inference(cnf,[status(esa)],[e_1_is_not_e_2]) ).
cnf(l8,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[2]) ).
cnf(l9,plain,
( ~ group_element(e_1)
| ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l10,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l11,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_2,e_1,e_1)
| ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_2)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(l28,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l15,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[2]) ).
cnf(l14,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l19,plain,
( ~ group_element(e_1)
| ~ group_element(e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l16,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(9,plain,
( ~ product(X0,X1,X2)
| ~ product(X3,X4,X2)
| ~ product(X5,X1,X0)
| ~ product(X5,X4,X3)
| equalish(X1,X4) ),
inference(cnf,[status(esa)],[qg1_2]) ).
cnf(l17,plain,
( ~ product(e_1,e_2,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)],[9]) ).
cnf(l44,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[2]) ).
cnf(l46,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l18,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[2]) ).
cnf(6,plain,
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| equalish(X1,X3) ),
inference(cnf,[status(esa)],[product_right_cancellation]) ).
cnf(l27,plain,
( ~ product(e_1,e_1,e_2)
| ~ product(e_1,e_2,e_2)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(l12,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l20,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(3,plain,
~ equalish(e_2,e_1),
inference(cnf,[status(esa)],[e_2_is_not_e_1]) ).
cnf(l47,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l48,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[2]) ).
cnf(l49,plain,
( ~ group_element(e_1)
| ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l50,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l23,plain,
( ~ group_element(e_1)
| ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l51,plain,
( ~ group_element(e_1)
| ~ group_element(e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l13,plain,
( ~ group_element(e_2)
| ~ group_element(e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l52,plain,
( ~ group_element(e_1)
| ~ group_element(e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l22,plain,
( ~ product(e_2,e_1,e_1)
| ~ product(e_2,e_2,e_1)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(l29,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[2]) ).
cnf(l26,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l43,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l55,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l21,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l40,plain,
( ~ group_element(e_2)
| ~ group_element(e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l53,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l24,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l45,plain,
( ~ group_element(e_1)
| ~ group_element(e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l25,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_2,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)],[9]) ).
cnf(l67,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l70,plain,
( ~ product(e_1,e_2,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)],[9]) ).
cnf(l71,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l68,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l58,plain,
( ~ group_element(e_2)
| ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l72,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l73,plain,
( ~ group_element(e_1)
| ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l59,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_2,e_1)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(l74,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l31,plain,
( ~ group_element(e_1)
| ~ group_element(e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l75,plain,
( ~ group_element(e_1)
| ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l57,plain,
( ~ product(e_1,e_1,e_2)
| ~ product(e_2,e_1,e_2)
| ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_1,e_2)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(l76,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_2,e_1,e_1)
| ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_2)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l56,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)],[9]) ).
cnf(l78,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l79,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l63,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l80,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l81,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l82,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l77,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[2]) ).
cnf(l91,plain,
( ~ group_element(e_1)
| ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l136,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l62,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l112,plain,
( ~ group_element(e_1)
| ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l88,plain,
( ~ group_element(e_1)
| ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l111,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l37,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l114,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l38,plain,
( ~ product(e_1,e_1,e_2)
| ~ product(e_2,e_2,e_2)
| ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_2,e_2)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(l85,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l101,plain,
( ~ group_element(e_2)
| ~ group_element(e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l120,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l102,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l92,plain,
( ~ product(e_1,e_2,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)],[9]) ).
cnf(l54,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l174,plain,
( ~ group_element(e_1)
| ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l95,plain,
( ~ group_element(e_2)
| ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l65,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)],[8]) ).
cnf(l104,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l116,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l134,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l100,plain,
( ~ group_element(e_2)
| ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l158,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l34,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l93,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l189,plain,
( ~ product(e_2,e_1,e_1)
| ~ product(e_1,e_1,e_1)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l103,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l182,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l42,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l86,plain,
( ~ group_element(e_2)
| ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l66,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l106,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)],[9]) ).
cnf(l115,plain,
( ~ product(e_1,e_2,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)],[9]) ).
cnf(l41,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l121,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l131,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_2,e_2,e_2)
| ~ product(e_2,e_1,e_2)
| ~ product(e_2,e_2,e_2)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l145,plain,
( ~ group_element(e_2)
| ~ group_element(e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l83,plain,
( ~ group_element(e_2)
| ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l196,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l183,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l152,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l195,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[2]) ).
cnf(l139,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[2]) ).
cnf(l178,plain,
( ~ group_element(e_2)
| ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l154,plain,
( ~ product(e_2,e_2,e_2)
| ~ product(e_1,e_2,e_2)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l90,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)],[9]) ).
cnf(l108,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l146,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l193,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l149,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_2,e_2,e_2)
| ~ product(e_2,e_1,e_2)
| ~ product(e_2,e_2,e_2)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l84,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l144,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l123,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l138,plain,
( ~ group_element(e_1)
| ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l98,plain,
( ~ group_element(e_2)
| ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l200,plain,
( ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_1,e_1)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(l188,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_2,e_2,e_2)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l99,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l163,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l241,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l179,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l107,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l198,plain,
( ~ group_element(e_1)
| ~ group_element(e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l175,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l133,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[2]) ).
cnf(l94,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l240,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l202,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l156,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l69,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[2]) ).
cnf(l151,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[2]) ).
cnf(l118,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)],[9]) ).
cnf(l171,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)],[8]) ).
cnf(l203,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l207,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l172,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[0]) ).
cnf(l205,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_2,e_1,e_1)
| equalish(e_1,e_2) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l141,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l110,plain,
( ~ product(e_2,e_2,e_2)
| ~ product(e_1,e_2,e_2)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l173,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[2]) ).
cnf(l140,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)],[9]) ).
cnf(l170,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l220,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[2]) ).
cnf(l255,plain,
( ~ group_element(e_2)
| ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l122,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l259,plain,
( ~ product(e_1,e_1,e_2)
| ~ product(e_1,e_2,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)],[9]) ).
cnf(l243,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[2]) ).
cnf(l264,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[2]) ).
cnf(l256,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l263,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l135,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_1,e_1,e_2)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l137,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l148,plain,
~ equalish(e_1,e_2),
inference(instantiation,[status(thm)],[2]) ).
cnf(l247,plain,
( ~ group_element(e_2)
| ~ group_element(e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l249,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l261,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[1]) ).
cnf(l253,plain,
( ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_1,e_1)
| ~ 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(l262,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l3,l4,l5,l6,l7,l8,l9,l10,l11,l28,l15,l14,l19,l16,l17,l44,l46,l18,l27,l12,l20,l47,l48,l49,l50,l23,l51,l13,l52,l22,l29,l26,l43,l55,l21,l40,l53,l24,l45,l25,l67,l70,l71,l68,l58,l72,l73,l59,l74,l31,l75,l57,l76,l56,l78,l79,l63,l80,l81,l82,l77,l91,l136,l62,l112,l88,l111,l37,l114,l38,l85,l101,l120,l102,l92,l54,l174,l95,l65,l104,l116,l134,l100,l158,l34,l93,l189,l103,l182,l42,l86,l66,l106,l115,l41,l121,l131,l145,l83,l196,l183,l152,l195,l139,l178,l154,l90,l108,l146,l193,l149,l84,l144,l123,l138,l98,l200,l188,l99,l163,l241,l179,l107,l198,l175,l133,l94,l240,l202,l156,l69,l151,l118,l171,l203,l207,l172,l205,l141,l110,l173,l140,l170,l220,l255,l122,l259,l243,l264,l256,l263,l135,l137,l148,l247,l249,l261,l253,l262]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP131-1.002 : TPTP v9.0.0. Released v1.2.0.
% 0.06/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Jul 20 14:04:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 6
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.34 % launching worker at depth: 9
% 0.12/0.34 % launching worker at depth: 10
% 0.12/0.38 % launching worker at depth: 11
% 1.48/0.51 % launching worker at depth: 12
% 2.98/0.77 % SZS status Theorem for theBenchmark
% 2.98/0.77 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------