%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : GRP135-2.002 : 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 : n026.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 06:26:57 PM UTC 2025
% Result : Unsatisfiable 0.11s 0.43s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named qg3)
% Comments :
%------------------------------------------------------------------------------
cnf(11,plain,
( ~ product(X0,X1,X2)
| ~ product(X2,X0,X3)
| product(X3,X0,X1) ),
inference(cnf,[status(esa)],[qg3]) ).
cnf(l0,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_2,e_1,e_1)
| product(e_1,e_1,e_2) ),
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_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(l2,plain,
( ~ product(e_2,e_2,e_2)
| ~ product(e_2,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l3,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_2)
| product(e_2,e_1,e_2) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(9,plain,
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| equalish(X1,X3) ),
inference(cnf,[status(esa)],[product_right_cancellation]) ).
cnf(l4,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(l5,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(l6,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(4,plain,
group_element(e_2),
inference(cnf,[status(esa)],[element_2]) ).
cnf(l7,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(3,plain,
group_element(e_1),
inference(cnf,[status(esa)],[element_1]) ).
cnf(l8,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l9,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(l10,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(l11,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l15,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l30,plain,
( ~ product(e_2,e_2,e_1)
| ~ product(e_1,e_2,e_2)
| product(e_2,e_2,e_2) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(6,plain,
~ equalish(e_2,e_1),
inference(cnf,[status(esa)],[e_2_is_not_e_1]) ).
cnf(l29,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[6]) ).
cnf(l31,plain,
( ~ product(e_2,e_2,e_1)
| ~ product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l32,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(l45,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_2)
| product(e_2,e_1,e_2) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l13,plain,
( ~ product(e_2,e_1,e_1)
| ~ product(e_1,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l18,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(8,plain,
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| equalish(X2,X3) ),
inference(cnf,[status(esa)],[product_total_function2]) ).
cnf(l17,plain,
( ~ 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(l33,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(l20,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(l24,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l35,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(l37,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l53,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(l34,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l16,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(l115,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[6]) ).
cnf(l68,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l74,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l38,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l36,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l25,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l19,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l12,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l79,plain,
( ~ product(e_1,e_1,e_2)
| ~ product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l40,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l70,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(10,plain,
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X2)
| equalish(X0,X3) ),
inference(cnf,[status(esa)],[product_left_cancellation]) ).
cnf(l58,plain,
( ~ product(e_2,e_2,e_1)
| ~ product(e_1,e_2,e_1)
| equalish(e_2,e_1) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(l14,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[6]) ).
cnf(l116,plain,
( ~ product(e_2,e_2,e_1)
| ~ product(e_1,e_2,e_2)
| product(e_2,e_2,e_2) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l39,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l82,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_2,e_2,e_1)
| product(e_1,e_2,e_1) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l75,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[6]) ).
cnf(l102,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(l88,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(l51,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l107,plain,
~ equalish(e_2,e_1),
inference(instantiation,[status(thm)],[6]) ).
cnf(l105,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(l69,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(l122,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l126,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l101,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l132,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_2,e_2,e_1)
| product(e_1,e_2,e_1) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l125,plain,
group_element(e_2),
inference(instantiation,[status(thm)],[4]) ).
cnf(l72,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(l112,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l121,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l104,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l103,plain,
group_element(e_1),
inference(instantiation,[status(thm)],[3]) ).
cnf(l133,plain,
( ~ product(e_2,e_2,e_1)
| ~ product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l3,l4,l5,l6,l7,l8,l9,l10,l11,l15,l30,l29,l31,l32,l45,l13,l18,l17,l33,l20,l24,l35,l37,l53,l34,l16,l115,l68,l74,l38,l36,l25,l19,l12,l79,l40,l70,l58,l14,l116,l39,l82,l75,l102,l88,l51,l107,l105,l69,l122,l126,l101,l132,l125,l72,l112,l121,l104,l103,l133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.07 % Problem : GRP135-2.002 : TPTP v9.0.0. Released v1.2.0.
% 0.04/0.07 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.26 % Computer : n026.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Sun Jul 20 14:07:49 EDT 2025
% 0.07/0.26 % CPUTime :
% 0.07/0.26 % launching worker at depth: 4
% 0.07/0.26 % launching worker at depth: 8
% 0.07/0.26 % launching worker at depth: 2
% 0.07/0.26 % launching worker at depth: 5
% 0.07/0.26 % launching worker at depth: 3
% 0.07/0.26 % launching worker at depth: 1
% 0.07/0.26 % launching worker at depth: 6
% 0.07/0.26 % launching worker at depth: 7
% 0.07/0.26 % launching worker at depth: 9
% 0.07/0.27 % launching worker at depth: 10
% 0.11/0.41 % launching worker at depth: 11
% 0.11/0.43 % SZS status Theorem for theBenchmark
% 0.11/0.43 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------