%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP506-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:39:58 PM UTC 2026
% Result : Unsatisfiable 118.73s 27.83s
% Output : CNFRefutation 118.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 2
% Syntax : Number of clauses : 66 ( 66 unt; 0 nHn; 15 RR)
% Number of literals : 66 ( 65 equ; 13 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 19 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 234 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(X3,X4)),multiply(X3,inverse(multiply(multiply(X5,inverse(X6)),inverse(X4))))))),X6) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
cnf(c_0_2,axiom,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(X3,X4)),multiply(X3,inverse(multiply(multiply(X5,inverse(X6)),inverse(X4))))))),X6) = X5,
single_axiom ).
cnf(c_0_3,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(X3,X4)),multiply(X3,inverse(multiply(X5,inverse(X4))))))),X6) = inverse(multiply(inverse(multiply(inverse(multiply(X7,X8)),multiply(X8,X7))),multiply(inverse(multiply(X9,X10)),multiply(X9,inverse(multiply(multiply(X5,inverse(inverse(X6))),inverse(X10))))))),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(X3,X4)),multiply(X3,inverse(multiply(X5,inverse(X4))))))),X6),inverse(X6)) = X5,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(X3,X4)),multiply(X3,inverse(multiply(X5,inverse(X4))))))),X6),X7),inverse(X7)) = multiply(X5,inverse(inverse(X6))),
inference(spm,[status(thm)],[c_0_4,c_0_3]) ).
cnf(c_0_6,plain,
multiply(multiply(X1,X2),inverse(X2)) = multiply(multiply(X1,inverse(X3)),inverse(inverse(X3))),
inference(spm,[status(thm)],[c_0_5,c_0_2]) ).
cnf(c_0_7,plain,
multiply(multiply(X1,X2),inverse(X2)) = multiply(multiply(X1,X3),inverse(X3)),
inference(spm,[status(thm)],[c_0_6,c_0_6]) ).
cnf(c_0_8,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(X3,inverse(X4))),multiply(X3,inverse(multiply(multiply(X5,X6),inverse(X6))))))),X4) = X5,
inference(spm,[status(thm)],[c_0_2,c_0_7]) ).
cnf(c_0_9,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(multiply(X3,multiply(multiply(X4,X5),inverse(X5))),inverse(X6))),multiply(multiply(X3,X7),inverse(X7))))),X6) = X4,
inference(spm,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_10,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(X3,X4)),multiply(X3,inverse(multiply(multiply(X5,X6),inverse(X6))))))),X7),inverse(X7)) = multiply(X5,X4),
inference(spm,[status(thm)],[c_0_4,c_0_7]) ).
cnf(c_0_11,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(X3),X3))),multiply(multiply(X4,X5),inverse(X5))) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_4]),c_0_4]) ).
cnf(c_0_12,plain,
multiply(X1,inverse(multiply(multiply(X1,X2),inverse(X2)))) = multiply(X3,inverse(multiply(multiply(X3,X4),inverse(X4)))),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,plain,
multiply(multiply(multiply(X1,X2),inverse(X2)),inverse(inverse(X3))) = multiply(multiply(multiply(X1,X3),X4),inverse(X4)),
inference(spm,[status(thm)],[c_0_7,c_0_7]) ).
cnf(c_0_14,plain,
multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1)))),multiply(inverse(X3),X3))),multiply(multiply(X4,X5),inverse(X5))) = X4,
inference(spm,[status(thm)],[c_0_11,c_0_11]) ).
cnf(c_0_15,plain,
multiply(multiply(X1,inverse(multiply(multiply(X1,X2),inverse(X2)))),inverse(inverse(X3))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_12]),c_0_4]) ).
cnf(c_0_16,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(b2,b2)),multiply(b2,b2))),multiply(inverse(multiply(b2,b2)),multiply(b2,inverse(multiply(X3,inverse(b2))))))),multiply(inverse(multiply(inverse(multiply(X4,X5)),multiply(X5,X4))),inverse(multiply(X6,inverse(multiply(inverse(multiply(X7,X8)),multiply(X7,inverse(multiply(X3,inverse(X8)))))))))))),X9) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(b2,b2)),multiply(b2,b2))),multiply(inverse(multiply(b2,b2)),multiply(b2,inverse(multiply(X6,inverse(b2))))))),X9),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_3]),c_0_3]),c_0_3]) ).
cnf(c_0_17,plain,
multiply(multiply(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1)))),multiply(inverse(X3),X3))),X4),X5),inverse(X5)) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_18,plain,
multiply(X1,multiply(inverse(multiply(X2,X3)),multiply(X2,inverse(multiply(X4,inverse(X3)))))) = multiply(X1,multiply(inverse(multiply(b2,b2)),multiply(b2,inverse(multiply(X4,inverse(b2)))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_16]),c_0_4]) ).
cnf(c_0_19,plain,
multiply(multiply(X1,inverse(multiply(multiply(X1,X2),inverse(X2)))),inverse(multiply(X3,inverse(inverse(inverse(X3)))))) = multiply(X4,inverse(multiply(multiply(X4,X5),inverse(X5)))),
inference(spm,[status(thm)],[c_0_12,c_0_15]) ).
cnf(c_0_20,plain,
multiply(X1,inverse(inverse(inverse(X1)))) = multiply(X2,inverse(inverse(inverse(X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_15]),c_0_4]) ).
cnf(c_0_21,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(multiply(X3,inverse(X2))))) = multiply(inverse(multiply(b2,b2)),multiply(b2,inverse(multiply(X3,inverse(b2))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_17]) ).
cnf(c_0_22,plain,
multiply(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1)))),multiply(inverse(X3),X3))),X4),inverse(X4)) = multiply(b2,inverse(multiply(multiply(b2,b2),inverse(b2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_17]),c_0_19]) ).
cnf(c_0_23,plain,
multiply(X1,inverse(inverse(inverse(X1)))) = inverse(multiply(X2,inverse(multiply(multiply(X2,X3),inverse(X3))))),
inference(spm,[status(thm)],[c_0_15,c_0_20]) ).
cnf(c_0_24,plain,
multiply(inverse(multiply(multiply(X1,multiply(X2,inverse(X3))),X3)),multiply(multiply(X1,X4),inverse(X4))) = multiply(inverse(multiply(b2,b2)),multiply(b2,inverse(multiply(X2,inverse(b2))))),
inference(spm,[status(thm)],[c_0_21,c_0_7]) ).
cnf(c_0_25,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(multiply(X3,multiply(X4,inverse(X5))),X5)),multiply(multiply(X3,X6),inverse(X6))))),X7),inverse(X7)) = X4,
inference(spm,[status(thm)],[c_0_4,c_0_7]) ).
cnf(c_0_26,plain,
multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1)))),multiply(inverse(X3),X3))),multiply(b2,inverse(inverse(inverse(b2))))) = multiply(b2,inverse(multiply(multiply(b2,b2),inverse(b2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_22]),c_0_19]),c_0_23]) ).
cnf(c_0_27,plain,
multiply(inverse(multiply(multiply(X1,multiply(multiply(X2,X3),inverse(X3))),X4)),multiply(multiply(X1,X5),inverse(X5))) = multiply(inverse(multiply(b2,b2)),multiply(b2,inverse(multiply(multiply(X2,X4),inverse(b2))))),
inference(spm,[status(thm)],[c_0_24,c_0_7]) ).
cnf(c_0_28,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(b2),multiply(b2,inverse(multiply(multiply(b2,b2),inverse(b2))))))),X3),inverse(X3)) = b2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_15]),c_0_22]) ).
cnf(c_0_29,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(multiply(X3,inverse(X2))))) = multiply(inverse(multiply(X4,X5)),multiply(X4,inverse(multiply(X3,inverse(X5))))),
inference(spm,[status(thm)],[c_0_21,c_0_21]) ).
cnf(c_0_30,plain,
multiply(inverse(multiply(b2,b2)),multiply(b2,inverse(multiply(multiply(X1,inverse(multiply(multiply(X1,X2),inverse(X2)))),inverse(b2))))) = multiply(inverse(b2),b2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_28]) ).
cnf(c_0_31,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(multiply(multiply(X3,inverse(multiply(multiply(X3,X4),inverse(X4)))),inverse(X2))))) = multiply(inverse(b2),b2),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_32,plain,
multiply(inverse(X1),X1) = multiply(inverse(b2),b2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_4]),c_0_15]),c_0_4]) ).
cnf(c_0_33,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_32,c_0_32]) ).
cnf(c_0_34,plain,
multiply(inverse(multiply(inverse(X1),X1)),multiply(multiply(X2,X3),inverse(X3))) = X2,
inference(spm,[status(thm)],[c_0_8,c_0_33]) ).
cnf(c_0_35,plain,
multiply(multiply(multiply(inverse(multiply(inverse(X1),X1)),X2),X3),inverse(X3)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_34]),c_0_15]) ).
cnf(c_0_36,plain,
multiply(multiply(multiply(inverse(X1),X1),X2),inverse(X2)) = multiply(inverse(X3),X3),
inference(spm,[status(thm)],[c_0_35,c_0_33]) ).
cnf(c_0_37,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(X3,X4)),multiply(X3,inverse(multiply(multiply(multiply(X5,X6),inverse(X6)),inverse(X4))))))) = X5,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_7]),c_0_2]) ).
cnf(c_0_38,plain,
multiply(multiply(inverse(X1),X1),X2) = inverse(inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_36]),c_0_37]) ).
cnf(c_0_39,plain,
multiply(multiply(inverse(X1),X2),inverse(X2)) = inverse(inverse(inverse(X1))),
inference(spm,[status(thm)],[c_0_7,c_0_38]) ).
cnf(c_0_40,plain,
multiply(multiply(X1,X2),inverse(X2)) = inverse(inverse(X1)),
inference(spm,[status(thm)],[c_0_39,c_0_37]) ).
cnf(c_0_41,plain,
inverse(inverse(multiply(inverse(X1),X1))) = multiply(inverse(b2),b2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_38]),c_0_33]) ).
cnf(c_0_42,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(fof_simplification,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_0_43,plain,
inverse(multiply(inverse(b2),b2)) = multiply(inverse(b2),b2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_41]),c_0_38]),c_0_41]),c_0_41]) ).
cnf(c_0_44,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
c_0_42 ).
cnf(c_0_45,plain,
inverse(multiply(inverse(X1),X1)) = multiply(inverse(X1),X1),
inference(spm,[status(thm)],[c_0_43,c_0_33]) ).
cnf(c_0_46,negated_conjecture,
multiply(multiply(inverse(X1),X1),a2) != a2,
inference(spm,[status(thm)],[c_0_44,c_0_32]) ).
cnf(c_0_47,plain,
inverse(inverse(inverse(inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_45]),c_0_40]),c_0_40]),c_0_40]),c_0_40]),c_0_45]),c_0_40]),c_0_40]),c_0_40]),c_0_40]),c_0_38]),c_0_45]),c_0_45]),c_0_40]),c_0_38]) ).
cnf(c_0_48,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),multiply(X4,X3))),multiply(inverse(multiply(X5,X6)),multiply(X5,inverse(multiply(multiply(X7,inverse(inverse(multiply(multiply(X8,inverse(X9)),inverse(X10))))),inverse(X6))))))),X10)),X7))),X9) = X8,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_49,negated_conjecture,
multiply(multiply(multiply(X1,inverse(inverse(inverse(X1)))),multiply(X2,inverse(multiply(multiply(X2,X3),inverse(X3))))),a2) != a2,
inference(spm,[status(thm)],[c_0_46,c_0_23]) ).
cnf(c_0_50,plain,
multiply(multiply(X1,inverse(inverse(inverse(X2)))),X2) = inverse(inverse(X1)),
inference(spm,[status(thm)],[c_0_40,c_0_47]) ).
cnf(c_0_51,plain,
multiply(X1,inverse(inverse(inverse(X1)))) = multiply(inverse(b2),b2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_45]),c_0_41]),c_0_38]),c_0_41]) ).
cnf(c_0_52,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(X3,X4)),multiply(X3,inverse(multiply(X5,inverse(X4))))))),X6) = inverse(multiply(inverse(multiply(inverse(multiply(X7,X8)),multiply(X8,X7))),multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(b2,b2)),multiply(b2,b2))),multiply(inverse(multiply(b2,b2)),multiply(b2,inverse(multiply(X9,inverse(b2))))))),multiply(multiply(X5,inverse(inverse(X6))),inverse(X10))),X10)),X9))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_48]),c_0_3]) ).
cnf(c_0_53,negated_conjecture,
multiply(inverse(inverse(multiply(multiply(X1,inverse(inverse(inverse(X2)))),inverse(multiply(inverse(inverse(X1)),inverse(X2)))))),a2) != a2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_38]) ).
cnf(c_0_54,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(b2,b2)),multiply(b2,b2))),multiply(inverse(multiply(b2,b2)),multiply(b2,inverse(multiply(X3,inverse(b2))))))),multiply(X4,inverse(X5))),X5)),X3))),X6) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(b2,b2)),multiply(b2,b2))),multiply(inverse(multiply(b2,b2)),multiply(b2,inverse(multiply(X4,inverse(b2))))))),X6),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_48]),c_0_3]),c_0_3]),c_0_52]) ).
cnf(c_0_55,negated_conjecture,
multiply(inverse(inverse(multiply(multiply(X1,inverse(inverse(X2))),inverse(multiply(inverse(inverse(X1)),X2))))),a2) != a2,
inference(spm,[status(thm)],[c_0_53,c_0_47]) ).
cnf(c_0_56,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(b2,b2)),multiply(b2,b2))),multiply(inverse(multiply(b2,b2)),multiply(b2,inverse(multiply(X1,inverse(b2))))))),inverse(X1)) = multiply(b2,inverse(multiply(multiply(b2,b2),inverse(b2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_54]),c_0_19]),c_0_4]),c_0_54]) ).
cnf(c_0_57,negated_conjecture,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(b2,b2)),multiply(b2,inverse(multiply(inverse(X1),inverse(b2)))))),X1)),a2) != a2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_40]),c_0_51]),c_0_32]),c_0_45]),c_0_38]),c_0_47]),c_0_38]),c_0_47]) ).
cnf(c_0_58,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(multiply(X3,inverse(X2))))) = multiply(inverse(X3),multiply(X4,inverse(multiply(multiply(X4,X5),inverse(X5))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_19]),c_0_15]) ).
cnf(c_0_59,negated_conjecture,
multiply(inverse(multiply(inverse(multiply(inverse(inverse(X1)),multiply(inverse(b2),b2))),X1)),a2) != a2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_40]),c_0_51]) ).
cnf(c_0_60,negated_conjecture,
multiply(inverse(multiply(inverse(multiply(X1,multiply(inverse(b2),b2))),inverse(inverse(X1)))),a2) != a2,
inference(spm,[status(thm)],[c_0_59,c_0_47]) ).
cnf(c_0_61,negated_conjecture,
multiply(inverse(multiply(inverse(multiply(X1,multiply(inverse(X2),X2))),inverse(inverse(X1)))),a2) != a2,
inference(spm,[status(thm)],[c_0_60,c_0_33]) ).
cnf(c_0_62,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(X3,X4)),multiply(X3,inverse(X5))))),X6) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(b2,b2)),multiply(b2,b2))),multiply(inverse(multiply(b2,b2)),multiply(b2,inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(b2,b2)),multiply(b2,b2))),multiply(inverse(multiply(b2,b2)),multiply(b2,inverse(multiply(X5,inverse(b2))))))),X4),inverse(b2))))))),X6),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_2]),c_0_3]),c_0_3]) ).
cnf(c_0_63,negated_conjecture,
multiply(inverse(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1)))),a2) != a2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_32]),c_0_45]),c_0_56]),c_0_40]),c_0_51]),c_0_40]),c_0_47]),c_0_32]),c_0_38]),c_0_41]),c_0_45]),c_0_38]),c_0_47]) ).
cnf(c_0_64,negated_conjecture,
multiply(multiply(X1,inverse(X1)),a2) != a2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_33]),c_0_45]),c_0_38]),c_0_47]) ).
cnf(c_0_65,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_50]),c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP506-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/10.59 % Computer : n019.cluster.edu
% 0.11/10.59 % Model : x86_64 x86_64
% 0.11/10.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.59 % Memory : 8046.5625MB
% 0.11/10.59 % OS : Linux 6.8.0-71-generic
% 0.11/10.60 % CPULimit : 300
% 0.11/10.60 % WCLimit : 300
% 0.11/10.60 % DateTime : Sun Sep 20 20:15:15 UTC 2026
% 0.15/10.60 % CPUTime :
% 0.15/10.60 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/10.64 Running first-order theorem proving
% 0.15/10.64 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 118.73/27.83 % Version: 3.5.1
% 118.73/27.83 % Preprocessing class: FSSSSMSSSSSNFFN.
% 118.73/27.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 118.73/27.83 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 118.73/27.83 % Starting new_bool_3 with 300s (1) cores
% 118.73/27.83 % Starting new_bool_1 with 300s (1) cores
% 118.73/27.83 % Starting sh5l with 300s (1) cores
% 118.73/27.83 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 831244 completed with status 0
% 118.73/27.83 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 118.73/27.83 % Preprocessing class: FSSSSMSSSSSNFFN.
% 118.73/27.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 118.73/27.83 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 118.73/27.83 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 118.73/27.83 % No SInE strategy applied
% 118.73/27.83 % Search class: FUUPF-FFSF21-DFFFFFNN
% 118.73/27.83 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 118.73/27.83 % Starting SubtermCWHack with 136s (1) cores
% 118.73/27.83 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 118.73/27.83 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 118.73/27.83 % Starting new_bool_3 with 136s (1) cores
% 118.73/27.83 % Starting new_bool_1 with 136s (1) cores
% 118.73/27.83 % U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 831252 completed with status 0
% 118.73/27.83 % Result found by U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 118.73/27.83 % Preprocessing class: FSSSSMSSSSSNFFN.
% 118.73/27.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 118.73/27.83 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 118.73/27.83 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 118.73/27.83 % No SInE strategy applied
% 118.73/27.83 % Search class: FUUPF-FFSF21-DFFFFFNN
% 118.73/27.83 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 118.73/27.83 % Starting SubtermCWHack with 136s (1) cores
% 118.73/27.83 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 118.73/27.83 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 118.73/27.83 % Preprocessing time : 0.001 s
% 118.73/27.83 % Presaturation interreduction done
% 118.73/27.83
% 118.73/27.83 % Proof found!
% 118.73/27.83 % SZS status Unsatisfiable
% 118.73/27.83 % SZS output start CNFRefutation
% See solution above
% 118.73/27.83 % Parsed axioms : 2
% 118.73/27.83 % Removed by relevancy pruning/SinE : 0
% 118.73/27.83 % Initial clauses : 2
% 118.73/27.83 % Removed in clause preprocessing : 0
% 118.73/27.83 % Initial clauses in saturation : 2
% 118.73/27.83 % Processed clauses : 4043
% 118.73/27.83 % ...of these trivial : 339
% 118.73/27.83 % ...subsumed : 3438
% 118.73/27.83 % ...remaining for further processing : 266
% 118.73/27.83 % Other redundant clauses eliminated : 0
% 118.73/27.83 % Clauses deleted for lack of memory : 0
% 118.73/27.83 % Backward-subsumed : 25
% 118.73/27.83 % Backward-rewritten : 103
% 118.73/27.83 % Generated clauses : 326598
% 118.73/27.83 % ...of the previous two non-redundant : 316320
% 118.73/27.83 % ...aggressively subsumed : 0
% 118.73/27.83 % Contextual simplify-reflections : 0
% 118.73/27.83 % Paramodulations : 326598
% 118.73/27.83 % Factorizations : 0
% 118.73/27.83 % NegExts : 0
% 118.73/27.83 % Equation resolutions : 0
% 118.73/27.83 % Disequality decompositions : 0
% 118.73/27.83 % Total rewrite steps : 238279
% 118.73/27.83 % ...of those cached : 216346
% 118.73/27.83 % Propositional unsat checks : 0
% 118.73/27.83 % Propositional check models : 0
% 118.73/27.83 % Propositional check unsatisfiable : 0
% 118.73/27.83 % Propositional clauses : 0
% 118.73/27.83 % Propositional clauses after purity: 0
% 118.73/27.83 % Propositional unsat core size : 0
% 118.73/27.83 % Propositional preprocessing time : 0.000
% 118.73/27.83 % Propositional encoding time : 0.000
% 118.73/27.83 % Propositional solver time : 0.000
% 118.73/27.83 % Success case prop preproc time : 0.000
% 118.73/27.83 % Success case prop encoding time : 0.000
% 118.73/27.83 % Success case prop solver time : 0.000
% 118.73/27.83 % Current number of processed clauses : 136
% 118.73/27.83 % Positive orientable unit clauses : 81
% 118.73/27.83 % Positive unorientable unit clauses: 34
% 118.73/27.83 % Negative unit clauses : 21
% 118.73/27.83 % Non-unit-clauses : 0
% 118.73/27.83 % Current number of unprocessed clauses: 310057
% 118.73/27.83 % ...number of literals in the above : 310057
% 118.73/27.83 % Current number of archived formulas : 0
% 118.73/27.83 % Current number of archived clauses : 130
% 118.73/27.83 % Clause-clause subsumption calls (NU) : 0
% 118.73/27.83 % Rec. Clause-clause subsumption calls : 0
% 118.73/27.83 % Non-unit clause-clause subsumptions : 0
% 118.73/27.83 % Unit Clause-clause subsumption calls : 2385
% 118.73/27.83 % Rewrite failures with RHS unbound : 0
% 118.73/27.83 % BW rewrite match attempts : 11068
% 118.73/27.83 % BW rewrite match successes : 695
% 118.73/27.83 % Condensation attempts : 0
% 118.73/27.83 % Condensation successes : 0
% 118.73/27.83 % Termbank termtop insertions : 30132654
% 118.73/27.83 % Search garbage collected termcells : 2
% 118.73/27.83
% 118.73/27.83 % -------------------------------------------------
% 118.73/27.83 % User time : 16.301 s
% 118.73/27.83 % System time : 0.511 s
% 118.73/27.83 % Total time : 16.812 s
% 118.73/27.83 % Maximum resident set size: 3584 pages
% 118.73/27.83
% 118.73/27.83 % -------------------------------------------------
% 118.73/27.83 % User time : 81.829 s
% 118.73/27.83 % System time : 2.555 s
% 118.73/27.83 % Total time : 84.384 s
% 118.73/27.83 % Maximum resident set size: 4608 pages
% 118.73/27.83 % E exiting
%------------------------------------------------------------------------------