%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP049-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:41:29 PM UTC 2026
% Result : Unsatisfiable 174.13s 25.75s
% Output : CNFRefutation 174.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),inverse(multiply(X2,multiply(inverse(X2),X2)))))) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(c_0_2,axiom,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),inverse(multiply(X2,multiply(inverse(X2),X2)))))) = X3,
single_axiom ).
cnf(c_0_3,plain,
multiply(X1,inverse(multiply(inverse(X2),inverse(multiply(X3,multiply(inverse(X3),X3)))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X3)),X4)),X2)),inverse(multiply(X4,multiply(inverse(X4),X4))))),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(multiply(inverse(X3),inverse(multiply(X2,multiply(inverse(X2),X2))))))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X3,inverse(multiply(inverse(X4),inverse(multiply(X5,multiply(inverse(X5),X5)))))))) = multiply(inverse(multiply(inverse(multiply(X3,X5)),X2)),X4),
inference(spm,[status(thm)],[c_0_4,c_0_3]) ).
cnf(c_0_6,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X1),a1)),multiply(inverse(X1),X2))),inverse(multiply(a1,multiply(inverse(a1),a1))))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_2]),c_0_3]),c_0_2]) ).
cnf(c_0_7,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(multiply(inverse(multiply(X4,X5)),X2)),multiply(inverse(multiply(X4,X5)),X3)),
inference(spm,[status(thm)],[c_0_5,c_0_2]) ).
cnf(c_0_8,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X1,a1)),multiply(X1,X2))),inverse(multiply(a1,multiply(inverse(a1),a1))))) = X2,
inference(spm,[status(thm)],[c_0_6,c_0_6]) ).
cnf(c_0_9,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(multiply(X4,X2)),multiply(X4,X3)),
inference(spm,[status(thm)],[c_0_7,c_0_7]) ).
cnf(c_0_10,plain,
multiply(inverse(multiply(X1,a1)),inverse(multiply(X2,inverse(multiply(multiply(X1,X2),multiply(inverse(multiply(X1,X2)),multiply(X1,X2))))))) = inverse(multiply(a1,multiply(inverse(a1),a1))),
inference(spm,[status(thm)],[c_0_2,c_0_8]) ).
cnf(c_0_11,plain,
multiply(inverse(multiply(X1,a1)),multiply(X1,X2)) = multiply(inverse(multiply(X3,a1)),multiply(X3,X2)),
inference(spm,[status(thm)],[c_0_4,c_0_8]) ).
cnf(c_0_12,plain,
multiply(inverse(multiply(X1,multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(X4,multiply(inverse(X4),X4)))))))),multiply(X1,X5)) = multiply(inverse(X3),multiply(inverse(multiply(X2,X4)),X5)),
inference(spm,[status(thm)],[c_0_9,c_0_4]) ).
cnf(c_0_13,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3))),inverse(multiply(X2,multiply(inverse(X2),X2))))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_9]),c_0_2]) ).
cnf(c_0_14,plain,
multiply(inverse(multiply(inverse(multiply(X1,a1)),multiply(X1,inverse(X2)))),inverse(multiply(a1,multiply(inverse(a1),a1)))) = X2,
inference(spm,[status(thm)],[c_0_4,c_0_10]) ).
cnf(c_0_15,plain,
multiply(inverse(multiply(X1,a1)),inverse(multiply(a1,inverse(multiply(multiply(X1,a1),multiply(inverse(multiply(X2,a1)),multiply(X2,a1))))))) = inverse(multiply(a1,multiply(inverse(a1),a1))),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
multiply(inverse(multiply(X1,multiply(X2,inverse(multiply(X3,inverse(multiply(X4,multiply(inverse(X4),X4)))))))),multiply(X1,X5)) = multiply(X3,multiply(inverse(multiply(X2,X4)),X5)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,a1)),a1)),inverse(multiply(a1,multiply(inverse(a1),a1))))),inverse(multiply(a1,multiply(inverse(a1),a1)))) = multiply(a1,inverse(multiply(multiply(X1,a1),multiply(inverse(multiply(X2,a1)),multiply(X2,a1))))),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,a1)),a1)),inverse(multiply(a1,multiply(inverse(a1),a1))))),multiply(inverse(multiply(X2,a1)),X3)) = multiply(a1,multiply(inverse(multiply(X2,multiply(X1,a1))),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_16]) ).
cnf(c_0_19,plain,
multiply(a1,multiply(inverse(multiply(inverse(multiply(X1,a1)),multiply(X1,a1))),X2)) = multiply(inverse(multiply(X3,inverse(multiply(a1,multiply(inverse(a1),a1))))),multiply(X3,X2)),
inference(spm,[status(thm)],[c_0_9,c_0_18]) ).
cnf(c_0_20,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,a1)),multiply(X1,inverse(X2)))),a1)),X2)),inverse(multiply(a1,multiply(inverse(a1),a1)))) = multiply(a1,multiply(inverse(a1),a1)),
inference(spm,[status(thm)],[c_0_14,c_0_14]) ).
cnf(c_0_21,plain,
multiply(a1,multiply(inverse(multiply(inverse(multiply(X1,a1)),multiply(X1,a1))),inverse(multiply(a1,multiply(inverse(a1),a1))))) = multiply(inverse(multiply(a1,multiply(inverse(a1),a1))),multiply(a1,multiply(inverse(a1),a1))),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,plain,
multiply(inverse(multiply(a1,multiply(inverse(a1),a1))),multiply(a1,multiply(inverse(a1),a1))) = multiply(inverse(X1),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_14]),c_0_21]) ).
cnf(c_0_23,plain,
multiply(inverse(a1),a1) = multiply(inverse(X1),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_22]),c_0_22]) ).
cnf(c_0_24,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_23,c_0_23]) ).
cnf(c_0_25,plain,
inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(X2,multiply(inverse(X2),X2))))) = X2,
inference(spm,[status(thm)],[c_0_13,c_0_24]) ).
cnf(c_0_26,plain,
multiply(inverse(multiply(X1,a1)),inverse(multiply(X2,inverse(multiply(multiply(X1,X2),multiply(inverse(multiply(X3,X2)),multiply(X3,X2))))))) = inverse(multiply(a1,multiply(inverse(a1),a1))),
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_27,plain,
inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(X2,multiply(inverse(X3),X3))))) = X2,
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_28,plain,
multiply(inverse(multiply(X1,a1)),multiply(X1,inverse(multiply(inverse(X2),X2)))) = inverse(multiply(a1,multiply(inverse(a1),a1))),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,plain,
multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),inverse(multiply(multiply(X1,inverse(multiply(inverse(X4),inverse(multiply(X2,multiply(inverse(X2),X2)))))),inverse(multiply(X4,multiply(inverse(X4),X4)))))) = inverse(multiply(X3,multiply(inverse(X3),X3))),
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_30,plain,
inverse(multiply(multiply(X1,inverse(multiply(inverse(X2),inverse(multiply(X3,multiply(inverse(X3),X3)))))),inverse(multiply(X2,multiply(inverse(X2),X2))))) = multiply(inverse(multiply(X1,X3)),inverse(multiply(inverse(a1),a1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_3]),c_0_24]) ).
cnf(c_0_31,plain,
multiply(inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),a1)),multiply(inverse(X2),X2)) = inverse(multiply(a1,multiply(inverse(a1),a1))),
inference(spm,[status(thm)],[c_0_28,c_0_24]) ).
cnf(c_0_32,plain,
multiply(inverse(multiply(a1,X1)),multiply(a1,inverse(multiply(inverse(a1),a1)))) = inverse(multiply(X1,multiply(inverse(X1),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_9]) ).
cnf(c_0_33,plain,
multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(a1),a1))) = multiply(inverse(X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_31]),c_0_24]) ).
cnf(c_0_34,plain,
inverse(multiply(inverse(multiply(inverse(a1),a1)),multiply(inverse(X1),X1))) = multiply(inverse(a1),a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_24]) ).
cnf(c_0_35,plain,
inverse(multiply(inverse(X1),X1)) = multiply(inverse(a1),a1),
inference(spm,[status(thm)],[c_0_34,c_0_24]) ).
cnf(c_0_36,plain,
inverse(multiply(multiply(inverse(a1),a1),multiply(inverse(X1),X1))) = multiply(inverse(a1),a1),
inference(spm,[status(thm)],[c_0_35,c_0_35]) ).
cnf(c_0_37,plain,
multiply(a1,multiply(inverse(multiply(inverse(a1),a1)),inverse(multiply(a1,multiply(inverse(a1),a1))))) = multiply(inverse(a1),a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_38,plain,
multiply(inverse(multiply(inverse(multiply(inverse(inverse(multiply(a1,multiply(inverse(a1),a1)))),a1)),multiply(inverse(a1),a1))),inverse(multiply(a1,multiply(inverse(a1),a1)))) = multiply(a1,multiply(inverse(a1),a1)),
inference(spm,[status(thm)],[c_0_20,c_0_32]) ).
cnf(c_0_39,plain,
inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(a1,multiply(inverse(a1),a1))))) = a1,
inference(spm,[status(thm)],[c_0_13,c_0_34]) ).
cnf(c_0_40,plain,
multiply(multiply(inverse(a1),a1),inverse(multiply(a1,multiply(inverse(a1),a1)))) = inverse(multiply(a1,multiply(inverse(a1),a1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_36]),c_0_35]) ).
cnf(c_0_41,plain,
inverse(multiply(inverse(a1),a1)) = multiply(inverse(a1),a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_18]),c_0_23]),c_0_37]),c_0_24]) ).
cnf(c_0_42,plain,
inverse(multiply(inverse(multiply(a1,multiply(inverse(a1),a1))),inverse(multiply(multiply(inverse(a1),a1),multiply(inverse(a1),a1))))) = multiply(inverse(inverse(multiply(a1,multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),a1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_38]),c_0_24]),c_0_24]) ).
cnf(c_0_43,plain,
inverse(multiply(multiply(inverse(a1),a1),multiply(inverse(a1),a1))) = multiply(inverse(a1),a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_35]),c_0_35]),c_0_35]) ).
cnf(c_0_44,plain,
inverse(inverse(multiply(a1,multiply(inverse(a1),a1)))) = a1,
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,plain,
multiply(inverse(inverse(multiply(inverse(X1),X1))),multiply(inverse(a1),a1)) = multiply(inverse(X2),X2),
inference(rw,[status(thm)],[c_0_33,c_0_41]) ).
cnf(c_0_46,plain,
inverse(multiply(inverse(multiply(a1,multiply(inverse(a1),a1))),multiply(inverse(a1),a1))) = multiply(inverse(inverse(multiply(a1,multiply(inverse(a1),a1)))),multiply(inverse(a1),a1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_41]),c_0_43]) ).
cnf(c_0_47,plain,
inverse(inverse(multiply(a1,multiply(inverse(X1),X1)))) = a1,
inference(spm,[status(thm)],[c_0_44,c_0_24]) ).
cnf(c_0_48,plain,
multiply(multiply(inverse(a1),a1),multiply(inverse(a1),a1)) = multiply(inverse(X1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_9]),c_0_24]),c_0_41]),c_0_41]) ).
cnf(c_0_49,plain,
multiply(X1,inverse(multiply(inverse(inverse(multiply(a1,multiply(inverse(a1),a1)))),inverse(multiply(a1,multiply(inverse(a1),a1)))))) = inverse(multiply(a1,inverse(multiply(multiply(X1,a1),multiply(inverse(multiply(X2,a1)),multiply(X2,a1)))))),
inference(spm,[status(thm)],[c_0_2,c_0_15]) ).
cnf(c_0_50,plain,
multiply(a1,multiply(multiply(inverse(a1),a1),inverse(multiply(a1,multiply(inverse(a1),a1))))) = multiply(inverse(a1),a1),
inference(spm,[status(thm)],[c_0_37,c_0_35]) ).
cnf(c_0_51,plain,
multiply(a1,inverse(multiply(multiply(inverse(inverse(multiply(a1,multiply(inverse(a1),a1)))),inverse(multiply(inverse(a1),a1))),inverse(multiply(multiply(inverse(a1),a1),multiply(inverse(a1),a1)))))) = inverse(multiply(multiply(inverse(a1),a1),multiply(inverse(a1),a1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_42]),c_0_24]) ).
cnf(c_0_52,plain,
multiply(inverse(multiply(a1,multiply(inverse(a1),a1))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,a1)),multiply(X1,inverse(X2)))),a1)),X2)),inverse(multiply(inverse(X3),multiply(a1,multiply(inverse(a1),a1)))))) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_20]),c_0_24]),c_0_46]),c_0_47]) ).
cnf(c_0_53,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,a1)),multiply(X1,inverse(X2)))),a1)),X2)),inverse(multiply(inverse(X3),multiply(a1,multiply(inverse(a1),a1))))) = multiply(a1,inverse(multiply(inverse(X3),multiply(inverse(a1),a1)))),
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_3,c_0_20]),c_0_24]),c_0_46]),c_0_47]),c_0_3]),c_0_24]),c_0_48]),c_0_35]) ).
cnf(c_0_54,plain,
inverse(multiply(inverse(X1),inverse(multiply(multiply(X2,inverse(X1)),multiply(inverse(a1),a1))))) = inverse(multiply(a1,inverse(multiply(multiply(X2,a1),multiply(inverse(a1),a1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_14]),c_0_24]),c_0_49]),c_0_24]) ).
cnf(c_0_55,plain,
multiply(a1,inverse(multiply(a1,multiply(inverse(a1),a1)))) = multiply(inverse(a1),a1),
inference(rw,[status(thm)],[c_0_50,c_0_40]) ).
cnf(c_0_56,plain,
multiply(a1,inverse(multiply(multiply(inverse(inverse(multiply(a1,multiply(inverse(a1),a1)))),multiply(inverse(a1),a1)),multiply(inverse(a1),a1)))) = multiply(inverse(a1),a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_35]),c_0_43]),c_0_43]) ).
cnf(c_0_57,plain,
multiply(inverse(multiply(a1,multiply(inverse(a1),a1))),multiply(a1,inverse(multiply(inverse(X1),multiply(inverse(a1),a1))))) = X1,
inference(rw,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,plain,
inverse(multiply(a1,inverse(multiply(multiply(a1,a1),multiply(inverse(a1),a1))))) = multiply(a1,multiply(inverse(a1),a1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_36]),c_0_46]),c_0_44]) ).
cnf(c_0_59,plain,
multiply(a1,inverse(multiply(multiply(a1,multiply(inverse(a1),a1)),multiply(inverse(a1),a1)))) = multiply(inverse(a1),a1),
inference(spm,[status(thm)],[c_0_56,c_0_47]) ).
cnf(c_0_60,plain,
multiply(inverse(multiply(a1,multiply(inverse(a1),a1))),multiply(inverse(a1),a1)) = multiply(a1,inverse(multiply(multiply(a1,a1),multiply(inverse(a1),a1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).
cnf(c_0_61,plain,
inverse(multiply(inverse(multiply(multiply(a1,multiply(inverse(a1),a1)),multiply(inverse(a1),a1))),multiply(inverse(a1),a1))) = multiply(a1,multiply(inverse(a1),a1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_59]),c_0_36]),c_0_58]) ).
cnf(c_0_62,plain,
multiply(inverse(multiply(a1,multiply(inverse(a1),a1))),multiply(a1,multiply(a1,multiply(inverse(a1),a1)))) = multiply(a1,multiply(inverse(a1),a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_60]),c_0_58]) ).
cnf(c_0_63,plain,
multiply(multiply(a1,multiply(inverse(a1),a1)),multiply(inverse(a1),a1)) = multiply(a1,multiply(inverse(a1),a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_61]),c_0_62]) ).
cnf(c_0_64,plain,
multiply(a1,multiply(inverse(a1),a1)) = a1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_63]),c_0_35]),c_0_40]),c_0_47]) ).
cnf(c_0_65,plain,
multiply(inverse(multiply(a1,a1)),multiply(a1,multiply(inverse(a1),a1))) = inverse(multiply(a1,multiply(inverse(a1),a1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_55]),c_0_36]),c_0_46]),c_0_44]) ).
cnf(c_0_66,plain,
multiply(inverse(a1),a1) = multiply(a1,inverse(a1)),
inference(spm,[status(thm)],[c_0_55,c_0_64]) ).
cnf(c_0_67,plain,
multiply(inverse(multiply(a1,a1)),a1) = inverse(a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_64]),c_0_64]) ).
cnf(c_0_68,plain,
inverse(inverse(a1)) = a1,
inference(spm,[status(thm)],[c_0_47,c_0_64]) ).
cnf(c_0_69,plain,
multiply(a1,multiply(a1,inverse(a1))) = a1,
inference(rw,[status(thm)],[c_0_64,c_0_66]) ).
cnf(c_0_70,plain,
multiply(multiply(a1,multiply(inverse(a1),a1)),multiply(a1,inverse(multiply(multiply(a1,a1),multiply(inverse(a1),a1))))) = multiply(inverse(a1),a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_58]),c_0_35]),c_0_35]),c_0_48]) ).
cnf(c_0_71,plain,
multiply(a1,inverse(multiply(a1,inverse(a1)))) = a1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_67]),c_0_68]),c_0_66]),c_0_69]) ).
cnf(c_0_72,plain,
multiply(inverse(X1),X1) = multiply(a1,inverse(a1)),
inference(spm,[status(thm)],[c_0_24,c_0_68]) ).
cnf(c_0_73,plain,
multiply(a1,multiply(a1,inverse(multiply(multiply(a1,a1),multiply(a1,inverse(a1)))))) = multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_64]),c_0_66]),c_0_66]) ).
cnf(c_0_74,plain,
inverse(multiply(inverse(multiply(a1,inverse(a1))),inverse(a1))) = a1,
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_54,c_0_71]),c_0_66]),c_0_69]),c_0_58]),c_0_66]),c_0_69]) ).
cnf(c_0_75,plain,
multiply(inverse(a1),multiply(a1,inverse(a1))) = inverse(a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_68]),c_0_64]),c_0_55]),c_0_66]) ).
cnf(c_0_76,plain,
inverse(multiply(a1,inverse(a1))) = multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_66]),c_0_72]) ).
cnf(c_0_77,plain,
inverse(multiply(X1,multiply(a1,inverse(a1)))) = multiply(inverse(multiply(a1,X1)),a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_72]),c_0_71]),c_0_72]) ).
cnf(c_0_78,plain,
multiply(inverse(multiply(inverse(multiply(a1,a1)),multiply(inverse(a1),a1))),inverse(multiply(a1,multiply(inverse(a1),a1)))) = multiply(a1,multiply(inverse(a1),a1)),
inference(spm,[status(thm)],[c_0_14,c_0_55]) ).
cnf(c_0_79,plain,
multiply(a1,inverse(multiply(multiply(a1,a1),multiply(a1,inverse(a1))))) = inverse(a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_73]),c_0_13]) ).
cnf(c_0_80,plain,
multiply(a1,inverse(multiply(a1,a1))) = inverse(a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_74]),c_0_68]),c_0_75]),c_0_68]) ).
cnf(c_0_81,plain,
multiply(a1,inverse(multiply(inverse(multiply(multiply(a1,inverse(a1)),X1)),a1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_76]),c_0_68]),c_0_75]),c_0_68]) ).
cnf(c_0_82,plain,
inverse(multiply(multiply(a1,inverse(a1)),multiply(inverse(multiply(a1,X1)),a1))) = X1,
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_27,c_0_77]),c_0_76]),c_0_69]),c_0_72]),c_0_72]),c_0_77]) ).
cnf(c_0_83,plain,
multiply(inverse(multiply(inverse(multiply(a1,a1)),multiply(a1,inverse(a1)))),inverse(a1)) = a1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_64]),c_0_64]),c_0_72]) ).
cnf(c_0_84,plain,
multiply(multiply(a1,inverse(a1)),inverse(a1)) = inverse(a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_64]),c_0_64]),c_0_66]) ).
cnf(c_0_85,plain,
inverse(multiply(inverse(a1),multiply(a1,inverse(a1)))) = a1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_64]),c_0_64]),c_0_64]),c_0_66]) ).
cnf(c_0_86,plain,
multiply(a1,multiply(inverse(multiply(a1,multiply(a1,a1))),a1)) = inverse(a1),
inference(rw,[status(thm)],[c_0_79,c_0_77]) ).
cnf(c_0_87,plain,
multiply(X1,inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),X4)),inverse(multiply(X3,multiply(inverse(X3),X3)))))),X5)),inverse(multiply(inverse(multiply(inverse(X4),inverse(multiply(X2,multiply(inverse(X2),X2))))),multiply(inverse(a1),a1)))))) = X5,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_3]),c_0_24]) ).
cnf(c_0_88,plain,
multiply(inverse(multiply(inverse(multiply(a1,a1)),inverse(a1))),inverse(a1)) = multiply(a1,a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_80]),c_0_72]),c_0_69]) ).
cnf(c_0_89,plain,
multiply(multiply(a1,inverse(a1)),multiply(a1,inverse(a1))) = multiply(a1,inverse(a1)),
inference(spm,[status(thm)],[c_0_72,c_0_76]) ).
cnf(c_0_90,plain,
multiply(inverse(multiply(a1,X1)),a1) = multiply(a1,inverse(multiply(X1,a1))),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_91,plain,
multiply(multiply(a1,a1),inverse(a1)) = a1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_77]),c_0_80]),c_0_68]) ).
cnf(c_0_92,plain,
multiply(multiply(a1,inverse(a1)),inverse(multiply(inverse(multiply(a1,X1)),a1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_84]),c_0_68]),c_0_68]),c_0_85]) ).
cnf(c_0_93,plain,
multiply(a1,inverse(multiply(inverse(multiply(a1,X1)),multiply(a1,a1)))) = X1,
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_2,c_0_86]),c_0_68]),c_0_72]),c_0_77]),c_0_86]),c_0_68]) ).
cnf(c_0_94,plain,
multiply(a1,multiply(a1,inverse(multiply(inverse(multiply(inverse(a1),X1)),a1)))) = 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_87,c_0_88]),c_0_68]),c_0_75]),c_0_68]),c_0_67]),c_0_68]),c_0_68]),c_0_72]),c_0_69]),c_0_76]),c_0_72]),c_0_89]),c_0_76]),c_0_77]),c_0_90]) ).
cnf(c_0_95,plain,
inverse(multiply(inverse(multiply(inverse(a1),multiply(multiply(a1,a1),X1))),a1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_91]),c_0_68]),c_0_75]),c_0_68]) ).
cnf(c_0_96,plain,
inverse(multiply(inverse(multiply(a1,X1)),a1)) = multiply(a1,inverse(multiply(inverse(X1),a1))),
inference(spm,[status(thm)],[c_0_81,c_0_92]) ).
cnf(c_0_97,plain,
multiply(inverse(multiply(X1,a1)),multiply(X1,multiply(a1,inverse(a1)))) = inverse(a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_35]),c_0_64]),c_0_72]) ).
cnf(c_0_98,plain,
multiply(a1,inverse(multiply(multiply(a1,inverse(a1)),multiply(a1,a1)))) = inverse(a1),
inference(spm,[status(thm)],[c_0_93,c_0_76]) ).
cnf(c_0_99,plain,
multiply(inverse(a1),multiply(multiply(a1,a1),inverse(multiply(inverse(X1),a1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_91]),c_0_68]),c_0_75]),c_0_68]) ).
cnf(c_0_100,plain,
multiply(multiply(a1,a1),X1) = multiply(a1,multiply(a1,X1)),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_101,plain,
multiply(multiply(a1,inverse(a1)),multiply(a1,inverse(multiply(inverse(X1),a1)))) = X1,
inference(rw,[status(thm)],[c_0_92,c_0_96]) ).
cnf(c_0_102,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(multiply(a1,multiply(inverse(a1),a1)))),a1)),multiply(inverse(a1),a1))),a1)),multiply(a1,multiply(inverse(a1),a1)))),inverse(multiply(a1,multiply(inverse(a1),a1)))) = multiply(a1,multiply(inverse(a1),a1)),
inference(spm,[status(thm)],[c_0_14,c_0_38]) ).
cnf(c_0_103,plain,
inverse(multiply(inverse(multiply(a1,multiply(a1,X1))),multiply(a1,a1))) = X1,
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_13,c_0_86]),c_0_68]),c_0_72]),c_0_77]),c_0_86]),c_0_68]) ).
cnf(c_0_104,plain,
multiply(a1,multiply(inverse(multiply(a1,a1)),multiply(a1,inverse(a1)))) = inverse(a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_67]),c_0_68]) ).
cnf(c_0_105,plain,
multiply(multiply(a1,inverse(a1)),multiply(a1,a1)) = multiply(a1,a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_98]),c_0_72]),c_0_69]),c_0_88]) ).
cnf(c_0_106,plain,
multiply(inverse(a1),multiply(a1,multiply(a1,inverse(multiply(inverse(X1),a1))))) = X1,
inference(rw,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_107,plain,
multiply(multiply(a1,inverse(a1)),X1) = multiply(a1,multiply(inverse(a1),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(spm,[status(thm)],[c_0_19,c_0_94]),c_0_23]),c_0_72]),c_0_76]),c_0_101]),c_0_72]),c_0_69]),c_0_76]) ).
cnf(c_0_108,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(a1,a1)),multiply(a1,inverse(a1)))),a1)),a1)),inverse(a1)) = a1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_47]),c_0_64]),c_0_64]),c_0_64]),c_0_72]) ).
cnf(c_0_109,plain,
multiply(inverse(multiply(a1,a1)),multiply(a1,inverse(a1))) = inverse(multiply(a1,a1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_76]),c_0_105]) ).
cnf(c_0_110,plain,
multiply(inverse(a1),multiply(a1,X1)) = multiply(a1,multiply(inverse(a1),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_81]),c_0_107]) ).
cnf(c_0_111,plain,
multiply(inverse(multiply(inverse(multiply(X1,a1)),X2)),inverse(multiply(a1,multiply(inverse(a1),a1)))) = multiply(inverse(multiply(inverse(multiply(X1,X3)),X2)),inverse(multiply(X3,multiply(inverse(X3),X3)))),
inference(spm,[status(thm)],[c_0_14,c_0_2]) ).
cnf(c_0_112,plain,
inverse(multiply(inverse(multiply(X1,multiply(a1,X2))),multiply(X1,a1))) = X2,
inference(spm,[status(thm)],[c_0_103,c_0_9]) ).
cnf(c_0_113,plain,
inverse(multiply(X1,multiply(a1,inverse(a1)))) = multiply(a1,inverse(multiply(X1,a1))),
inference(rw,[status(thm)],[c_0_77,c_0_90]) ).
cnf(c_0_114,plain,
multiply(inverse(multiply(inverse(multiply(multiply(a1,a1),a1)),a1)),inverse(a1)) = a1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_77]),c_0_80]),c_0_68]) ).
cnf(c_0_115,plain,
inverse(inverse(multiply(a1,a1))) = multiply(a1,a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_109]),c_0_80]),c_0_68]) ).
cnf(c_0_116,plain,
multiply(inverse(multiply(a1,multiply(a1,a1))),a1) = inverse(multiply(a1,a1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_86]),c_0_76]),c_0_105]) ).
cnf(c_0_117,plain,
inverse(multiply(a1,inverse(multiply(X1,a1)))) = multiply(a1,inverse(multiply(inverse(X1),a1))),
inference(rw,[status(thm)],[c_0_96,c_0_90]) ).
cnf(c_0_118,plain,
inverse(multiply(a1,multiply(a1,multiply(inverse(a1),inverse(multiply(X1,a1)))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_107]),c_0_90]),c_0_110]) ).
cnf(c_0_119,plain,
multiply(X1,multiply(inverse(multiply(a1,multiply(a1,X1))),a1)) = inverse(a1),
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_111,c_0_103]),c_0_24]),c_0_72]),c_0_76]),c_0_72]),c_0_69]),c_0_84]),c_0_72]),c_0_77]) ).
cnf(c_0_120,plain,
inverse(multiply(multiply(a1,inverse(multiply(X1,a1))),multiply(X1,a1))) = inverse(a1),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_121,plain,
multiply(inverse(multiply(X1,a1)),multiply(X1,inverse(a1))) = inverse(multiply(a1,a1)),
inference(spm,[status(thm)],[c_0_9,c_0_109]) ).
cnf(c_0_122,plain,
inverse(multiply(inverse(a1),inverse(a1))) = multiply(multiply(a1,a1),multiply(a1,inverse(a1))),
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_3,c_0_114]),c_0_68]),c_0_72]),c_0_69]),c_0_76]),c_0_72]),c_0_69]) ).
cnf(c_0_123,plain,
multiply(inverse(a1),inverse(a1)) = inverse(multiply(a1,a1)),
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_57,c_0_115]),c_0_72]),c_0_69]),c_0_72]),c_0_77]),c_0_116]),c_0_80]) ).
cnf(c_0_124,plain,
multiply(a1,inverse(multiply(inverse(inverse(multiply(a1,multiply(inverse(a1),X1)))),a1))) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_81]),c_0_107]) ).
cnf(c_0_125,plain,
multiply(inverse(a1),inverse(multiply(X1,a1))) = inverse(multiply(X1,multiply(a1,a1))),
inference(spm,[status(thm)],[c_0_103,c_0_118]) ).
cnf(c_0_126,plain,
multiply(a1,multiply(a1,inverse(multiply(inverse(X1),multiply(a1,a1))))) = X1,
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_4,c_0_86]),c_0_68]),c_0_72]),c_0_77]),c_0_86]),c_0_68]) ).
cnf(c_0_127,plain,
multiply(inverse(multiply(X1,a1)),inverse(multiply(X2,inverse(multiply(multiply(X1,X2),multiply(a1,inverse(a1))))))) = inverse(a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_24]),c_0_64]),c_0_72]) ).
cnf(c_0_128,plain,
multiply(a1,inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,a1)))) = X2,
inference(spm,[status(thm)],[c_0_93,c_0_9]) ).
cnf(c_0_129,plain,
multiply(X1,multiply(a1,inverse(multiply(multiply(a1,X1),a1)))) = inverse(a1),
inference(rw,[status(thm)],[c_0_119,c_0_90]) ).
cnf(c_0_130,plain,
multiply(multiply(a1,inverse(multiply(X1,a1))),multiply(X1,a1)) = a1,
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_14,c_0_120]),c_0_121]),c_0_115]),c_0_72]),c_0_69]),c_0_100]),c_0_69]) ).
cnf(c_0_131,plain,
multiply(multiply(a1,a1),multiply(a1,inverse(a1))) = multiply(a1,a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_123]),c_0_115]) ).
cnf(c_0_132,plain,
inverse(multiply(a1,multiply(inverse(a1),X1))) = multiply(a1,multiply(inverse(a1),inverse(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(spm,[status(thm)],[c_0_19,c_0_124]),c_0_23]),c_0_72]),c_0_76]),c_0_107]),c_0_125]),c_0_126]),c_0_72]),c_0_69]),c_0_76]),c_0_107]) ).
cnf(c_0_133,plain,
multiply(inverse(multiply(inverse(X1),a1)),multiply(a1,inverse(multiply(X1,a1)))) = inverse(a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_72]),c_0_89]),c_0_76]),c_0_77]),c_0_90]) ).
cnf(c_0_134,plain,
multiply(a1,inverse(multiply(multiply(a1,X1),a1))) = multiply(a1,inverse(multiply(a1,multiply(X1,a1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_68]) ).
cnf(c_0_135,plain,
multiply(X1,multiply(a1,inverse(multiply(multiply(inverse(a1),X1),a1)))) = a1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_81]),c_0_107]),c_0_90]) ).
cnf(c_0_136,plain,
inverse(multiply(inverse(multiply(inverse(a1),X1)),a1)) = inverse(multiply(inverse(X1),multiply(a1,a1))),
inference(spm,[status(thm)],[c_0_103,c_0_94]) ).
cnf(c_0_137,plain,
multiply(inverse(multiply(multiply(a1,a1),a1)),multiply(a1,a1)) = inverse(a1),
inference(spm,[status(thm)],[c_0_97,c_0_131]) ).
cnf(c_0_138,plain,
multiply(inverse(multiply(inverse(multiply(X1,a1)),multiply(X1,inverse(X2)))),inverse(a1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_132]),c_0_123]),c_0_80]) ).
cnf(c_0_139,plain,
inverse(multiply(a1,multiply(inverse(multiply(inverse(X1),a1)),a1))) = inverse(multiply(X1,a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_133]),c_0_68]) ).
cnf(c_0_140,plain,
inverse(multiply(multiply(a1,X1),a1)) = inverse(multiply(a1,multiply(X1,a1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_134]),c_0_128]) ).
cnf(c_0_141,plain,
inverse(multiply(multiply(inverse(a1),X1),a1)) = inverse(multiply(inverse(a1),multiply(X1,a1))),
inference(spm,[status(thm)],[c_0_112,c_0_135]) ).
cnf(c_0_142,plain,
multiply(inverse(multiply(inverse(a1),X1)),a1) = multiply(inverse(X1),multiply(a1,a1)),
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_57,c_0_136]),c_0_72]),c_0_69]),c_0_72]),c_0_77]),c_0_90]),c_0_110]),c_0_110]),c_0_125]),c_0_126]) ).
cnf(c_0_143,plain,
multiply(multiply(a1,a1),a1) = multiply(a1,multiply(a1,a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_137]),c_0_68]) ).
cnf(c_0_144,plain,
multiply(a1,multiply(a1,inverse(multiply(multiply(a1,a1),multiply(a1,a1))))) = inverse(multiply(a1,a1)),
inference(spm,[status(thm)],[c_0_126,c_0_115]) ).
cnf(c_0_145,plain,
multiply(X1,inverse(multiply(multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(X4,multiply(inverse(X4),X4)))))),inverse(multiply(X5,multiply(inverse(X5),X5)))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X5)),X6)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X4)),X7)),X3)),inverse(multiply(X7,multiply(inverse(X7),X7)))))),inverse(multiply(X6,multiply(inverse(X6),X6))))),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_146,plain,
multiply(a1,multiply(inverse(multiply(inverse(X1),a1)),a1)) = multiply(X1,a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_138]) ).
cnf(c_0_147,plain,
inverse(multiply(inverse(multiply(multiply(a1,inverse(a1)),multiply(a1,X1))),a1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_76]),c_0_68]),c_0_75]),c_0_68]) ).
cnf(c_0_148,plain,
multiply(multiply(a1,X1),a1) = multiply(a1,multiply(X1,a1)),
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_57,c_0_140]),c_0_72]),c_0_69]),c_0_72]),c_0_113]),c_0_96]),c_0_110]),c_0_110]),c_0_110]),c_0_125]),c_0_126]) ).
cnf(c_0_149,plain,
multiply(multiply(inverse(a1),X1),a1) = multiply(inverse(a1),multiply(X1,a1)),
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_57,c_0_141]),c_0_72]),c_0_69]),c_0_72]),c_0_113]),c_0_142]),c_0_126]) ).
cnf(c_0_150,plain,
multiply(a1,multiply(inverse(multiply(a1,multiply(a1,multiply(a1,a1)))),a1)) = inverse(multiply(a1,a1)),
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_17,c_0_143]),c_0_116]),c_0_115]),c_0_72]),c_0_69]),c_0_91]),c_0_72]),c_0_69]),c_0_123]),c_0_23]),c_0_72]),c_0_77]) ).
cnf(c_0_151,plain,
multiply(a1,inverse(multiply(multiply(a1,a1),multiply(a1,a1)))) = inverse(multiply(a1,multiply(a1,a1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_144]),c_0_80]),c_0_68]) ).
cnf(c_0_152,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X5)),X6)),X7)),multiply(a1,inverse(multiply(X6,a1)))))),multiply(a1,inverse(multiply(X3,a1)))))),X8)),X9)),multiply(a1,inverse(multiply(X8,a1))))) = multiply(X1,inverse(multiply(inverse(X9),multiply(a1,inverse(multiply(inverse(multiply(multiply(X4,inverse(multiply(inverse(X7),multiply(a1,inverse(multiply(X5,a1)))))),multiply(a1,inverse(multiply(X2,a1))))),a1)))))),
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(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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_145]),c_0_72]),c_0_77]),c_0_90]),c_0_72]),c_0_77]),c_0_90]),c_0_72]),c_0_77]),c_0_90]),c_0_72]),c_0_77]),c_0_90]),c_0_72]),c_0_77]),c_0_90]),c_0_72]),c_0_77]),c_0_90]),c_0_72]),c_0_113]),c_0_72]),c_0_77]),c_0_90]),c_0_72]),c_0_77]),c_0_90]),c_0_72]),c_0_77]),c_0_90]) ).
cnf(c_0_153,plain,
multiply(X1,inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X5)),X6)),X7)),multiply(a1,inverse(multiply(X6,a1)))))),multiply(a1,inverse(multiply(X3,a1)))))),X8)),multiply(a1,inverse(multiply(inverse(multiply(multiply(X4,inverse(multiply(inverse(X7),multiply(a1,inverse(multiply(X5,a1)))))),multiply(a1,inverse(multiply(X2,a1))))),a1)))))) = X8,
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(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_2,c_0_145]),c_0_72]),c_0_77]),c_0_90]),c_0_72]),c_0_77]),c_0_90]),c_0_72]),c_0_77]),c_0_90]),c_0_72]),c_0_77]),c_0_90]),c_0_72]),c_0_77]),c_0_90]),c_0_72]),c_0_77]),c_0_90]),c_0_72]),c_0_77]),c_0_90]),c_0_72]),c_0_77]),c_0_90]),c_0_72]),c_0_113]) ).
cnf(c_0_154,plain,
multiply(a1,multiply(a1,multiply(inverse(a1),multiply(X1,a1)))) = multiply(a1,multiply(X1,a1)),
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_146,c_0_147]),c_0_107]),c_0_110]),c_0_148]),c_0_148]),c_0_149]) ).
cnf(c_0_155,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(fof_simplification,[status(thm)],[prove_these_axioms]) ).
cnf(c_0_156,plain,
multiply(inverse(multiply(a1,multiply(a1,multiply(a1,a1)))),a1) = inverse(multiply(a1,multiply(a1,a1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_150]),c_0_115]),c_0_151]) ).
cnf(c_0_157,plain,
inverse(multiply(a1,inverse(multiply(a1,multiply(inverse(a1),multiply(X1,a1)))))) = 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(spm,[status(thm)],[c_0_152,c_0_19]),c_0_35]),c_0_72]),c_0_107]),c_0_72]),c_0_69]),c_0_72]),c_0_76]),c_0_69]),c_0_90]),c_0_140]),c_0_153]),c_0_149]) ).
cnf(c_0_158,plain,
multiply(a1,multiply(inverse(a1),multiply(X1,a1))) = multiply(X1,a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_154]),c_0_128]) ).
cnf(c_0_159,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
c_0_155 ).
cnf(c_0_160,plain,
inverse(inverse(multiply(a1,multiply(a1,a1)))) = multiply(a1,multiply(a1,a1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_156]),c_0_116]),c_0_115]) ).
cnf(c_0_161,plain,
multiply(a1,inverse(multiply(a1,multiply(a1,a1)))) = inverse(multiply(a1,a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_80]),c_0_68]) ).
cnf(c_0_162,plain,
multiply(a1,inverse(multiply(inverse(X1),a1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_117]) ).
cnf(c_0_163,negated_conjecture,
( multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(sr,[status(thm)],[c_0_159,c_0_23]) ).
cnf(c_0_164,plain,
multiply(inverse(a1),inverse(multiply(a1,a1))) = inverse(multiply(a1,multiply(a1,a1))),
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_57,c_0_160]),c_0_72]),c_0_69]),c_0_72]),c_0_77]),c_0_156]),c_0_161]) ).
cnf(c_0_165,plain,
multiply(a1,multiply(inverse(a1),X1)) = X1,
inference(rw,[status(thm)],[c_0_94,c_0_162]) ).
cnf(c_0_166,negated_conjecture,
( multiply(multiply(inverse(X1),X1),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(spm,[status(thm)],[c_0_163,c_0_24]) ).
cnf(c_0_167,plain,
multiply(a1,multiply(inverse(multiply(a1,a1)),inverse(a1))) = inverse(multiply(a1,a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_67]),c_0_68]) ).
cnf(c_0_168,plain,
inverse(multiply(inverse(multiply(a1,a1)),multiply(a1,multiply(a1,a1)))) = inverse(a1),
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_54,c_0_164]),c_0_72]),c_0_77]),c_0_161]),c_0_115]),c_0_143]),c_0_36]),c_0_72]),c_0_69]) ).
cnf(c_0_169,plain,
multiply(multiply(a1,inverse(a1)),X1) = X1,
inference(rw,[status(thm)],[c_0_107,c_0_165]) ).
cnf(c_0_170,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(X1,multiply(inverse(multiply(inverse(multiply(X2,X3)),multiply(X2,X1))),inverse(multiply(X3,multiply(inverse(X3),X3))))),a2) != a2 ),
inference(spm,[status(thm)],[c_0_166,c_0_13]) ).
cnf(c_0_171,plain,
multiply(inverse(multiply(a1,a1)),inverse(a1)) = inverse(multiply(a1,multiply(a1,a1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_167]),c_0_115]),c_0_151]) ).
cnf(c_0_172,plain,
multiply(inverse(multiply(a1,a1)),multiply(a1,multiply(a1,a1))) = a1,
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_14,c_0_168]),c_0_121]),c_0_115]),c_0_72]),c_0_69]),c_0_91]) ).
cnf(c_0_173,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(X2),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_169]),c_0_107]),c_0_165]) ).
cnf(c_0_174,plain,
multiply(inverse(X1),multiply(a1,inverse(a1))) = multiply(a1,inverse(multiply(X1,a1))),
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_2,c_0_133]),c_0_68]),c_0_132]),c_0_123]),c_0_80]),c_0_76]) ).
cnf(c_0_175,plain,
inverse(multiply(inverse(X1),a1)) = multiply(inverse(a1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_165]),c_0_107]),c_0_165]) ).
cnf(c_0_176,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(X1,multiply(inverse(multiply(a1,multiply(a1,X1))),multiply(a1,a1))),a2) != a2 ),
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_170,c_0_86]),c_0_68]),c_0_72]),c_0_77]),c_0_86]),c_0_68]) ).
cnf(c_0_177,plain,
multiply(inverse(inverse(multiply(a1,multiply(a1,a1)))),inverse(a1)) = multiply(a1,a1),
inference(spm,[status(thm)],[c_0_88,c_0_171]) ).
cnf(c_0_178,plain,
multiply(inverse(multiply(X1,a1)),multiply(X1,multiply(a1,a1))) = a1,
inference(spm,[status(thm)],[c_0_9,c_0_172]) ).
cnf(c_0_179,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
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_173,c_0_174]),c_0_117]),c_0_175]),c_0_165]),c_0_76]),c_0_107]),c_0_165]) ).
cnf(c_0_180,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(X1,multiply(inverse(multiply(X2,multiply(a1,X1))),multiply(X2,a1))),a2) != a2 ),
inference(spm,[status(thm)],[c_0_176,c_0_9]) ).
cnf(c_0_181,plain,
multiply(multiply(a1,multiply(a1,a1)),inverse(a1)) = multiply(a1,a1),
inference(rw,[status(thm)],[c_0_177,c_0_160]) ).
cnf(c_0_182,plain,
multiply(inverse(multiply(a1,multiply(a1,a1))),multiply(multiply(a1,a1),multiply(a1,a1))) = a1,
inference(spm,[status(thm)],[c_0_178,c_0_143]) ).
cnf(c_0_183,plain,
multiply(inverse(multiply(inverse(multiply(X1,a1)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),X4)),inverse(multiply(X3,multiply(inverse(X3),X3))))))),inverse(multiply(a1,multiply(inverse(a1),a1)))) = multiply(inverse(X4),inverse(multiply(X2,multiply(inverse(X2),X2)))),
inference(spm,[status(thm)],[c_0_14,c_0_3]) ).
cnf(c_0_184,plain,
multiply(inverse(X1),multiply(X2,multiply(X3,inverse(multiply(inverse(X4),inverse(multiply(X5,multiply(inverse(X5),X5)))))))) = multiply(inverse(multiply(inverse(multiply(X3,X5)),inverse(multiply(inverse(multiply(inverse(multiply(X2,X6)),X1)),inverse(multiply(X6,multiply(inverse(X6),X6))))))),X4),
inference(spm,[status(thm)],[c_0_5,c_0_2]) ).
cnf(c_0_185,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_179]),c_0_72]),c_0_76]),c_0_107]),c_0_165]) ).
cnf(c_0_186,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(a1,multiply(X1,multiply(inverse(multiply(a1,multiply(a1,X1))),a1))),a2) != a2 ),
inference(spm,[status(thm)],[c_0_180,c_0_103]) ).
cnf(c_0_187,plain,
multiply(inverse(multiply(multiply(a1,multiply(a1,a1)),a1)),multiply(a1,a1)) = inverse(multiply(a1,a1)),
inference(spm,[status(thm)],[c_0_121,c_0_181]) ).
cnf(c_0_188,plain,
multiply(multiply(a1,a1),multiply(a1,a1)) = multiply(a1,multiply(a1,multiply(a1,a1))),
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_2,c_0_182]),c_0_24]),c_0_72]),c_0_131]),c_0_164]),c_0_160]) ).
cnf(c_0_189,plain,
multiply(inverse(X1),multiply(inverse(multiply(X2,X3)),inverse(multiply(a1,inverse(multiply(multiply(X2,a1),multiply(inverse(a1),a1))))))) = multiply(inverse(X1),inverse(multiply(X3,multiply(inverse(X3),X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_183,c_0_184]),c_0_49]),c_0_24]) ).
cnf(c_0_190,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_179,c_0_185]) ).
cnf(c_0_191,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_185]),c_0_72]),c_0_76]),c_0_169]),c_0_185]) ).
cnf(c_0_192,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(a1,multiply(X1,multiply(a1,inverse(multiply(multiply(a1,X1),a1))))),a2) != a2 ),
inference(spm,[status(thm)],[c_0_186,c_0_90]) ).
cnf(c_0_193,plain,
multiply(multiply(a1,multiply(a1,a1)),a1) = multiply(a1,multiply(a1,multiply(a1,a1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_187]),c_0_115]) ).
cnf(c_0_194,plain,
multiply(a1,inverse(multiply(a1,multiply(a1,multiply(a1,a1))))) = inverse(multiply(a1,multiply(a1,a1))),
inference(spm,[status(thm)],[c_0_151,c_0_188]) ).
cnf(c_0_195,plain,
multiply(multiply(X1,X2),inverse(X2)) = 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(spm,[status(thm)],[c_0_189,c_0_190]),c_0_72]),c_0_191]),c_0_117]),c_0_175]),c_0_179]),c_0_185]),c_0_72]),c_0_191]) ).
cnf(c_0_196,negated_conjecture,
( multiply(a1,multiply(inverse(a1),a2)) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
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_192,c_0_100]),c_0_193]),c_0_194]),c_0_161]),c_0_80]),c_0_107]) ).
cnf(c_0_197,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(spm,[status(thm)],[c_0_195,c_0_190]) ).
cnf(c_0_198,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_196,c_0_165])]) ).
cnf(c_0_199,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_197]),c_0_185]),c_0_185]) ).
cnf(c_0_200,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_198,c_0_199])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP049-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 19:55:48 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 174.13/25.75 % Version: 3.5.1
% 174.13/25.75 % Preprocessing class: FSSSSMSSSSSNFFN.
% 174.13/25.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 174.13/25.75 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 174.13/25.75 % Starting new_bool_3 with 300s (1) cores
% 174.13/25.75 % Starting new_bool_1 with 300s (1) cores
% 174.13/25.75 % Starting sh5l with 300s (1) cores
% 174.13/25.75 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1625395 completed with status 0
% 174.13/25.75 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 174.13/25.75 % Preprocessing class: FSSSSMSSSSSNFFN.
% 174.13/25.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 174.13/25.75 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 174.13/25.75 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 174.13/25.75 % No SInE strategy applied
% 174.13/25.75 % Search class: FUHPF-FFSF21-DFFFFFNN
% 174.13/25.75 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 174.13/25.75 % Starting SubtermCWHack with 136s (1) cores
% 174.13/25.75 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 174.13/25.75 % Starting G-E--_208_C18_F1_SE_CS_SSP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 174.13/25.75 % Starting new_bool_3 with 136s (1) cores
% 174.13/25.75 % Starting new_bool_1 with 136s (1) cores
% 174.13/25.75 % G-E--_208_C18_F1_SE_CS_SSP_PS_S5PRR_RG_S04AN with pid 1625401 completed with status 0
% 174.13/25.75 % Result found by G-E--_208_C18_F1_SE_CS_SSP_PS_S5PRR_RG_S04AN
% 174.13/25.75 % Preprocessing class: FSSSSMSSSSSNFFN.
% 174.13/25.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 174.13/25.75 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 174.13/25.75 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 174.13/25.75 % No SInE strategy applied
% 174.13/25.75 % Search class: FUHPF-FFSF21-DFFFFFNN
% 174.13/25.75 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 174.13/25.75 % Starting SubtermCWHack with 136s (1) cores
% 174.13/25.75 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 174.13/25.75 % Starting G-E--_208_C18_F1_SE_CS_SSP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 174.13/25.75 % Preprocessing time : 0.002 s
% 174.13/25.75 % Presaturation interreduction done
% 174.13/25.75
% 174.13/25.75 % Proof found!
% 174.13/25.75 % SZS status Unsatisfiable
% 174.13/25.75 % SZS output start CNFRefutation
% See solution above
% 174.13/25.75 % Parsed axioms : 2
% 174.13/25.75 % Removed by relevancy pruning/SinE : 0
% 174.13/25.75 % Initial clauses : 2
% 174.13/25.75 % Removed in clause preprocessing : 0
% 174.13/25.75 % Initial clauses in saturation : 2
% 174.13/25.75 % Processed clauses : 2848
% 174.13/25.75 % ...of these trivial : 289
% 174.13/25.75 % ...subsumed : 1950
% 174.13/25.75 % ...remaining for further processing : 609
% 174.13/25.75 % Other redundant clauses eliminated : 0
% 174.13/25.75 % Clauses deleted for lack of memory : 0
% 174.13/25.75 % Backward-subsumed : 83
% 174.13/25.75 % Backward-rewritten : 485
% 174.13/25.75 % Generated clauses : 341056
% 174.13/25.75 % ...of the previous two non-redundant : 333755
% 174.13/25.75 % ...aggressively subsumed : 0
% 174.13/25.75 % Contextual simplify-reflections : 0
% 174.13/25.75 % Paramodulations : 341055
% 174.13/25.75 % Factorizations : 0
% 174.13/25.75 % NegExts : 0
% 174.13/25.75 % Equation resolutions : 0
% 174.13/25.75 % Disequality decompositions : 0
% 174.13/25.75 % Total rewrite steps : 1854831
% 174.13/25.75 % ...of those cached : 1782170
% 174.13/25.75 % Propositional unsat checks : 0
% 174.13/25.75 % Propositional check models : 0
% 174.13/25.75 % Propositional check unsatisfiable : 0
% 174.13/25.75 % Propositional clauses : 0
% 174.13/25.75 % Propositional clauses after purity: 0
% 174.13/25.75 % Propositional unsat core size : 0
% 174.13/25.75 % Propositional preprocessing time : 0.000
% 174.13/25.75 % Propositional encoding time : 0.000
% 174.13/25.75 % Propositional solver time : 0.000
% 174.13/25.75 % Success case prop preproc time : 0.000
% 174.13/25.75 % Success case prop encoding time : 0.000
% 174.13/25.75 % Success case prop solver time : 0.000
% 174.13/25.75 % Current number of processed clauses : 38
% 174.13/25.75 % Positive orientable unit clauses : 38
% 174.13/25.75 % Positive unorientable unit clauses: 0
% 174.13/25.75 % Negative unit clauses : 0
% 174.13/25.75 % Non-unit-clauses : 0
% 174.13/25.75 % Current number of unprocessed clauses: 316628
% 174.13/25.75 % ...number of literals in the above : 316628
% 174.13/25.75 % Current number of archived formulas : 0
% 174.13/25.75 % Current number of archived clauses : 571
% 174.13/25.75 % Clause-clause subsumption calls (NU) : 6235
% 174.13/25.75 % Rec. Clause-clause subsumption calls : 6235
% 174.13/25.75 % Non-unit clause-clause subsumptions : 1875
% 174.13/25.75 % Unit Clause-clause subsumption calls : 1392
% 174.13/25.75 % Rewrite failures with RHS unbound : 0
% 174.13/25.75 % BW rewrite match attempts : 17709
% 174.13/25.75 % BW rewrite match successes : 750
% 174.13/25.75 % Condensation attempts : 0
% 174.13/25.75 % Condensation successes : 0
% 174.13/25.75 % Termbank termtop insertions : 51055542
% 174.13/25.75 % Search garbage collected termcells : 8
% 174.13/25.75
% 174.13/25.75 % -------------------------------------------------
% 174.13/25.75 % User time : 23.463 s
% 174.13/25.75 % System time : 0.870 s
% 174.13/25.75 % Total time : 24.333 s
% 174.13/25.75 % Maximum resident set size: 3584 pages
% 174.13/25.75
% 174.13/25.75 % -------------------------------------------------
% 174.13/25.75 % User time : 121.257 s
% 174.13/25.75 % System time : 2.903 s
% 174.13/25.75 % Total time : 124.161 s
% 174.13/25.75 % Maximum resident set size: 4608 pages
% 174.13/25.75 % E exiting
%------------------------------------------------------------------------------