%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP411-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:43:34 PM UTC 2026
% Result : Unsatisfiable 0.44s 0.54s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(multiply(inverse(multiply(X1,inverse(multiply(X2,X3)))),multiply(X1,inverse(X3))),inverse(multiply(inverse(X3),X3))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
cnf(c_0_2,axiom,
multiply(multiply(inverse(multiply(X1,inverse(multiply(X2,X3)))),multiply(X1,inverse(X3))),inverse(multiply(inverse(X3),X3))) = X2,
single_axiom ).
cnf(c_0_3,plain,
multiply(multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(inverse(multiply(inverse(X3),X3))))),inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(multiply(inverse(X3),X3))))) = multiply(inverse(multiply(X4,inverse(multiply(X2,X3)))),multiply(X4,inverse(X3))),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(inverse(multiply(X1,inverse(multiply(multiply(X2,inverse(multiply(inverse(X3),X3))),X3)))),multiply(X1,inverse(X3))) = X2,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
multiply(inverse(multiply(X1,inverse(multiply(X2,X3)))),multiply(X1,inverse(X3))) = multiply(inverse(multiply(X4,inverse(multiply(X2,X3)))),multiply(X4,inverse(X3))),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_6,plain,
multiply(inverse(multiply(multiply(inverse(multiply(X1,inverse(multiply(X2,X3)))),multiply(X1,inverse(X3))),inverse(multiply(multiply(X4,inverse(multiply(inverse(multiply(inverse(X3),X3)),multiply(inverse(X3),X3)))),multiply(inverse(X3),X3))))),X2) = X4,
inference(spm,[status(thm)],[c_0_4,c_0_2]) ).
cnf(c_0_7,plain,
multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(X3))) = multiply(inverse(multiply(X4,inverse(X2))),multiply(X4,inverse(X3))),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
multiply(multiply(inverse(multiply(X1,inverse(multiply(X2,multiply(X3,inverse(X4)))))),multiply(X1,inverse(multiply(X3,inverse(X4))))),inverse(multiply(inverse(multiply(X5,inverse(X4))),multiply(X5,inverse(X4))))) = X2,
inference(spm,[status(thm)],[c_0_2,c_0_7]) ).
cnf(c_0_9,plain,
multiply(multiply(inverse(X1),multiply(multiply(inverse(multiply(X2,inverse(multiply(X1,X3)))),multiply(X2,inverse(X3))),inverse(X3))),inverse(multiply(inverse(X3),X3))) = inverse(X3),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_10,plain,
multiply(multiply(inverse(multiply(X1,inverse(multiply(X2,multiply(X3,inverse(X4)))))),multiply(X1,inverse(multiply(X3,inverse(X4))))),inverse(multiply(inverse(X5),X5))) = X2,
inference(spm,[status(thm)],[c_0_8,c_0_6]) ).
cnf(c_0_11,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X2)))),multiply(X1,inverse(X2))) = multiply(inverse(X3),multiply(multiply(inverse(multiply(X4,inverse(multiply(X3,X2)))),multiply(X4,inverse(X2))),inverse(X2))),
inference(spm,[status(thm)],[c_0_4,c_0_9]) ).
cnf(c_0_12,plain,
multiply(multiply(inverse(multiply(X1,inverse(multiply(X2,X3)))),multiply(X1,inverse(X3))),inverse(multiply(inverse(X4),X4))) = X2,
inference(spm,[status(thm)],[c_0_10,c_0_10]) ).
cnf(c_0_13,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_12]),c_0_12]) ).
cnf(c_0_14,plain,
multiply(multiply(inverse(multiply(multiply(inverse(multiply(X1,inverse(multiply(X2,X3)))),multiply(X1,inverse(X3))),inverse(multiply(X4,multiply(inverse(X3),X3))))),X2),inverse(multiply(inverse(multiply(inverse(X3),X3)),multiply(inverse(X3),X3)))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_15,plain,
multiply(multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(inverse(multiply(inverse(X3),X3))))),inverse(multiply(inverse(X4),X4))) = multiply(inverse(multiply(X5,inverse(multiply(X2,X6)))),multiply(X5,inverse(X6))),
inference(spm,[status(thm)],[c_0_12,c_0_12]) ).
cnf(c_0_16,plain,
multiply(inverse(multiply(X1,inverse(multiply(multiply(X2,inverse(multiply(inverse(X3),X3))),X4)))),multiply(X1,inverse(X4))) = X2,
inference(spm,[status(thm)],[c_0_4,c_0_13]) ).
cnf(c_0_17,plain,
multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(a3),a3))) = inverse(multiply(inverse(a3),a3)),
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_15]),c_0_16]),c_0_13]),c_0_13]),c_0_13]),c_0_13]) ).
cnf(c_0_18,plain,
multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(X2),X2))) = inverse(multiply(inverse(X2),X2)),
inference(spm,[status(thm)],[c_0_17,c_0_13]) ).
cnf(c_0_19,plain,
inverse(multiply(inverse(X1),X1)) = multiply(inverse(X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_18]),c_0_18]) ).
cnf(c_0_20,plain,
multiply(inverse(multiply(X1,inverse(multiply(multiply(inverse(X2),X2),X3)))),multiply(X1,inverse(X3))) = inverse(inverse(multiply(inverse(X3),X3))),
inference(spm,[status(thm)],[c_0_4,c_0_13]) ).
cnf(c_0_21,plain,
multiply(inverse(multiply(X1,inverse(multiply(multiply(X2,multiply(inverse(X3),X3)),X4)))),multiply(X1,inverse(X4))) = X2,
inference(spm,[status(thm)],[c_0_16,c_0_19]) ).
cnf(c_0_22,plain,
multiply(inverse(multiply(X1,inverse(multiply(multiply(inverse(X2),X2),X3)))),multiply(X1,inverse(X3))) = multiply(inverse(a3),a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_19]),c_0_19]) ).
cnf(c_0_23,plain,
multiply(inverse(multiply(inverse(inverse(X1)),inverse(X2))),multiply(inverse(X3),X3)) = multiply(inverse(multiply(X4,inverse(X2))),multiply(X4,inverse(X1))),
inference(spm,[status(thm)],[c_0_7,c_0_13]) ).
cnf(c_0_24,plain,
multiply(inverse(multiply(a3,multiply(inverse(a3),a3))),multiply(a3,inverse(X1))) = multiply(multiply(inverse(a3),a3),multiply(multiply(inverse(a3),a3),inverse(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_11,c_0_13]),c_0_19]),c_0_19]),c_0_19]),c_0_11]),c_0_19]) ).
cnf(c_0_25,plain,
multiply(multiply(inverse(multiply(X1,inverse(multiply(X2,X3)))),multiply(X1,inverse(X3))),multiply(inverse(a3),a3)) = X2,
inference(rw,[status(thm)],[c_0_12,c_0_19]) ).
cnf(c_0_26,plain,
inverse(multiply(inverse(inverse(X1)),inverse(multiply(multiply(inverse(X2),X2),X1)))) = multiply(inverse(a3),a3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_22]) ).
cnf(c_0_27,plain,
multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(X3))) = multiply(multiply(inverse(a3),a3),multiply(inverse(inverse(X2)),inverse(X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_13]),c_0_19]) ).
cnf(c_0_28,plain,
multiply(multiply(inverse(X1),X1),multiply(inverse(X2),X2)) = multiply(inverse(a3),a3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_19]),c_0_19]) ).
cnf(c_0_29,plain,
multiply(inverse(multiply(X1,multiply(inverse(a3),a3))),multiply(X1,inverse(X2))) = multiply(multiply(inverse(a3),a3),multiply(multiply(inverse(a3),a3),inverse(X2))),
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_11,c_0_13]),c_0_19]),c_0_23]),c_0_11]),c_0_19]),c_0_24]) ).
cnf(c_0_30,plain,
multiply(multiply(inverse(multiply(X1,inverse(multiply(X2,X3)))),multiply(X1,inverse(X3))),multiply(inverse(X4),X4)) = X2,
inference(spm,[status(thm)],[c_0_25,c_0_13]) ).
cnf(c_0_31,plain,
multiply(inverse(X1),X1) = multiply(inverse(multiply(a3,inverse(X2))),multiply(a3,inverse(multiply(multiply(inverse(X3),X3),X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_26]),c_0_27]) ).
cnf(c_0_32,plain,
multiply(inverse(multiply(X1,inverse(multiply(multiply(X2,multiply(inverse(a3),a3)),multiply(inverse(X3),X3))))),multiply(X1,multiply(inverse(a3),a3))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_16]),c_0_19]),c_0_28]),c_0_19]),c_0_19]) ).
cnf(c_0_33,plain,
multiply(inverse(multiply(inverse(inverse(X1)),multiply(inverse(a3),a3))),multiply(inverse(X2),X2)) = multiply(multiply(inverse(a3),a3),multiply(multiply(inverse(a3),a3),inverse(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_13]),c_0_19]),c_0_11]),c_0_19]),c_0_29]) ).
cnf(c_0_34,plain,
multiply(multiply(multiply(inverse(a3),a3),multiply(multiply(inverse(a3),a3),inverse(X1))),multiply(inverse(X2),X2)) = inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_13]),c_0_19]),c_0_29]) ).
cnf(c_0_35,plain,
multiply(multiply(inverse(multiply(multiply(inverse(multiply(X1,inverse(multiply(X2,X3)))),multiply(X1,inverse(X3))),inverse(multiply(X4,multiply(inverse(X3),X3))))),X2),multiply(inverse(a3),a3)) = X4,
inference(rw,[status(thm)],[c_0_14,c_0_19]) ).
cnf(c_0_36,plain,
multiply(inverse(X1),X1) = multiply(inverse(multiply(X2,inverse(X3))),multiply(X2,inverse(multiply(multiply(inverse(X4),X4),X3)))),
inference(spm,[status(thm)],[c_0_7,c_0_31]) ).
cnf(c_0_37,plain,
multiply(multiply(inverse(X1),X1),multiply(inverse(a3),a3)) = multiply(inverse(a3),a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_19]) ).
cnf(c_0_38,plain,
multiply(inverse(multiply(X1,inverse(inverse(X2)))),multiply(X1,multiply(inverse(a3),a3))) = inverse(multiply(inverse(inverse(X2)),multiply(inverse(a3),a3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_39,plain,
inverse(multiply(inverse(inverse(multiply(multiply(inverse(X1),X1),X2))),inverse(X2))) = multiply(inverse(a3),a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_19]),c_0_30]),c_0_37]) ).
cnf(c_0_40,plain,
multiply(inverse(multiply(X1,multiply(inverse(X2),X2))),multiply(X1,inverse(X3))) = multiply(multiply(inverse(a3),a3),multiply(multiply(inverse(a3),a3),inverse(X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_19]),c_0_19]) ).
cnf(c_0_41,plain,
multiply(multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,multiply(inverse(a3),a3))),multiply(inverse(a3),a3)) = multiply(inverse(multiply(X3,inverse(multiply(X2,X4)))),multiply(X3,inverse(X4))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_19]),c_0_19]),c_0_19]) ).
cnf(c_0_42,plain,
multiply(inverse(multiply(multiply(inverse(a3),a3),inverse(inverse(X1)))),multiply(inverse(a3),a3)) = inverse(multiply(inverse(inverse(X1)),multiply(inverse(a3),a3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_19]),c_0_19]),c_0_19]) ).
cnf(c_0_43,plain,
inverse(inverse(multiply(multiply(inverse(X1),X1),X2))) = inverse(inverse(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_39]),c_0_40]),c_0_34]) ).
cnf(c_0_44,plain,
inverse(multiply(inverse(inverse(multiply(inverse(inverse(X1)),multiply(inverse(a3),a3)))),multiply(inverse(a3),a3))) = multiply(multiply(inverse(a3),a3),multiply(multiply(inverse(a3),a3),inverse(inverse(inverse(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_41,c_0_42]),c_0_43]),c_0_38]),c_0_33]),c_0_19]),c_0_38]) ).
cnf(c_0_45,plain,
multiply(multiply(inverse(a3),a3),multiply(inverse(inverse(inverse(X1))),multiply(inverse(a3),a3))) = inverse(multiply(inverse(inverse(X1)),multiply(inverse(a3),a3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_13]),c_0_19]) ).
cnf(c_0_46,plain,
multiply(multiply(inverse(a3),a3),multiply(multiply(inverse(a3),a3),inverse(multiply(inverse(inverse(X1)),multiply(inverse(a3),a3))))) = inverse(inverse(inverse(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_44]),c_0_34]) ).
cnf(c_0_47,plain,
inverse(inverse(inverse(multiply(inverse(inverse(X1)),multiply(inverse(a3),a3))))) = inverse(inverse(multiply(inverse(inverse(inverse(X1))),multiply(inverse(a3),a3)))),
inference(spm,[status(thm)],[c_0_43,c_0_45]) ).
cnf(c_0_48,plain,
inverse(inverse(multiply(inverse(inverse(inverse(X1))),multiply(inverse(a3),a3)))) = inverse(inverse(inverse(inverse(inverse(X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_46]),c_0_43]),c_0_47]) ).
cnf(c_0_49,plain,
inverse(inverse(inverse(multiply(inverse(inverse(X1)),multiply(inverse(a3),a3))))) = inverse(inverse(inverse(inverse(inverse(X1))))),
inference(rw,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_50,plain,
inverse(inverse(inverse(inverse(inverse(inverse(inverse(X1))))))) = inverse(inverse(inverse(inverse(inverse(X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_44]),c_0_43]),c_0_43]),c_0_47]),c_0_48]) ).
cnf(c_0_51,plain,
inverse(multiply(inverse(inverse(inverse(inverse(inverse(inverse(X1)))))),multiply(inverse(a3),a3))) = inverse(multiply(inverse(inverse(inverse(inverse(X1)))),multiply(inverse(a3),a3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_50]),c_0_45]) ).
cnf(c_0_52,plain,
inverse(inverse(inverse(inverse(inverse(inverse(X1)))))) = inverse(inverse(inverse(inverse(X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_51]),c_0_35]) ).
cnf(c_0_53,plain,
inverse(multiply(inverse(inverse(inverse(inverse(inverse(X1))))),multiply(inverse(a3),a3))) = inverse(multiply(inverse(inverse(inverse(X1))),multiply(inverse(a3),a3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_52]),c_0_45]) ).
cnf(c_0_54,plain,
inverse(inverse(inverse(inverse(inverse(X1))))) = inverse(inverse(inverse(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_53]),c_0_35]) ).
cnf(c_0_55,plain,
inverse(inverse(multiply(inverse(inverse(inverse(X1))),multiply(inverse(a3),a3)))) = inverse(inverse(inverse(X1))),
inference(rw,[status(thm)],[c_0_48,c_0_54]) ).
cnf(c_0_56,plain,
multiply(inverse(inverse(inverse(X1))),multiply(inverse(X2),X2)) = inverse(multiply(inverse(inverse(X1)),multiply(inverse(a3),a3))),
inference(spm,[status(thm)],[c_0_34,c_0_46]) ).
cnf(c_0_57,plain,
multiply(inverse(inverse(inverse(X1))),multiply(inverse(a3),a3)) = inverse(inverse(inverse(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56]),c_0_56]),c_0_54]) ).
cnf(c_0_58,plain,
multiply(inverse(multiply(multiply(inverse(a3),a3),inverse(inverse(X1)))),multiply(inverse(a3),a3)) = inverse(inverse(inverse(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_56]),c_0_57]) ).
cnf(c_0_59,plain,
multiply(inverse(inverse(inverse(X1))),multiply(inverse(X2),X2)) = inverse(inverse(inverse(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_57]),c_0_19]),c_0_38]),c_0_57]),c_0_54]) ).
cnf(c_0_60,plain,
inverse(multiply(multiply(inverse(a3),a3),inverse(inverse(X1)))) = inverse(inverse(inverse(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_30,c_0_58]),c_0_19]),c_0_38]),c_0_57]),c_0_54]),c_0_59]) ).
cnf(c_0_61,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X3)))),multiply(X1,inverse(X3))) = inverse(inverse(inverse(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_60]),c_0_37]),c_0_59]),c_0_59]) ).
cnf(c_0_62,plain,
inverse(inverse(inverse(X1))) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_61]),c_0_59]) ).
cnf(c_0_63,plain,
multiply(inverse(X1),multiply(inverse(X2),X2)) = inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_62]),c_0_62]) ).
cnf(c_0_64,plain,
multiply(inverse(multiply(a3,inverse(multiply(X1,a3)))),multiply(a3,inverse(a3))) = multiply(inverse(multiply(X2,inverse(multiply(X1,X3)))),multiply(X2,inverse(X3))),
inference(rw,[status(thm)],[c_0_3,c_0_15]) ).
cnf(c_0_65,plain,
multiply(multiply(inverse(a3),a3),inverse(inverse(inverse(X1)))) = inverse(inverse(inverse(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_56]),c_0_59]),c_0_59]) ).
cnf(c_0_66,plain,
multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(X3))) = inverse(multiply(inverse(inverse(X3)),inverse(X2))),
inference(rw,[status(thm)],[c_0_23,c_0_63]) ).
cnf(c_0_67,plain,
multiply(inverse(X1),multiply(multiply(inverse(multiply(a3,inverse(multiply(X1,a3)))),multiply(a3,inverse(a3))),inverse(X2))) = multiply(multiply(inverse(a3),a3),multiply(multiply(inverse(a3),a3),inverse(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_64]),c_0_19]),c_0_40]) ).
cnf(c_0_68,plain,
multiply(multiply(inverse(a3),a3),inverse(X1)) = inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_62]),c_0_62]) ).
cnf(c_0_69,plain,
inverse(multiply(inverse(inverse(X1)),inverse(multiply(X2,X1)))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_66]),c_0_63]) ).
cnf(c_0_70,plain,
multiply(inverse(X1),multiply(multiply(inverse(multiply(a3,inverse(multiply(X1,a3)))),multiply(a3,inverse(a3))),inverse(X2))) = inverse(X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68]),c_0_68]) ).
cnf(c_0_71,plain,
multiply(inverse(multiply(multiply(inverse(multiply(X1,inverse(multiply(X2,X3)))),multiply(X1,inverse(X3))),inverse(multiply(multiply(X4,multiply(inverse(a3),a3)),multiply(inverse(X5),X5))))),X2) = X4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_13]),c_0_19]),c_0_28]),c_0_19]) ).
cnf(c_0_72,plain,
multiply(X1,multiply(inverse(X2),X2)) = X1,
inference(spm,[status(thm)],[c_0_63,c_0_69]) ).
cnf(c_0_73,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_69]),c_0_66]),c_0_69]) ).
cnf(c_0_74,plain,
multiply(inverse(multiply(X1,inverse(X2))),X1) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_13]),c_0_66]),c_0_69]),c_0_72]),c_0_72]) ).
cnf(c_0_75,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_62,c_0_69]) ).
cnf(c_0_76,plain,
multiply(multiply(X1,inverse(X2)),X2) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]) ).
cnf(c_0_77,plain,
multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,X3)) = inverse(multiply(inverse(X3),inverse(X2))),
inference(spm,[status(thm)],[c_0_66,c_0_69]) ).
cnf(c_0_78,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_76]),c_0_75]) ).
cnf(c_0_79,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(fof_simplification,[status(thm)],[prove_these_axioms_3]) ).
cnf(c_0_80,plain,
multiply(multiply(X1,inverse(X2)),multiply(X2,X3)) = multiply(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_78]),c_0_78]),c_0_75]) ).
cnf(c_0_81,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
c_0_79 ).
cnf(c_0_82,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_73]),c_0_75]) ).
cnf(c_0_83,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP411-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:15:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 0.44/0.54 % Version: 3.5.1
% 0.44/0.54 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.44/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.44/0.54 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.44/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.44/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.44/0.54 % Starting sh5l with 300s (1) cores
% 0.44/0.54 % new_bool_3 with pid 503413 completed with status 9
% 0.44/0.54 % new_bool_1 with pid 503414 completed with status 9
% 0.44/0.54 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 503412 completed with status 0
% 0.44/0.54 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.44/0.54 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.44/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.44/0.54 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.44/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.44/0.54 % No SInE strategy applied
% 0.44/0.54 % Search class: FUUPF-FFSF21-DFFFFFNN
% 0.44/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.44/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.44/0.54 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.44/0.54 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.44/0.54 % Starting new_bool_3 with 136s (1) cores
% 0.44/0.54 % Starting new_bool_1 with 136s (1) cores
% 0.44/0.54 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 503417 completed with status 0
% 0.44/0.54 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.44/0.54 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.44/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.44/0.54 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.44/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.44/0.54 % No SInE strategy applied
% 0.44/0.54 % Search class: FUUPF-FFSF21-DFFFFFNN
% 0.44/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.44/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.44/0.54 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.44/0.54 % Preprocessing time : 0.001 s
% 0.44/0.54
% 0.44/0.54 % Proof found!
% 0.44/0.54 % SZS status Unsatisfiable
% 0.44/0.54 % SZS output start CNFRefutation
% See solution above
% 0.44/0.54 % Parsed axioms : 2
% 0.44/0.54 % Removed by relevancy pruning/SinE : 0
% 0.44/0.54 % Initial clauses : 2
% 0.44/0.54 % Removed in clause preprocessing : 0
% 0.44/0.54 % Initial clauses in saturation : 2
% 0.44/0.54 % Processed clauses : 586
% 0.44/0.54 % ...of these trivial : 160
% 0.44/0.54 % ...subsumed : 271
% 0.44/0.54 % ...remaining for further processing : 155
% 0.44/0.54 % Other redundant clauses eliminated : 0
% 0.44/0.54 % Clauses deleted for lack of memory : 0
% 0.44/0.54 % Backward-subsumed : 3
% 0.44/0.54 % Backward-rewritten : 140
% 0.44/0.54 % Generated clauses : 9703
% 0.44/0.54 % ...of the previous two non-redundant : 7791
% 0.44/0.54 % ...aggressively subsumed : 0
% 0.44/0.54 % Contextual simplify-reflections : 0
% 0.44/0.54 % Paramodulations : 9703
% 0.44/0.54 % Factorizations : 0
% 0.44/0.54 % NegExts : 0
% 0.44/0.54 % Equation resolutions : 0
% 0.44/0.54 % Disequality decompositions : 0
% 0.44/0.54 % Total rewrite steps : 14641
% 0.44/0.54 % ...of those cached : 13006
% 0.44/0.54 % Propositional unsat checks : 0
% 0.44/0.54 % Propositional check models : 0
% 0.44/0.54 % Propositional check unsatisfiable : 0
% 0.44/0.54 % Propositional clauses : 0
% 0.44/0.54 % Propositional clauses after purity: 0
% 0.44/0.54 % Propositional unsat core size : 0
% 0.44/0.54 % Propositional preprocessing time : 0.000
% 0.44/0.54 % Propositional encoding time : 0.000
% 0.44/0.54 % Propositional solver time : 0.000
% 0.44/0.54 % Success case prop preproc time : 0.000
% 0.44/0.54 % Success case prop encoding time : 0.000
% 0.44/0.54 % Success case prop solver time : 0.000
% 0.44/0.54 % Current number of processed clauses : 12
% 0.44/0.54 % Positive orientable unit clauses : 10
% 0.44/0.54 % Positive unorientable unit clauses: 2
% 0.44/0.54 % Negative unit clauses : 0
% 0.44/0.54 % Non-unit-clauses : 0
% 0.44/0.54 % Current number of unprocessed clauses: 3541
% 0.44/0.54 % ...number of literals in the above : 3541
% 0.44/0.54 % Current number of archived formulas : 0
% 0.44/0.54 % Current number of archived clauses : 143
% 0.44/0.54 % Clause-clause subsumption calls (NU) : 0
% 0.44/0.54 % Rec. Clause-clause subsumption calls : 0
% 0.44/0.54 % Non-unit clause-clause subsumptions : 0
% 0.44/0.54 % Unit Clause-clause subsumption calls : 176
% 0.44/0.54 % Rewrite failures with RHS unbound : 0
% 0.44/0.54 % BW rewrite match attempts : 1009
% 0.44/0.54 % BW rewrite match successes : 260
% 0.44/0.54 % Condensation attempts : 0
% 0.44/0.54 % Condensation successes : 0
% 0.44/0.54 % Termbank termtop insertions : 246581
% 0.44/0.54 % Search garbage collected termcells : 2
% 0.44/0.54
% 0.44/0.54 % -------------------------------------------------
% 0.44/0.54 % User time : 0.104 s
% 0.44/0.54 % System time : 0.011 s
% 0.44/0.54 % Total time : 0.115 s
% 0.44/0.54 % Maximum resident set size: 3632 pages
% 0.44/0.54
% 0.44/0.54 % -------------------------------------------------
% 0.44/0.54 % User time : 0.543 s
% 0.44/0.54 % System time : 0.061 s
% 0.44/0.54 % Total time : 0.604 s
% 0.44/0.54 % Maximum resident set size: 4608 pages
% 0.44/0.54 % E exiting
%------------------------------------------------------------------------------