TSTP Solution File: GRP161-1 by iProverMo---2.5-0.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProverMo---2.5-0.1
% Problem  : GRP161-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : iprover_modulo %s %d

% Computer : n014.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Sat Jul 16 09:45:28 EDT 2022

% Result   : Unsatisfiable 0.19s 0.42s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named input)

% Comments : 
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy Equiv(ClausalAll)
% Orienting axioms whose shape is orientable
cnf(monotony_glb2,axiom,
    multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)),
    input ).

fof(monotony_glb2_0,plain,
    ! [X,Y,Z] :
      ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X))
      | $false ),
    inference(orientation,[status(thm)],[monotony_glb2]) ).

cnf(monotony_lub2,axiom,
    multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)),
    input ).

fof(monotony_lub2_0,plain,
    ! [X,Y,Z] :
      ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X))
      | $false ),
    inference(orientation,[status(thm)],[monotony_lub2]) ).

cnf(monotony_glb1,axiom,
    multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
    input ).

fof(monotony_glb1_0,plain,
    ! [X,Y,Z] :
      ( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z))
      | $false ),
    inference(orientation,[status(thm)],[monotony_glb1]) ).

cnf(monotony_lub1,axiom,
    multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
    input ).

fof(monotony_lub1_0,plain,
    ! [X,Y,Z] :
      ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z))
      | $false ),
    inference(orientation,[status(thm)],[monotony_lub1]) ).

cnf(glb_absorbtion,axiom,
    greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
    input ).

fof(glb_absorbtion_0,plain,
    ! [X,Y] :
      ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X
      | $false ),
    inference(orientation,[status(thm)],[glb_absorbtion]) ).

cnf(lub_absorbtion,axiom,
    least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
    input ).

fof(lub_absorbtion_0,plain,
    ! [X,Y] :
      ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X
      | $false ),
    inference(orientation,[status(thm)],[lub_absorbtion]) ).

cnf(idempotence_of_gld,axiom,
    greatest_lower_bound(X,X) = X,
    input ).

fof(idempotence_of_gld_0,plain,
    ! [X] :
      ( greatest_lower_bound(X,X) = X
      | $false ),
    inference(orientation,[status(thm)],[idempotence_of_gld]) ).

cnf(idempotence_of_lub,axiom,
    least_upper_bound(X,X) = X,
    input ).

fof(idempotence_of_lub_0,plain,
    ! [X] :
      ( least_upper_bound(X,X) = X
      | $false ),
    inference(orientation,[status(thm)],[idempotence_of_lub]) ).

cnf(associativity_of_lub,axiom,
    least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z),
    input ).

fof(associativity_of_lub_0,plain,
    ! [X,Y,Z] :
      ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z)
      | $false ),
    inference(orientation,[status(thm)],[associativity_of_lub]) ).

cnf(associativity_of_glb,axiom,
    greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z),
    input ).

fof(associativity_of_glb_0,plain,
    ! [X,Y,Z] :
      ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z)
      | $false ),
    inference(orientation,[status(thm)],[associativity_of_glb]) ).

cnf(symmetry_of_lub,axiom,
    least_upper_bound(X,Y) = least_upper_bound(Y,X),
    input ).

fof(symmetry_of_lub_0,plain,
    ! [X,Y] :
      ( least_upper_bound(X,Y) = least_upper_bound(Y,X)
      | $false ),
    inference(orientation,[status(thm)],[symmetry_of_lub]) ).

cnf(symmetry_of_glb,axiom,
    greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
    input ).

fof(symmetry_of_glb_0,plain,
    ! [X,Y] :
      ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X)
      | $false ),
    inference(orientation,[status(thm)],[symmetry_of_glb]) ).

cnf(associativity,axiom,
    multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
    input ).

fof(associativity_0,plain,
    ! [X,Y,Z] :
      ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z))
      | $false ),
    inference(orientation,[status(thm)],[associativity]) ).

cnf(left_inverse,axiom,
    multiply(inverse(X),X) = identity,
    input ).

fof(left_inverse_0,plain,
    ! [X] :
      ( multiply(inverse(X),X) = identity
      | $false ),
    inference(orientation,[status(thm)],[left_inverse]) ).

cnf(left_identity,axiom,
    multiply(identity,X) = X,
    input ).

fof(left_identity_0,plain,
    ! [X] :
      ( multiply(identity,X) = X
      | $false ),
    inference(orientation,[status(thm)],[left_identity]) ).

fof(def_lhs_atom1,axiom,
    ! [X] :
      ( lhs_atom1(X)
    <=> multiply(identity,X) = X ),
    inference(definition,[],]) ).

fof(to_be_clausified_0,plain,
    ! [X] :
      ( lhs_atom1(X)
      | $false ),
    inference(fold_definition,[status(thm)],[left_identity_0,def_lhs_atom1]) ).

fof(def_lhs_atom2,axiom,
    ! [X] :
      ( lhs_atom2(X)
    <=> multiply(inverse(X),X) = identity ),
    inference(definition,[],]) ).

fof(to_be_clausified_1,plain,
    ! [X] :
      ( lhs_atom2(X)
      | $false ),
    inference(fold_definition,[status(thm)],[left_inverse_0,def_lhs_atom2]) ).

fof(def_lhs_atom3,axiom,
    ! [Z,Y,X] :
      ( lhs_atom3(Z,Y,X)
    <=> multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_2,plain,
    ! [X,Y,Z] :
      ( lhs_atom3(Z,Y,X)
      | $false ),
    inference(fold_definition,[status(thm)],[associativity_0,def_lhs_atom3]) ).

fof(def_lhs_atom4,axiom,
    ! [Y,X] :
      ( lhs_atom4(Y,X)
    <=> greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
    inference(definition,[],]) ).

fof(to_be_clausified_3,plain,
    ! [X,Y] :
      ( lhs_atom4(Y,X)
      | $false ),
    inference(fold_definition,[status(thm)],[symmetry_of_glb_0,def_lhs_atom4]) ).

fof(def_lhs_atom5,axiom,
    ! [Y,X] :
      ( lhs_atom5(Y,X)
    <=> least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
    inference(definition,[],]) ).

fof(to_be_clausified_4,plain,
    ! [X,Y] :
      ( lhs_atom5(Y,X)
      | $false ),
    inference(fold_definition,[status(thm)],[symmetry_of_lub_0,def_lhs_atom5]) ).

fof(def_lhs_atom6,axiom,
    ! [Z,Y,X] :
      ( lhs_atom6(Z,Y,X)
    <=> greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ),
    inference(definition,[],]) ).

fof(to_be_clausified_5,plain,
    ! [X,Y,Z] :
      ( lhs_atom6(Z,Y,X)
      | $false ),
    inference(fold_definition,[status(thm)],[associativity_of_glb_0,def_lhs_atom6]) ).

fof(def_lhs_atom7,axiom,
    ! [Z,Y,X] :
      ( lhs_atom7(Z,Y,X)
    <=> least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ),
    inference(definition,[],]) ).

fof(to_be_clausified_6,plain,
    ! [X,Y,Z] :
      ( lhs_atom7(Z,Y,X)
      | $false ),
    inference(fold_definition,[status(thm)],[associativity_of_lub_0,def_lhs_atom7]) ).

fof(def_lhs_atom8,axiom,
    ! [X] :
      ( lhs_atom8(X)
    <=> least_upper_bound(X,X) = X ),
    inference(definition,[],]) ).

fof(to_be_clausified_7,plain,
    ! [X] :
      ( lhs_atom8(X)
      | $false ),
    inference(fold_definition,[status(thm)],[idempotence_of_lub_0,def_lhs_atom8]) ).

fof(def_lhs_atom9,axiom,
    ! [X] :
      ( lhs_atom9(X)
    <=> greatest_lower_bound(X,X) = X ),
    inference(definition,[],]) ).

fof(to_be_clausified_8,plain,
    ! [X] :
      ( lhs_atom9(X)
      | $false ),
    inference(fold_definition,[status(thm)],[idempotence_of_gld_0,def_lhs_atom9]) ).

fof(def_lhs_atom10,axiom,
    ! [Y,X] :
      ( lhs_atom10(Y,X)
    <=> least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
    inference(definition,[],]) ).

fof(to_be_clausified_9,plain,
    ! [X,Y] :
      ( lhs_atom10(Y,X)
      | $false ),
    inference(fold_definition,[status(thm)],[lub_absorbtion_0,def_lhs_atom10]) ).

fof(def_lhs_atom11,axiom,
    ! [Y,X] :
      ( lhs_atom11(Y,X)
    <=> greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
    inference(definition,[],]) ).

fof(to_be_clausified_10,plain,
    ! [X,Y] :
      ( lhs_atom11(Y,X)
      | $false ),
    inference(fold_definition,[status(thm)],[glb_absorbtion_0,def_lhs_atom11]) ).

fof(def_lhs_atom12,axiom,
    ! [Z,Y,X] :
      ( lhs_atom12(Z,Y,X)
    <=> multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_11,plain,
    ! [X,Y,Z] :
      ( lhs_atom12(Z,Y,X)
      | $false ),
    inference(fold_definition,[status(thm)],[monotony_lub1_0,def_lhs_atom12]) ).

fof(def_lhs_atom13,axiom,
    ! [Z,Y,X] :
      ( lhs_atom13(Z,Y,X)
    <=> multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_12,plain,
    ! [X,Y,Z] :
      ( lhs_atom13(Z,Y,X)
      | $false ),
    inference(fold_definition,[status(thm)],[monotony_glb1_0,def_lhs_atom13]) ).

fof(def_lhs_atom14,axiom,
    ! [Z,Y,X] :
      ( lhs_atom14(Z,Y,X)
    <=> multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_13,plain,
    ! [X,Y,Z] :
      ( lhs_atom14(Z,Y,X)
      | $false ),
    inference(fold_definition,[status(thm)],[monotony_lub2_0,def_lhs_atom14]) ).

fof(def_lhs_atom15,axiom,
    ! [Z,Y,X] :
      ( lhs_atom15(Z,Y,X)
    <=> multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_14,plain,
    ! [X,Y,Z] :
      ( lhs_atom15(Z,Y,X)
      | $false ),
    inference(fold_definition,[status(thm)],[monotony_glb2_0,def_lhs_atom15]) ).

% Start CNF derivation
fof(c_0_0,axiom,
    ! [X2,X3,X1] :
      ( lhs_atom15(X2,X3,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_14) ).

fof(c_0_1,axiom,
    ! [X2,X3,X1] :
      ( lhs_atom14(X2,X3,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_13) ).

fof(c_0_2,axiom,
    ! [X2,X3,X1] :
      ( lhs_atom13(X2,X3,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_12) ).

fof(c_0_3,axiom,
    ! [X2,X3,X1] :
      ( lhs_atom12(X2,X3,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_11) ).

fof(c_0_4,axiom,
    ! [X2,X3,X1] :
      ( lhs_atom7(X2,X3,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_6) ).

fof(c_0_5,axiom,
    ! [X2,X3,X1] :
      ( lhs_atom6(X2,X3,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_5) ).

fof(c_0_6,axiom,
    ! [X2,X3,X1] :
      ( lhs_atom3(X2,X3,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_2) ).

fof(c_0_7,axiom,
    ! [X3,X1] :
      ( lhs_atom11(X3,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_10) ).

fof(c_0_8,axiom,
    ! [X3,X1] :
      ( lhs_atom10(X3,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_9) ).

fof(c_0_9,axiom,
    ! [X3,X1] :
      ( lhs_atom5(X3,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_4) ).

fof(c_0_10,axiom,
    ! [X3,X1] :
      ( lhs_atom4(X3,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_3) ).

fof(c_0_11,axiom,
    ! [X1] :
      ( lhs_atom9(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_8) ).

fof(c_0_12,axiom,
    ! [X1] :
      ( lhs_atom8(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_7) ).

fof(c_0_13,axiom,
    ! [X1] :
      ( lhs_atom2(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_1) ).

fof(c_0_14,axiom,
    ! [X1] :
      ( lhs_atom1(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_0) ).

fof(c_0_15,plain,
    ! [X2,X3,X1] : lhs_atom15(X2,X3,X1),
    inference(fof_simplification,[status(thm)],[c_0_0]) ).

fof(c_0_16,plain,
    ! [X2,X3,X1] : lhs_atom14(X2,X3,X1),
    inference(fof_simplification,[status(thm)],[c_0_1]) ).

fof(c_0_17,plain,
    ! [X2,X3,X1] : lhs_atom13(X2,X3,X1),
    inference(fof_simplification,[status(thm)],[c_0_2]) ).

fof(c_0_18,plain,
    ! [X2,X3,X1] : lhs_atom12(X2,X3,X1),
    inference(fof_simplification,[status(thm)],[c_0_3]) ).

fof(c_0_19,plain,
    ! [X2,X3,X1] : lhs_atom7(X2,X3,X1),
    inference(fof_simplification,[status(thm)],[c_0_4]) ).

fof(c_0_20,plain,
    ! [X2,X3,X1] : lhs_atom6(X2,X3,X1),
    inference(fof_simplification,[status(thm)],[c_0_5]) ).

fof(c_0_21,plain,
    ! [X2,X3,X1] : lhs_atom3(X2,X3,X1),
    inference(fof_simplification,[status(thm)],[c_0_6]) ).

fof(c_0_22,plain,
    ! [X3,X1] : lhs_atom11(X3,X1),
    inference(fof_simplification,[status(thm)],[c_0_7]) ).

fof(c_0_23,plain,
    ! [X3,X1] : lhs_atom10(X3,X1),
    inference(fof_simplification,[status(thm)],[c_0_8]) ).

fof(c_0_24,plain,
    ! [X3,X1] : lhs_atom5(X3,X1),
    inference(fof_simplification,[status(thm)],[c_0_9]) ).

fof(c_0_25,plain,
    ! [X3,X1] : lhs_atom4(X3,X1),
    inference(fof_simplification,[status(thm)],[c_0_10]) ).

fof(c_0_26,plain,
    ! [X1] : lhs_atom9(X1),
    inference(fof_simplification,[status(thm)],[c_0_11]) ).

fof(c_0_27,plain,
    ! [X1] : lhs_atom8(X1),
    inference(fof_simplification,[status(thm)],[c_0_12]) ).

fof(c_0_28,plain,
    ! [X1] : lhs_atom2(X1),
    inference(fof_simplification,[status(thm)],[c_0_13]) ).

fof(c_0_29,plain,
    ! [X1] : lhs_atom1(X1),
    inference(fof_simplification,[status(thm)],[c_0_14]) ).

fof(c_0_30,plain,
    ! [X4,X5,X6] : lhs_atom15(X4,X5,X6),
    inference(variable_rename,[status(thm)],[c_0_15]) ).

fof(c_0_31,plain,
    ! [X4,X5,X6] : lhs_atom14(X4,X5,X6),
    inference(variable_rename,[status(thm)],[c_0_16]) ).

fof(c_0_32,plain,
    ! [X4,X5,X6] : lhs_atom13(X4,X5,X6),
    inference(variable_rename,[status(thm)],[c_0_17]) ).

fof(c_0_33,plain,
    ! [X4,X5,X6] : lhs_atom12(X4,X5,X6),
    inference(variable_rename,[status(thm)],[c_0_18]) ).

fof(c_0_34,plain,
    ! [X4,X5,X6] : lhs_atom7(X4,X5,X6),
    inference(variable_rename,[status(thm)],[c_0_19]) ).

fof(c_0_35,plain,
    ! [X4,X5,X6] : lhs_atom6(X4,X5,X6),
    inference(variable_rename,[status(thm)],[c_0_20]) ).

fof(c_0_36,plain,
    ! [X4,X5,X6] : lhs_atom3(X4,X5,X6),
    inference(variable_rename,[status(thm)],[c_0_21]) ).

fof(c_0_37,plain,
    ! [X4,X5] : lhs_atom11(X4,X5),
    inference(variable_rename,[status(thm)],[c_0_22]) ).

fof(c_0_38,plain,
    ! [X4,X5] : lhs_atom10(X4,X5),
    inference(variable_rename,[status(thm)],[c_0_23]) ).

fof(c_0_39,plain,
    ! [X4,X5] : lhs_atom5(X4,X5),
    inference(variable_rename,[status(thm)],[c_0_24]) ).

fof(c_0_40,plain,
    ! [X4,X5] : lhs_atom4(X4,X5),
    inference(variable_rename,[status(thm)],[c_0_25]) ).

fof(c_0_41,plain,
    ! [X2] : lhs_atom9(X2),
    inference(variable_rename,[status(thm)],[c_0_26]) ).

fof(c_0_42,plain,
    ! [X2] : lhs_atom8(X2),
    inference(variable_rename,[status(thm)],[c_0_27]) ).

fof(c_0_43,plain,
    ! [X2] : lhs_atom2(X2),
    inference(variable_rename,[status(thm)],[c_0_28]) ).

fof(c_0_44,plain,
    ! [X2] : lhs_atom1(X2),
    inference(variable_rename,[status(thm)],[c_0_29]) ).

cnf(c_0_45,plain,
    lhs_atom15(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_46,plain,
    lhs_atom14(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_47,plain,
    lhs_atom13(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_48,plain,
    lhs_atom12(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_49,plain,
    lhs_atom7(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_50,plain,
    lhs_atom6(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_51,plain,
    lhs_atom3(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_52,plain,
    lhs_atom11(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_53,plain,
    lhs_atom10(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_54,plain,
    lhs_atom5(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_55,plain,
    lhs_atom4(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_56,plain,
    lhs_atom9(X1),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_57,plain,
    lhs_atom8(X1),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

cnf(c_0_58,plain,
    lhs_atom2(X1),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_59,plain,
    lhs_atom1(X1),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_60,plain,
    lhs_atom15(X1,X2,X3),
    c_0_45,
    [final] ).

cnf(c_0_61,plain,
    lhs_atom14(X1,X2,X3),
    c_0_46,
    [final] ).

cnf(c_0_62,plain,
    lhs_atom13(X1,X2,X3),
    c_0_47,
    [final] ).

cnf(c_0_63,plain,
    lhs_atom12(X1,X2,X3),
    c_0_48,
    [final] ).

cnf(c_0_64,plain,
    lhs_atom7(X1,X2,X3),
    c_0_49,
    [final] ).

cnf(c_0_65,plain,
    lhs_atom6(X1,X2,X3),
    c_0_50,
    [final] ).

cnf(c_0_66,plain,
    lhs_atom3(X1,X2,X3),
    c_0_51,
    [final] ).

cnf(c_0_67,plain,
    lhs_atom11(X1,X2),
    c_0_52,
    [final] ).

cnf(c_0_68,plain,
    lhs_atom10(X1,X2),
    c_0_53,
    [final] ).

cnf(c_0_69,plain,
    lhs_atom5(X1,X2),
    c_0_54,
    [final] ).

cnf(c_0_70,plain,
    lhs_atom4(X1,X2),
    c_0_55,
    [final] ).

cnf(c_0_71,plain,
    lhs_atom9(X1),
    c_0_56,
    [final] ).

cnf(c_0_72,plain,
    lhs_atom8(X1),
    c_0_57,
    [final] ).

cnf(c_0_73,plain,
    lhs_atom2(X1),
    c_0_58,
    [final] ).

cnf(c_0_74,plain,
    lhs_atom1(X1),
    c_0_59,
    [final] ).

% End CNF derivation
cnf(c_0_60_0,axiom,
    multiply(greatest_lower_bound(X2,X1),X3) = greatest_lower_bound(multiply(X2,X3),multiply(X1,X3)),
    inference(unfold_definition,[status(thm)],[c_0_60,def_lhs_atom15]) ).

cnf(c_0_61_0,axiom,
    multiply(least_upper_bound(X2,X1),X3) = least_upper_bound(multiply(X2,X3),multiply(X1,X3)),
    inference(unfold_definition,[status(thm)],[c_0_61,def_lhs_atom14]) ).

cnf(c_0_62_0,axiom,
    multiply(X3,greatest_lower_bound(X2,X1)) = greatest_lower_bound(multiply(X3,X2),multiply(X3,X1)),
    inference(unfold_definition,[status(thm)],[c_0_62,def_lhs_atom13]) ).

cnf(c_0_63_0,axiom,
    multiply(X3,least_upper_bound(X2,X1)) = least_upper_bound(multiply(X3,X2),multiply(X3,X1)),
    inference(unfold_definition,[status(thm)],[c_0_63,def_lhs_atom12]) ).

cnf(c_0_64_0,axiom,
    least_upper_bound(X3,least_upper_bound(X2,X1)) = least_upper_bound(least_upper_bound(X3,X2),X1),
    inference(unfold_definition,[status(thm)],[c_0_64,def_lhs_atom7]) ).

cnf(c_0_65_0,axiom,
    greatest_lower_bound(X3,greatest_lower_bound(X2,X1)) = greatest_lower_bound(greatest_lower_bound(X3,X2),X1),
    inference(unfold_definition,[status(thm)],[c_0_65,def_lhs_atom6]) ).

cnf(c_0_66_0,axiom,
    multiply(multiply(X3,X2),X1) = multiply(X3,multiply(X2,X1)),
    inference(unfold_definition,[status(thm)],[c_0_66,def_lhs_atom3]) ).

cnf(c_0_67_0,axiom,
    greatest_lower_bound(X2,least_upper_bound(X2,X1)) = X2,
    inference(unfold_definition,[status(thm)],[c_0_67,def_lhs_atom11]) ).

cnf(c_0_68_0,axiom,
    least_upper_bound(X2,greatest_lower_bound(X2,X1)) = X2,
    inference(unfold_definition,[status(thm)],[c_0_68,def_lhs_atom10]) ).

cnf(c_0_69_0,axiom,
    least_upper_bound(X2,X1) = least_upper_bound(X1,X2),
    inference(unfold_definition,[status(thm)],[c_0_69,def_lhs_atom5]) ).

cnf(c_0_70_0,axiom,
    greatest_lower_bound(X2,X1) = greatest_lower_bound(X1,X2),
    inference(unfold_definition,[status(thm)],[c_0_70,def_lhs_atom4]) ).

cnf(c_0_71_0,axiom,
    greatest_lower_bound(X1,X1) = X1,
    inference(unfold_definition,[status(thm)],[c_0_71,def_lhs_atom9]) ).

cnf(c_0_72_0,axiom,
    least_upper_bound(X1,X1) = X1,
    inference(unfold_definition,[status(thm)],[c_0_72,def_lhs_atom8]) ).

cnf(c_0_73_0,axiom,
    multiply(inverse(X1),X1) = identity,
    inference(unfold_definition,[status(thm)],[c_0_73,def_lhs_atom2]) ).

cnf(c_0_74_0,axiom,
    multiply(identity,X1) = X1,
    inference(unfold_definition,[status(thm)],[c_0_74,def_lhs_atom1]) ).

% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,negated_conjecture,
    greatest_lower_bound(a,a) != a,
    file('<stdin>',prove_ax_reflb) ).

fof(c_0_1_002,negated_conjecture,
    greatest_lower_bound(a,a) != a,
    c_0_0 ).

fof(c_0_2_003,negated_conjecture,
    greatest_lower_bound(a,a) != a,
    c_0_1 ).

cnf(c_0_3_004,negated_conjecture,
    greatest_lower_bound(a,a) != a,
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_4_005,negated_conjecture,
    greatest_lower_bound(a,a) != a,
    c_0_3,
    [final] ).

% End CNF derivation

%-------------------------------------------------------------
% Proof by iprover

cnf(c_3,plain,
    greatest_lower_bound(X0,X0) = X0,
    file('/export/starexec/sandbox2/tmp/iprover_modulo_008ba1.p',c_0_71_0) ).

cnf(c_27,plain,
    greatest_lower_bound(a,a) = a,
    inference(instantiation,[status(thm)],[c_3]) ).

cnf(c_15,negated_conjecture,
    greatest_lower_bound(a,a) != a,
    file('/export/starexec/sandbox2/tmp/iprover_modulo_008ba1.p',c_0_4) ).

cnf(contradiction,plain,
    $false,
    inference(minisat,[status(thm)],[c_27,c_15]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.11  % Problem  : GRP161-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.13/0.12  % Command  : iprover_modulo %s %d
% 0.13/0.33  % Computer : n014.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon Jun 13 09:46:52 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.19/0.34  % Running in mono-core mode
% 0.19/0.39  % Orienting using strategy Equiv(ClausalAll)
% 0.19/0.39  % Orientation found
% 0.19/0.39  % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format  " --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_2b3bad.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_008ba1.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_bee815 | grep -v "SZS"
% 0.19/0.41  
% 0.19/0.41  %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.19/0.41  
% 0.19/0.41  % 
% 0.19/0.41  % ------  iProver source info 
% 0.19/0.41  
% 0.19/0.41  % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.19/0.41  % git: non_committed_changes: true
% 0.19/0.41  % git: last_make_outside_of_git: true
% 0.19/0.41  
% 0.19/0.41  % 
% 0.19/0.41  % ------ Input Options
% 0.19/0.41  
% 0.19/0.41  % --out_options                         all
% 0.19/0.41  % --tptp_safe_out                       true
% 0.19/0.41  % --problem_path                        ""
% 0.19/0.41  % --include_path                        ""
% 0.19/0.41  % --clausifier                          .//eprover
% 0.19/0.41  % --clausifier_options                  --tstp-format  
% 0.19/0.41  % --stdin                               false
% 0.19/0.41  % --dbg_backtrace                       false
% 0.19/0.41  % --dbg_dump_prop_clauses               false
% 0.19/0.41  % --dbg_dump_prop_clauses_file          -
% 0.19/0.41  % --dbg_out_stat                        false
% 0.19/0.41  
% 0.19/0.41  % ------ General Options
% 0.19/0.41  
% 0.19/0.41  % --fof                                 false
% 0.19/0.41  % --time_out_real                       150.
% 0.19/0.41  % --time_out_prep_mult                  0.2
% 0.19/0.41  % --time_out_virtual                    -1.
% 0.19/0.41  % --schedule                            none
% 0.19/0.41  % --ground_splitting                    input
% 0.19/0.41  % --splitting_nvd                       16
% 0.19/0.41  % --non_eq_to_eq                        false
% 0.19/0.41  % --prep_gs_sim                         true
% 0.19/0.41  % --prep_unflatten                      false
% 0.19/0.41  % --prep_res_sim                        true
% 0.19/0.41  % --prep_upred                          true
% 0.19/0.41  % --res_sim_input                       true
% 0.19/0.41  % --clause_weak_htbl                    true
% 0.19/0.41  % --gc_record_bc_elim                   false
% 0.19/0.41  % --symbol_type_check                   false
% 0.19/0.41  % --clausify_out                        false
% 0.19/0.41  % --large_theory_mode                   false
% 0.19/0.41  % --prep_sem_filter                     none
% 0.19/0.41  % --prep_sem_filter_out                 false
% 0.19/0.41  % --preprocessed_out                    false
% 0.19/0.41  % --sub_typing                          false
% 0.19/0.41  % --brand_transform                     false
% 0.19/0.41  % --pure_diseq_elim                     true
% 0.19/0.41  % --min_unsat_core                      false
% 0.19/0.41  % --pred_elim                           true
% 0.19/0.41  % --add_important_lit                   false
% 0.19/0.41  % --soft_assumptions                    false
% 0.19/0.41  % --reset_solvers                       false
% 0.19/0.41  % --bc_imp_inh                          []
% 0.19/0.41  % --conj_cone_tolerance                 1.5
% 0.19/0.41  % --prolific_symb_bound                 500
% 0.19/0.41  % --lt_threshold                        2000
% 0.19/0.41  
% 0.19/0.41  % ------ SAT Options
% 0.19/0.41  
% 0.19/0.41  % --sat_mode                            false
% 0.19/0.41  % --sat_fm_restart_options              ""
% 0.19/0.41  % --sat_gr_def                          false
% 0.19/0.41  % --sat_epr_types                       true
% 0.19/0.41  % --sat_non_cyclic_types                false
% 0.19/0.41  % --sat_finite_models                   false
% 0.19/0.41  % --sat_fm_lemmas                       false
% 0.19/0.41  % --sat_fm_prep                         false
% 0.19/0.41  % --sat_fm_uc_incr                      true
% 0.19/0.41  % --sat_out_model                       small
% 0.19/0.41  % --sat_out_clauses                     false
% 0.19/0.41  
% 0.19/0.41  % ------ QBF Options
% 0.19/0.41  
% 0.19/0.41  % --qbf_mode                            false
% 0.19/0.41  % --qbf_elim_univ                       true
% 0.19/0.41  % --qbf_sk_in                           true
% 0.19/0.41  % --qbf_pred_elim                       true
% 0.19/0.41  % --qbf_split                           32
% 0.19/0.41  
% 0.19/0.41  % ------ BMC1 Options
% 0.19/0.41  
% 0.19/0.41  % --bmc1_incremental                    false
% 0.19/0.41  % --bmc1_axioms                         reachable_all
% 0.19/0.41  % --bmc1_min_bound                      0
% 0.19/0.41  % --bmc1_max_bound                      -1
% 0.19/0.41  % --bmc1_max_bound_default              -1
% 0.19/0.41  % --bmc1_symbol_reachability            true
% 0.19/0.41  % --bmc1_property_lemmas                false
% 0.19/0.41  % --bmc1_k_induction                    false
% 0.19/0.41  % --bmc1_non_equiv_states               false
% 0.19/0.41  % --bmc1_deadlock                       false
% 0.19/0.41  % --bmc1_ucm                            false
% 0.19/0.41  % --bmc1_add_unsat_core                 none
% 0.19/0.41  % --bmc1_unsat_core_children            false
% 0.19/0.41  % --bmc1_unsat_core_extrapolate_axioms  false
% 0.19/0.41  % --bmc1_out_stat                       full
% 0.19/0.41  % --bmc1_ground_init                    false
% 0.19/0.41  % --bmc1_pre_inst_next_state            false
% 0.19/0.41  % --bmc1_pre_inst_state                 false
% 0.19/0.41  % --bmc1_pre_inst_reach_state           false
% 0.19/0.41  % --bmc1_out_unsat_core                 false
% 0.19/0.41  % --bmc1_aig_witness_out                false
% 0.19/0.41  % --bmc1_verbose                        false
% 0.19/0.41  % --bmc1_dump_clauses_tptp              false
% 0.19/0.41  % --bmc1_dump_unsat_core_tptp           false
% 0.19/0.41  % --bmc1_dump_file                      -
% 0.19/0.41  % --bmc1_ucm_expand_uc_limit            128
% 0.19/0.41  % --bmc1_ucm_n_expand_iterations        6
% 0.19/0.41  % --bmc1_ucm_extend_mode                1
% 0.19/0.41  % --bmc1_ucm_init_mode                  2
% 0.19/0.41  % --bmc1_ucm_cone_mode                  none
% 0.19/0.41  % --bmc1_ucm_reduced_relation_type      0
% 0.19/0.41  % --bmc1_ucm_relax_model                4
% 0.19/0.41  % --bmc1_ucm_full_tr_after_sat          true
% 0.19/0.41  % --bmc1_ucm_expand_neg_assumptions     false
% 0.19/0.41  % --bmc1_ucm_layered_model              none
% 0.19/0.41  % --bmc1_ucm_max_lemma_size             10
% 0.19/0.41  
% 0.19/0.41  % ------ AIG Options
% 0.19/0.41  
% 0.19/0.41  % --aig_mode                            false
% 0.19/0.41  
% 0.19/0.41  % ------ Instantiation Options
% 0.19/0.41  
% 0.19/0.41  % --instantiation_flag                  true
% 0.19/0.41  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 0.19/0.41  % --inst_solver_per_active              750
% 0.19/0.41  % --inst_solver_calls_frac              0.5
% 0.19/0.41  % --inst_passive_queue_type             priority_queues
% 0.19/0.41  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.19/0.41  % --inst_passive_queues_freq            [25;2]
% 0.19/0.41  % --inst_dismatching                    true
% 0.19/0.41  % --inst_eager_unprocessed_to_passive   true
% 0.19/0.41  % --inst_prop_sim_given                 true
% 0.19/0.41  % --inst_prop_sim_new                   false
% 0.19/0.41  % --inst_orphan_elimination             true
% 0.19/0.41  % --inst_learning_loop_flag             true
% 0.19/0.41  % --inst_learning_start                 3000
% 0.19/0.41  % --inst_learning_factor                2
% 0.19/0.41  % --inst_start_prop_sim_after_learn     3
% 0.19/0.41  % --inst_sel_renew                      solver
% 0.19/0.41  % --inst_lit_activity_flag              true
% 0.19/0.41  % --inst_out_proof                      true
% 0.19/0.41  
% 0.19/0.41  % ------ Resolution Options
% 0.19/0.41  
% 0.19/0.41  % --resolution_flag                     true
% 0.19/0.41  % --res_lit_sel                         kbo_max
% 0.19/0.41  % --res_to_prop_solver                  none
% 0.19/0.41  % --res_prop_simpl_new                  false
% 0.19/0.41  % --res_prop_simpl_given                false
% 0.19/0.41  % --res_passive_queue_type              priority_queues
% 0.19/0.41  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.19/0.41  % --res_passive_queues_freq             [15;5]
% 0.19/0.41  % --res_forward_subs                    full
% 0.19/0.41  % --res_backward_subs                   full
% 0.19/0.41  % --res_forward_subs_resolution         true
% 0.19/0.41  % --res_backward_subs_resolution        true
% 0.19/0.41  % --res_orphan_elimination              false
% 0.19/0.41  % --res_time_limit                      1000.
% 0.19/0.41  % --res_out_proof                       true
% 0.19/0.41  % --proof_out_file                      /export/starexec/sandbox2/tmp/iprover_proof_2b3bad.s
% 0.19/0.41  % --modulo                              true
% 0.19/0.41  
% 0.19/0.41  % ------ Combination Options
% 0.19/0.41  
% 0.19/0.41  % --comb_res_mult                       1000
% 0.19/0.41  % --comb_inst_mult                      300
% 0.19/0.41  % ------ 
% 0.19/0.41  
% 0.19/0.41  % ------ Parsing...% successful
% 0.19/0.41  
% 0.19/0.41  % 
% 0.19/0.41  
% 0.19/0.41  
% 0.19/0.41  % ------                             Statistics
% 0.19/0.41  
% 0.19/0.41  % ------ General
% 0.19/0.41  
% 0.19/0.41  % num_of_input_clauses:                 16
% 0.19/0.41  % num_of_input_neg_conjectures:         1
% 0.19/0.41  % num_of_splits:                        0
% 0.19/0.41  % num_of_split_atoms:                   0
% 0.19/0.41  % num_of_sem_filtered_clauses:          0
% 0.19/0.41  % num_of_subtypes:                      0
% 0.19/0.41  % monotx_restored_types:                0
% 0.19/0.41  % sat_num_of_epr_types:                 0
% 0.19/0.41  % sat_num_of_non_cyclic_types:          0
% 0.19/0.41  % sat_guarded_non_collapsed_types:      0
% 0.19/0.41  % is_epr:                               0
% 0.19/0.41  % is_horn:                              0
% 0.19/0.41  % has_eq:                               0
% 0.19/0.41  % num_pure_diseq_elim:                  0
% 0.19/0.41  % simp_replaced_by:                     0
% 0.19/0.41  % res_preprocessed:                     0
% 0.19/0.41  % prep_upred:                           0
% 0.19/0.41  % prep_unflattend:                      0
% 0.19/0.41  % pred_elim_cands:                      0
% 0.19/0.41  % pred_elim:                            0
% 0.19/0.41  % pred_elim_cl:                         0
% 0.19/0.41  % pred_elim_cycles:                     0
% 0.19/0.41  % forced_gc_time:                       0
% 0.19/0.41  % gc_basic_clause_elim:                 0
% 0.19/0.41  % parsing_time:                         0.001
% 0.19/0.41  % sem_filter_time:                      0.
% 0.19/0.41  % pred_elim_time:                       0.
% 0.19/0.41  % out_proof_time:                       0.
% 0.19/0.41  % monotx_time:                          0.
% 0.19/0.41  % subtype_inf_time:                     0.
% 0.19/0.41  % unif_index_cands_time:                0.
% 0.19/0.41  % unif_index_add_time:                  0.
% 0.19/0.41  % total_time:                           0.018
% 0.19/0.41  % num_of_symbols:                       31
% 0.19/0.41  % num_of_terms:                         120
% 0.19/0.41  
% 0.19/0.41  % ------ Propositional Solver
% 0.19/0.41  
% 0.19/0.41  % prop_solver_calls:                    0
% 0.19/0.41  % prop_fast_solver_calls:               0
% 0.19/0.41  % prop_num_of_clauses:                  24
% 0.19/0.41  % prop_preprocess_simplified:           1
% 0.19/0.41  % prop_fo_subsumed:                     0
% 0.19/0.41  % prop_solver_time:                     0.
% 0.19/0.41  % prop_fast_solver_time:                0.
% 0.19/0.41  % prop_unsat_core_time:                 0.
% 0.19/0.41  
% 0.19/0.41  % ------ QBF 
% 0.19/0.41  
% 0.19/0.41  % qbf_q_res:                            0
% 0.19/0.41  % qbf_num_tautologies:                  0
% 0.19/0.41  % qbf_prep_cycles:                      0
% 0.19/0.41  
% 0.19/0.41  % ------ BMC1
% 0.19/0.41  
% 0.19/0.41  % bmc1_current_bound:                   -1
% 0.19/0.41  % bmc1_last_solved_bound:               -1
% 0.19/0.41  % bmc1_unsat_core_size:                 -1
% 0.19/0.41  % bmc1_unsat_core_parents_size:         -1
% 0.19/0.41  % bmc1_merge_next_fun:                  0
% 0.19/0.41  % bmc1_unsat_core_clauses_time:         0.
% 0.19/0.41  
% 0.19/0.41  % ------ Instantiation
% 0.19/0.41  
% 0.19/0.41  % inst_num_of_clauses:                  undef
% 0.19/0.41  % inst_num_in_passive:                  undef
% 0.19/0.41  % inst_num_in_active:                   0
% 0.19/0.41  % inst_num_in_unprocessed:              0
% 0.19/0.41  % inst_num_of_loops:                    0
% 0.19/0.41  % inst_num_of_learning_restarts:        0
% 0.19/0.41  % inst_num_moves_active_passive:        0
% 0.19/0.41  % inst_lit_activity:                    0
% 0.19/0.41  % inst_lit_activity_moves:              0
% 0.19/0.41  % inst_num_tautologies:                 0
% 0.19/0.41  % inst_num_prop_implied:                0
% 0.19/0.41  % inst_num_existing_simplified:         0
% 0.19/0.41  % inst_num_eq_res_simplified:           0
% 0.19/0.41  % inst_num_child_elim:                  0
% 0.19/0.41  % inst_num_of_dismatching_blockings:    0
% 0.19/0.41  % inst_num_of_non_proper_insts:         0
% 0.19/0.41  % inst_num_of_duplicates:               0
% 0.19/0.41  % inst_inst_num_from_inst_to_res:       0
% 0.19/0.41  % inst_dismatching_checking_time:       0.
% 0.19/0.41  
% 0.19/0.41  % ------ Resolution
% 0.19/0.41  
% 0.19/0.41  % res_num_of_clauses:                   undef
% 0.19/0.41  % res_num_in_passive:                   undef
% 0.19/0.41  % res_num_in_active:                    0
% 0.19/0.41  % res_num_of_loops:                     0
% 0.19/0.41  % res_forward_subset_subsumed:          0
% 0.19/0.41  % res_backward_subset_subsumed:         0
% 0.19/0.41  % res_forward_subsumed:                 0
% 0.19/0.41  % res_backward_subsumed:                0
% 0.19/0.41  % res_forward_subsumption_resolution:   0
% 0.19/0.41  % res_backward_subsumption_resolution:  0
% 0.19/0.41  % res_clause_to_clause_subsumption:     0
% 0.19/0.41  % res_orphan_elimination:               0
% 0.19/0.41  % res_tautology_del:                    0
% 0.19/0.41  % res_num_eq_res_simplified:            0
% 0.19/0.41  % res_num_sel_changes:                  0
% 0.19/0.41  % res_moves_from_active_to_pass:        0
% 0.19/0.41  
% 0.19/0.42  % Status Unsatisfiable
% 0.19/0.42  % SZS status Unsatisfiable
% 0.19/0.42  % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------