TSTP Solution File: SET601+3 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET601+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 14:34:44 EDT 2023

% Result   : Theorem 0.21s 0.76s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   45 (  36 unt;   9 typ;   0 def)
%            Number of atoms       :   36 (  35 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    5 (   5   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (   6   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   76 (   4 sgn;  38   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    union: ( $i * $i ) > $i ).

tff(decl_23,type,
    intersection: ( $i * $i ) > $i ).

tff(decl_24,type,
    member: ( $i * $i ) > $o ).

tff(decl_25,type,
    subset: ( $i * $i ) > $o ).

tff(decl_26,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_27,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_28,type,
    esk3_0: $i ).

tff(decl_29,type,
    esk4_0: $i ).

tff(decl_30,type,
    esk5_0: $i ).

fof(union_distributes_over_intersection,axiom,
    ! [X1,X2,X3] : union(X1,intersection(X2,X3)) = intersection(union(X1,X2),union(X1,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_distributes_over_intersection) ).

fof(union_intersection,axiom,
    ! [X1,X2] : union(X1,intersection(X1,X2)) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_intersection) ).

fof(associativity_of_intersection,axiom,
    ! [X1,X2,X3] : intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_intersection) ).

fof(commutativity_of_union,axiom,
    ! [X1,X2] : union(X1,X2) = union(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).

fof(prove_th72,conjecture,
    ! [X1,X2,X3] : union(union(intersection(X1,X2),intersection(X2,X3)),intersection(X3,X1)) = intersection(intersection(union(X1,X2),union(X2,X3)),union(X3,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th72) ).

fof(commutativity_of_intersection,axiom,
    ! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).

fof(associativity_of_union,axiom,
    ! [X1,X2,X3] : union(union(X1,X2),X3) = union(X1,union(X2,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_union) ).

fof(idempotency_of_intersection,axiom,
    ! [X1] : intersection(X1,X1) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotency_of_intersection) ).

fof(c_0_8,plain,
    ! [X13,X14,X15] : union(X13,intersection(X14,X15)) = intersection(union(X13,X14),union(X13,X15)),
    inference(variable_rename,[status(thm)],[union_distributes_over_intersection]) ).

fof(c_0_9,plain,
    ! [X11,X12] : union(X11,intersection(X11,X12)) = X11,
    inference(variable_rename,[status(thm)],[union_intersection]) ).

fof(c_0_10,plain,
    ! [X8,X9,X10] : intersection(intersection(X8,X9),X10) = intersection(X8,intersection(X9,X10)),
    inference(variable_rename,[status(thm)],[associativity_of_intersection]) ).

cnf(c_0_11,plain,
    union(X1,intersection(X2,X3)) = intersection(union(X1,X2),union(X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,plain,
    union(X1,intersection(X1,X2)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,plain,
    intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_14,plain,
    ! [X24,X25] : union(X24,X25) = union(X25,X24),
    inference(variable_rename,[status(thm)],[commutativity_of_union]) ).

fof(c_0_15,negated_conjecture,
    ~ ! [X1,X2,X3] : union(union(intersection(X1,X2),intersection(X2,X3)),intersection(X3,X1)) = intersection(intersection(union(X1,X2),union(X2,X3)),union(X3,X1)),
    inference(assume_negation,[status(cth)],[prove_th72]) ).

cnf(c_0_16,plain,
    intersection(X1,union(X1,X2)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_12]) ).

cnf(c_0_17,plain,
    union(X1,X2) = union(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_18,negated_conjecture,
    union(union(intersection(esk3_0,esk4_0),intersection(esk4_0,esk5_0)),intersection(esk5_0,esk3_0)) != intersection(intersection(union(esk3_0,esk4_0),union(esk4_0,esk5_0)),union(esk5_0,esk3_0)),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).

fof(c_0_19,plain,
    ! [X26,X27] : intersection(X26,X27) = intersection(X27,X26),
    inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).

fof(c_0_20,plain,
    ! [X4,X5,X6] : union(union(X4,X5),X6) = union(X4,union(X5,X6)),
    inference(variable_rename,[status(thm)],[associativity_of_union]) ).

cnf(c_0_21,plain,
    intersection(X1,union(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_22,negated_conjecture,
    union(union(intersection(esk3_0,esk4_0),intersection(esk4_0,esk5_0)),intersection(esk5_0,esk3_0)) != intersection(intersection(union(esk3_0,esk4_0),union(esk4_0,esk5_0)),union(esk5_0,esk3_0)),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_23,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_24,plain,
    union(union(X1,X2),X3) = union(X1,union(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_25,plain,
    intersection(union(X1,X2),union(X3,X1)) = union(X1,intersection(X2,X3)),
    inference(spm,[status(thm)],[c_0_11,c_0_17]) ).

cnf(c_0_26,plain,
    intersection(X1,intersection(union(X2,X1),X3)) = intersection(X1,X3),
    inference(spm,[status(thm)],[c_0_13,c_0_21]) ).

cnf(c_0_27,negated_conjecture,
    intersection(union(esk3_0,esk4_0),intersection(union(esk3_0,esk5_0),union(esk4_0,esk5_0))) != union(intersection(esk3_0,esk4_0),union(intersection(esk3_0,esk5_0),intersection(esk4_0,esk5_0))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_17]),c_0_13]),c_0_23]),c_0_23]),c_0_24]),c_0_17]) ).

cnf(c_0_28,plain,
    intersection(union(X1,X2),union(X3,X2)) = union(X2,intersection(X1,X3)),
    inference(spm,[status(thm)],[c_0_25,c_0_17]) ).

cnf(c_0_29,plain,
    intersection(X1,union(X2,intersection(X1,X3))) = intersection(X1,union(X2,X3)),
    inference(spm,[status(thm)],[c_0_26,c_0_11]) ).

fof(c_0_30,plain,
    ! [X7] : intersection(X7,X7) = X7,
    inference(variable_rename,[status(thm)],[idempotency_of_intersection]) ).

cnf(c_0_31,negated_conjecture,
    intersection(union(esk3_0,esk4_0),union(esk5_0,intersection(esk3_0,esk4_0))) != union(intersection(esk3_0,esk4_0),union(intersection(esk3_0,esk5_0),intersection(esk4_0,esk5_0))),
    inference(rw,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_32,plain,
    intersection(X1,union(X2,X3)) = union(intersection(X1,X3),intersection(X1,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_12]),c_0_29]) ).

cnf(c_0_33,plain,
    intersection(X1,intersection(X2,X3)) = intersection(X3,intersection(X1,X2)),
    inference(spm,[status(thm)],[c_0_23,c_0_13]) ).

cnf(c_0_34,plain,
    intersection(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_35,negated_conjecture,
    $false,
    inference(cn,[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)],[c_0_31,c_0_32]),c_0_33]),c_0_23]),c_0_32]),c_0_34]),c_0_17]),c_0_12]),c_0_23]),c_0_23]),c_0_32]),c_0_23]),c_0_23]),c_0_17])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET601+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n013.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sat Aug 26 14:06:47 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.21/0.58  start to proof: theBenchmark
% 0.21/0.76  % Version  : CSE_E---1.5
% 0.21/0.76  % Problem  : theBenchmark.p
% 0.21/0.76  % Proof found
% 0.21/0.76  % SZS status Theorem for theBenchmark.p
% 0.21/0.76  % SZS output start Proof
% See solution above
% 0.21/0.76  % Total time : 0.171000 s
% 0.21/0.76  % SZS output end Proof
% 0.21/0.76  % Total time : 0.174000 s
%------------------------------------------------------------------------------