TSTP Solution File: PUZ062-2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : PUZ062-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n012.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 13:12:27 EDT 2023

% Result   : Unsatisfiable 0.19s 0.57s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   34
% Syntax   : Number of formulae    :   61 (  24 unt;  21 typ;   0 def)
%            Number of atoms       :   64 (  13 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   53 (  29   ~;  24   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  10   >;  12   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :   20 (  20 usr;  11 con; 0-4 aty)
%            Number of variables   :   42 (  10 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    c_Finite__Set_OFinites: $i ).

tff(decl_23,type,
    tc_set: $i > $i ).

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

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

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

tff(decl_27,type,
    c_Suc: $i > $i ).

tff(decl_28,type,
    c_inter: ( $i * $i * $i ) > $i ).

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

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

tff(decl_31,type,
    tc_prod: ( $i * $i ) > $i ).

tff(decl_32,type,
    c_Mutil_Otiling: ( $i * $i ) > $i ).

tff(decl_33,type,
    c_emptyset: $i ).

tff(decl_34,type,
    v_t: $i ).

tff(decl_35,type,
    c_0: $i ).

tff(decl_36,type,
    c_Mutil_Ocoloured: $i > $i ).

tff(decl_37,type,
    v_a: $i ).

tff(decl_38,type,
    v_i: $i ).

tff(decl_39,type,
    v_j: $i ).

tff(decl_40,type,
    c_Pair: ( $i * $i * $i * $i ) > $i ).

tff(decl_41,type,
    v_m: $i ).

tff(decl_42,type,
    v_n: $i ).

cnf(cls_Set_OInt__iff_1,axiom,
    ( c_in(X1,X3,X4)
    | ~ c_in(X1,c_inter(X2,X3,X4),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).

cnf(cls_conjecture_4,negated_conjecture,
    c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

cnf(cls_conjecture_5,negated_conjecture,
    c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).

cnf(cls_Finite__Set_Ocard__insert__disjoint_0,axiom,
    ( c_in(X3,X1,X2)
    | c_Finite__Set_Ocard(c_insert(X3,X1,X2),X2) = c_Suc(c_Finite__Set_Ocard(X1,X2))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__insert__disjoint_0) ).

cnf(cls_conjecture_1,negated_conjecture,
    c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

cnf(cls_Set_OInt__iff_2,axiom,
    ( c_in(X1,c_inter(X4,X2,X3),X3)
    | ~ c_in(X1,X2,X3)
    | ~ c_in(X1,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__iff_2) ).

cnf(cls_conjecture_2,negated_conjecture,
    c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat)) = c_emptyset,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

cnf(cls_Set_Oempty__iff_0,axiom,
    ~ c_in(X1,c_emptyset,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).

cnf(cls_Set_Oinsert__iff_1,axiom,
    c_in(X1,c_insert(X1,X2,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).

cnf(cls_conjecture_3,negated_conjecture,
    c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

cnf(cls_Mutil_Otiling__domino__finite_0,axiom,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
    | ~ c_in(X1,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Mutil_Otiling__domino__finite_0) ).

cnf(cls_conjecture_0,negated_conjecture,
    c_in(v_t,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

cnf(cls_Finite__Set_Ofinite__Int_1,axiom,
    ( c_in(c_inter(X3,X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).

cnf(c_0_13,axiom,
    ( c_in(X1,X3,X4)
    | ~ c_in(X1,c_inter(X2,X3,X4),X4) ),
    cls_Set_OInt__iff_1 ).

cnf(c_0_14,negated_conjecture,
    c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),
    cls_conjecture_4 ).

cnf(c_0_15,negated_conjecture,
    c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
    cls_conjecture_5 ).

cnf(c_0_16,axiom,
    ( c_in(X3,X1,X2)
    | c_Finite__Set_Ocard(c_insert(X3,X1,X2),X2) = c_Suc(c_Finite__Set_Ocard(X1,X2))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
    cls_Finite__Set_Ocard__insert__disjoint_0 ).

cnf(c_0_17,negated_conjecture,
    c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
    cls_conjecture_1 ).

cnf(c_0_18,axiom,
    ( c_in(X1,c_inter(X4,X2,X3),X3)
    | ~ c_in(X1,X2,X3)
    | ~ c_in(X1,X4,X3) ),
    cls_Set_OInt__iff_2 ).

cnf(c_0_19,negated_conjecture,
    c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat)) = c_emptyset,
    cls_conjecture_2 ).

cnf(c_0_20,axiom,
    ~ c_in(X1,c_emptyset,X2),
    cls_Set_Oempty__iff_0 ).

cnf(c_0_21,negated_conjecture,
    ( c_in(X1,v_a,tc_prod(tc_nat,tc_nat))
    | ~ c_in(X1,c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_22,axiom,
    c_in(X1,c_insert(X1,X2,X3),X3),
    cls_Set_Oinsert__iff_1 ).

cnf(c_0_23,negated_conjecture,
    ( c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
    | c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Suc(c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))
    | ~ c_in(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).

cnf(c_0_24,negated_conjecture,
    ( ~ c_in(X1,v_a,tc_prod(tc_nat,tc_nat))
    | ~ c_in(X1,v_t,tc_prod(tc_nat,tc_nat)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).

cnf(c_0_25,negated_conjecture,
    c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_26,negated_conjecture,
    c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),
    cls_conjecture_3 ).

cnf(c_0_27,negated_conjecture,
    ( c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
    | c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
    | ~ c_in(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
    | ~ c_in(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) ),
    inference(spm,[status(thm)],[c_0_23,c_0_16]) ).

cnf(c_0_28,negated_conjecture,
    ~ c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_29,axiom,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
    | ~ c_in(X1,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))) ),
    cls_Mutil_Otiling__domino__finite_0 ).

cnf(c_0_30,negated_conjecture,
    c_in(v_t,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))),
    cls_conjecture_0 ).

cnf(c_0_31,negated_conjecture,
    c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
    inference(spm,[status(thm)],[c_0_22,c_0_26]) ).

cnf(c_0_32,negated_conjecture,
    ( c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
    | ~ c_in(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
    | ~ c_in(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_27]),c_0_28]) ).

cnf(c_0_33,axiom,
    ( c_in(c_inter(X3,X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
    cls_Finite__Set_Ofinite__Int_1 ).

cnf(c_0_34,negated_conjecture,
    c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_35,negated_conjecture,
    c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)),
    inference(spm,[status(thm)],[c_0_13,c_0_31]) ).

cnf(c_0_36,negated_conjecture,
    ( c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
    | ~ c_in(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).

cnf(c_0_37,negated_conjecture,
    ~ c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)),
    inference(spm,[status(thm)],[c_0_24,c_0_35]) ).

cnf(c_0_38,negated_conjecture,
    ~ c_in(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_36]),c_0_37]) ).

cnf(c_0_39,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_33]),c_0_34])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : PUZ062-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n012.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 22:13:40 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.57  % Version  : CSE_E---1.5
% 0.19/0.57  % Problem  : theBenchmark.p
% 0.19/0.57  % Proof found
% 0.19/0.57  % SZS status Theorem for theBenchmark.p
% 0.19/0.57  % SZS output start Proof
% See solution above
% 0.19/0.58  % Total time : 0.007000 s
% 0.19/0.58  % SZS output end Proof
% 0.19/0.58  % Total time : 0.010000 s
%------------------------------------------------------------------------------