TSTP Solution File: PUZ062-2 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : PUZ062-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n019.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 : Tue Apr 30 20:37:02 EDT 2024

% Result   : Unsatisfiable 0.12s 0.35s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   46 (  30 unt;   0 def)
%            Number of atoms       :   67 (  19 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   48 (  27   ~;  21   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            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   :   56 (  56   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [V_A,T_a,V_x] :
      ( ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
      | c_in(V_x,V_A,T_a)
      | c_Finite__Set_Ocard(c_insert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [V_G,T_a,V_F] :
      ( ~ c_in(V_G,c_Finite__Set_OFinites,tc_set(T_a))
      | c_in(c_inter(V_F,V_G,T_a),c_Finite__Set_OFinites,tc_set(T_a)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [V_t] :
      ( ~ c_in(V_t,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat)))
      | c_in(V_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [V_c,V_A,V_B,T_a] :
      ( ~ c_in(V_c,c_inter(V_A,V_B,T_a),T_a)
      | c_in(V_c,V_B,T_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [V_c,V_B,T_a,V_A] :
      ( ~ c_in(V_c,V_B,T_a)
      | ~ c_in(V_c,V_A,T_a)
      | c_in(V_c,c_inter(V_A,V_B,T_a),T_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [V_x,V_A,T_a] : c_in(V_x,c_insert(V_x,V_A,T_a),T_a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [V_c,T_a] : ~ c_in(V_c,c_emptyset,T_a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,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/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,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/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,negated_conjecture,
    c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat)) = c_emptyset,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f11,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/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,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/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,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/sandbox2/benchmark/theBenchmark.p') ).

fof(f14,plain,
    ! [X0,X1,X2] :
      ( ~ c_in(X0,c_Finite__Set_OFinites,tc_set(X1))
      | c_in(X2,X0,X1)
      | c_Finite__Set_Ocard(c_insert(X2,X0,X1),X1) = c_Suc(c_Finite__Set_Ocard(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f15,plain,
    ! [V_G,T_a] :
      ( ~ c_in(V_G,c_Finite__Set_OFinites,tc_set(T_a))
      | ! [V_F] : c_in(c_inter(V_F,V_G,T_a),c_Finite__Set_OFinites,tc_set(T_a)) ),
    inference(miniscoping,[status(esa)],[f2]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( ~ c_in(X0,c_Finite__Set_OFinites,tc_set(X1))
      | c_in(c_inter(X2,X0,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f17,plain,
    ! [X0] :
      ( ~ c_in(X0,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat)))
      | c_in(X0,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) ),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f18,plain,
    ! [V_c,V_B,T_a] :
      ( ! [V_A] : ~ c_in(V_c,c_inter(V_A,V_B,T_a),T_a)
      | c_in(V_c,V_B,T_a) ),
    inference(miniscoping,[status(esa)],[f4]) ).

fof(f19,plain,
    ! [X0,X1,X2,X3] :
      ( ~ c_in(X0,c_inter(X1,X2,X3),X3)
      | c_in(X0,X2,X3) ),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f20,plain,
    ! [X0,X1,X2,X3] :
      ( ~ c_in(X0,X1,X2)
      | ~ c_in(X0,X3,X2)
      | c_in(X0,c_inter(X3,X1,X2),X2) ),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f21,plain,
    ! [X0,X1,X2] : c_in(X0,c_insert(X0,X1,X2),X2),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f22,plain,
    ! [X0,X1] : ~ c_in(X0,c_emptyset,X1),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f23,plain,
    c_in(v_t,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f24,plain,
    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)),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f25,plain,
    c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat)) = c_emptyset,
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f26,plain,
    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)),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f27,plain,
    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)),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f28,plain,
    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)),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f29,plain,
    c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
    inference(paramodulation,[status(thm)],[f27,f21]) ).

fof(f30,plain,
    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(paramodulation,[status(thm)],[f26,f21]) ).

fof(f32,plain,
    ! [X0] :
      ( ~ c_in(X0,v_t,tc_prod(tc_nat,tc_nat))
      | ~ c_in(X0,v_a,tc_prod(tc_nat,tc_nat))
      | c_in(X0,c_emptyset,tc_prod(tc_nat,tc_nat)) ),
    inference(paramodulation,[status(thm)],[f25,f20]) ).

fof(f33,plain,
    ! [X0] :
      ( ~ c_in(X0,v_t,tc_prod(tc_nat,tc_nat))
      | ~ c_in(X0,v_a,tc_prod(tc_nat,tc_nat)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f32,f22]) ).

fof(f34,plain,
    c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)),
    inference(resolution,[status(thm)],[f30,f19]) ).

fof(f35,plain,
    ~ c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)),
    inference(resolution,[status(thm)],[f34,f33]) ).

fof(f36,plain,
    c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))),
    inference(resolution,[status(thm)],[f17,f23]) ).

fof(f37,plain,
    c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)),
    inference(resolution,[status(thm)],[f29,f19]) ).

fof(f39,plain,
    ! [X0] : c_in(c_inter(X0,v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))),
    inference(resolution,[status(thm)],[f16,f36]) ).

fof(f40,plain,
    ~ c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)),
    inference(resolution,[status(thm)],[f37,f33]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( c_in(X0,c_inter(X1,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
      | c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,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(X1,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))) ),
    inference(resolution,[status(thm)],[f39,f14]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,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(X1,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))
      | c_in(X0,v_t,tc_prod(tc_nat,tc_nat)) ),
    inference(resolution,[status(thm)],[f42,f19]) ).

fof(f81,plain,
    ! [X0] : c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(X0,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(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))),
    inference(resolution,[status(thm)],[f63,f40]) ).

fof(f82,plain,
    ! [X0] : c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(X0,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(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))),
    inference(resolution,[status(thm)],[f63,f35]) ).

fof(f85,plain,
    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_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))),
    inference(backward_demodulation,[status(thm)],[f81,f28]) ).

fof(f86,plain,
    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))),
    inference(forward_demodulation,[status(thm)],[f24,f85]) ).

fof(f91,plain,
    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_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))),
    inference(forward_demodulation,[status(thm)],[f82,f86]) ).

fof(f92,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f91]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : PUZ062-2 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34  % Computer : n019.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Mon Apr 29 22:08:44 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  % Drodi V3.6.0
% 0.12/0.35  % Refutation found
% 0.12/0.35  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.35  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.38  % Elapsed time: 0.017722 seconds
% 0.12/0.38  % CPU time: 0.031884 seconds
% 0.12/0.38  % Total memory used: 13.533 MB
% 0.12/0.38  % Net memory used: 13.442 MB
%------------------------------------------------------------------------------