TSTP Solution File: PUZ062-2 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : PUZ062-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %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  : 600s
% DateTime : Mon Jul 18 18:27:26 EDT 2022

% Result   : Unsatisfiable 0.20s 0.42s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   13
% Syntax   : Number of clauses     :   34 (  18 unt;   4 nHn;  34 RR)
%            Number of literals    :   64 (   0 equ;  35 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   24 (  24 usr;  15 con; 0-4 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ c_in(u,c_Finite__Set_OFinites,tc_set(v))
    | equal(c_Finite__Set_Ocard(c_insert(w,u,v),v),c_Suc(c_Finite__Set_Ocard(u,v)))
    | c_in(w,u,v) ),
    file('PUZ062-2.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ c_in(u,c_Finite__Set_OFinites,tc_set(v))
    | c_in(c_inter(w,u,v),c_Finite__Set_OFinites,tc_set(v)) ),
    file('PUZ062-2.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ c_in(u,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat)))
    | c_in(u,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) ),
    file('PUZ062-2.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ c_in(u,c_inter(v,w,x),x)
    | c_in(u,w,x) ),
    file('PUZ062-2.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ c_in(u,v,w)
    | ~ c_in(u,x,w)
    | c_in(u,c_inter(v,x,w),w) ),
    file('PUZ062-2.p',unknown),
    [] ).

cnf(6,axiom,
    c_in(u,c_insert(u,v,w),w),
    file('PUZ062-2.p',unknown),
    [] ).

cnf(7,axiom,
    ~ c_in(u,c_emptyset,v),
    file('PUZ062-2.p',unknown),
    [] ).

cnf(8,axiom,
    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('PUZ062-2.p',unknown),
    [] ).

cnf(9,axiom,
    equal(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)),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))),
    file('PUZ062-2.p',unknown),
    [] ).

cnf(10,axiom,
    equal(c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat)),c_emptyset),
    file('PUZ062-2.p',unknown),
    [] ).

cnf(11,axiom,
    equal(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat))),
    file('PUZ062-2.p',unknown),
    [] ).

cnf(12,axiom,
    equal(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat))),
    file('PUZ062-2.p',unknown),
    [] ).

cnf(13,axiom,
    ~ equal(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)),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))),
    file('PUZ062-2.p',unknown),
    [] ).

cnf(16,plain,
    c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))),
    inference(res,[status(thm),theory(equality)],[8,3]),
    [iquote('0:Res:8.0,3.0')] ).

cnf(21,plain,
    ( ~ c_in(u,v_a,tc_prod(tc_nat,tc_nat))
    | ~ c_in(u,v_t,tc_prod(tc_nat,tc_nat))
    | c_in(u,c_emptyset,tc_prod(tc_nat,tc_nat)) ),
    inference(spr,[status(thm),theory(equality)],[10,5]),
    [iquote('0:SpR:10.0,5.2')] ).

cnf(23,plain,
    ( ~ c_in(u,v_a,tc_prod(tc_nat,tc_nat))
    | ~ c_in(u,v_t,tc_prod(tc_nat,tc_nat)) ),
    inference(mrr,[status(thm)],[21,7]),
    [iquote('0:MRR:21.2,7.0')] ).

cnf(24,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(spr,[status(thm),theory(equality)],[11,6]),
    [iquote('0:SpR:11.0,6.0')] ).

cnf(26,plain,
    c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)),
    inference(res,[status(thm),theory(equality)],[24,4]),
    [iquote('0:Res:24.0,4.0')] ).

cnf(27,plain,
    ~ c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)),
    inference(res,[status(thm),theory(equality)],[26,23]),
    [iquote('0:Res:26.0,23.0')] ).

cnf(28,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(spr,[status(thm),theory(equality)],[12,6]),
    [iquote('0:SpR:12.0,6.0')] ).

cnf(30,plain,
    c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)),
    inference(res,[status(thm),theory(equality)],[28,4]),
    [iquote('0:Res:28.0,4.0')] ).

cnf(31,plain,
    ~ c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)),
    inference(res,[status(thm),theory(equality)],[30,23]),
    [iquote('0:Res:30.0,23.0')] ).

cnf(41,plain,
    ( ~ 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)))
    | ~ equal(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))))
    | 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)) ),
    inference(spl,[status(thm),theory(equality)],[1,13]),
    [iquote('0:SpL:1.1,13.0')] ).

cnf(42,plain,
    ( ~ 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)))
    | ~ equal(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_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)) ),
    inference(rew,[status(thm),theory(equality)],[9,41]),
    [iquote('0:Rew:9.0,41.1')] ).

cnf(43,plain,
    ( ~ 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)))
    | ~ 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)))
    | ~ equal(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))))
    | 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_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)) ),
    inference(spl,[status(thm),theory(equality)],[1,42]),
    [iquote('0:SpL:1.1,42.1')] ).

cnf(44,plain,
    ( ~ 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)))
    | ~ 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_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_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)) ),
    inference(obv,[status(thm),theory(equality)],[43]),
    [iquote('0:Obv:43.2')] ).

cnf(45,plain,
    ( ~ 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)))
    | ~ 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_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_Pair(v_m,v_n,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)) ),
    inference(res,[status(thm),theory(equality)],[44,4]),
    [iquote('0:Res:44.3,4.0')] ).

cnf(46,plain,
    ( ~ 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)))
    | ~ 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_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)) ),
    inference(mrr,[status(thm)],[45,31]),
    [iquote('0:MRR:45.3,31.0')] ).

cnf(47,plain,
    ( ~ 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)))
    | ~ 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_Pair(v_i,v_j,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)) ),
    inference(res,[status(thm),theory(equality)],[46,4]),
    [iquote('0:Res:46.2,4.0')] ).

cnf(48,plain,
    ( ~ 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)))
    | ~ 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(mrr,[status(thm)],[47,27]),
    [iquote('0:MRR:47.2,27.0')] ).

cnf(49,plain,
    ( ~ c_in(v_t,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(res,[status(thm),theory(equality)],[2,48]),
    [iquote('0:Res:2.1,48.1')] ).

cnf(50,plain,
    ~ 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(mrr,[status(thm)],[49,16]),
    [iquote('0:MRR:49.0,16.0')] ).

cnf(51,plain,
    ~ c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))),
    inference(res,[status(thm),theory(equality)],[2,50]),
    [iquote('0:Res:2.1,50.0')] ).

cnf(52,plain,
    $false,
    inference(mrr,[status(thm)],[51,16]),
    [iquote('0:MRR:51.0,16.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : PUZ062-2 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n019.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  : 600
% 0.13/0.34  % DateTime : Sat May 28 22:54:41 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.42  
% 0.20/0.42  SPASS V 3.9 
% 0.20/0.42  SPASS beiseite: Proof found.
% 0.20/0.42  % SZS status Theorem
% 0.20/0.42  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.42  SPASS derived 27 clauses, backtracked 0 clauses, performed 0 splits and kept 30 clauses.
% 0.20/0.42  SPASS allocated 63168 KBytes.
% 0.20/0.42  SPASS spent	0:00:00.07 on the problem.
% 0.20/0.42  		0:00:00.04 for the input.
% 0.20/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.42  		0:00:00.00 for inferences.
% 0.20/0.42  		0:00:00.00 for the backtracking.
% 0.20/0.42  		0:00:00.00 for the reduction.
% 0.20/0.42  
% 0.20/0.42  
% 0.20/0.42  Here is a proof with depth 6, length 34 :
% 0.20/0.42  % SZS output start Refutation
% See solution above
% 0.20/0.42  Formulae used in the proof : cls_Finite__Set_Ocard__insert__disjoint_0 cls_Finite__Set_Ofinite__Int_1 cls_Mutil_Otiling__domino__finite_0 cls_Set_OInt__iff_1 cls_Set_OInt__iff_2 cls_Set_Oinsert__iff_1 cls_Set_Oempty__iff_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4 cls_conjecture_5
% 0.20/0.42  
%------------------------------------------------------------------------------