TSTP Solution File: SEU353+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU353+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n025.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 : Tue Jul 19 14:36:32 EDT 2022

% Result   : Theorem 0.18s 0.47s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   23
% Syntax   : Number of clauses     :   52 (  30 unt;   3 nHn;  52 RR)
%            Number of literals    :   98 (   0 equ;  51 neg)
%            Maximal clause size   :    6 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   18 (  17 usr;   1 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-4 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    one_sorted_str(skc7),
    file('SEU353+1.p',unknown),
    [] ).

cnf(10,axiom,
    ~ empty_carrier(skc7),
    file('SEU353+1.p',unknown),
    [] ).

cnf(12,axiom,
    relation(identity_relation(u)),
    file('SEU353+1.p',unknown),
    [] ).

cnf(14,axiom,
    reflexive(identity_relation(u)),
    file('SEU353+1.p',unknown),
    [] ).

cnf(15,axiom,
    symmetric(identity_relation(u)),
    file('SEU353+1.p',unknown),
    [] ).

cnf(16,axiom,
    antisymmetric(identity_relation(u)),
    file('SEU353+1.p',unknown),
    [] ).

cnf(17,axiom,
    transitive(identity_relation(u)),
    file('SEU353+1.p',unknown),
    [] ).

cnf(30,axiom,
    element(skc8,the_carrier(skc7)),
    file('SEU353+1.p',unknown),
    [] ).

cnf(37,axiom,
    v1_partfun1(identity_as_relation_of(u),u,u),
    file('SEU353+1.p',unknown),
    [] ).

cnf(47,axiom,
    equal(identity_as_relation_of(u),identity_relation(u)),
    file('SEU353+1.p',unknown),
    [] ).

cnf(48,axiom,
    ( ~ one_sorted_str(u)
    | function(identity_on_carrier(u)) ),
    file('SEU353+1.p',unknown),
    [] ).

cnf(58,axiom,
    ( ~ empty(u)
    | ~ in(v,u) ),
    file('SEU353+1.p',unknown),
    [] ).

cnf(63,axiom,
    ( ~ one_sorted_str(u)
    | equal(identity_as_relation_of(the_carrier(u)),identity_on_carrier(u)) ),
    file('SEU353+1.p',unknown),
    [] ).

cnf(64,axiom,
    ( ~ one_sorted_str(u)
    | ~ empty(the_carrier(u))
    | empty_carrier(u) ),
    file('SEU353+1.p',unknown),
    [] ).

cnf(67,axiom,
    ( ~ relation_of2_as_subset(u,v,w)
    | relation_of2(u,v,w) ),
    file('SEU353+1.p',unknown),
    [] ).

cnf(69,axiom,
    ( ~ element(u,v)
    | empty(v)
    | in(u,v) ),
    file('SEU353+1.p',unknown),
    [] ).

cnf(71,axiom,
    ( ~ one_sorted_str(u)
    | quasi_total(identity_on_carrier(u),the_carrier(u),the_carrier(u)) ),
    file('SEU353+1.p',unknown),
    [] ).

cnf(72,axiom,
    ( ~ one_sorted_str(u)
    | relation_of2_as_subset(identity_on_carrier(u),the_carrier(u),the_carrier(u)) ),
    file('SEU353+1.p',unknown),
    [] ).

cnf(73,axiom,
    ( ~ in(u,v)
    | equal(apply(identity_relation(v),u),u) ),
    file('SEU353+1.p',unknown),
    [] ).

cnf(74,axiom,
    ~ equal(apply_as_element(the_carrier(skc7),the_carrier(skc7),identity_on_carrier(skc7),skc8),skc8),
    file('SEU353+1.p',unknown),
    [] ).

cnf(79,axiom,
    ( ~ function(u)
    | ~ relation_of2(u,v,w)
    | ~ v1_partfun1(u,v,w)
    | quasi_total(u,v,w) ),
    file('SEU353+1.p',unknown),
    [] ).

cnf(85,axiom,
    ( ~ reflexive(u)
    | ~ function(u)
    | ~ quasi_total(u,v,v)
    | ~ relation_of2(u,v,v)
    | ~ v1_partfun1(u,v,v)
    | one_to_one(u) ),
    file('SEU353+1.p',unknown),
    [] ).

cnf(90,axiom,
    ( ~ function(u)
    | ~ element(v,w)
    | ~ quasi_total(u,w,x)
    | ~ relation_of2(u,w,x)
    | empty(w)
    | equal(apply_as_element(w,x,u,v),apply(u,v)) ),
    file('SEU353+1.p',unknown),
    [] ).

cnf(92,plain,
    v1_partfun1(identity_relation(u),u,u),
    inference(rew,[status(thm),theory(equality)],[47,37]),
    [iquote('0:Rew:47.0,37.0')] ).

cnf(93,plain,
    ( ~ one_sorted_str(u)
    | equal(identity_relation(the_carrier(u)),identity_on_carrier(u)) ),
    inference(rew,[status(thm),theory(equality)],[47,63]),
    [iquote('0:Rew:47.0,63.1')] ).

cnf(94,plain,
    ( ~ function(u)
    | ~ reflexive(u)
    | ~ v1_partfun1(u,v,v)
    | ~ relation_of2(u,v,v)
    | one_to_one(u) ),
    inference(mrr,[status(thm)],[85,79]),
    [iquote('0:MRR:85.2,79.3')] ).

cnf(98,plain,
    quasi_total(identity_on_carrier(skc7),the_carrier(skc7),the_carrier(skc7)),
    inference(res,[status(thm),theory(equality)],[1,71]),
    [iquote('0:Res:1.0,71.0')] ).

cnf(99,plain,
    relation_of2_as_subset(identity_on_carrier(skc7),the_carrier(skc7),the_carrier(skc7)),
    inference(res,[status(thm),theory(equality)],[1,72]),
    [iquote('0:Res:1.0,72.0')] ).

cnf(100,plain,
    equal(identity_relation(the_carrier(skc7)),identity_on_carrier(skc7)),
    inference(res,[status(thm),theory(equality)],[1,93]),
    [iquote('0:Res:1.0,93.0')] ).

cnf(101,plain,
    ( ~ empty(the_carrier(skc7))
    | empty_carrier(skc7) ),
    inference(res,[status(thm),theory(equality)],[1,64]),
    [iquote('0:Res:1.0,64.0')] ).

cnf(103,plain,
    function(identity_on_carrier(skc7)),
    inference(res,[status(thm),theory(equality)],[1,48]),
    [iquote('0:Res:1.0,48.0')] ).

cnf(106,plain,
    ( in(skc8,the_carrier(skc7))
    | empty(the_carrier(skc7)) ),
    inference(res,[status(thm),theory(equality)],[30,69]),
    [iquote('0:Res:30.0,69.0')] ).

cnf(111,plain,
    ~ empty(the_carrier(skc7)),
    inference(mrr,[status(thm)],[101,10]),
    [iquote('0:MRR:101.1,10.0')] ).

cnf(113,plain,
    in(skc8,the_carrier(skc7)),
    inference(mrr,[status(thm)],[106,111]),
    [iquote('0:MRR:106.1,111.0')] ).

cnf(116,plain,
    antisymmetric(identity_on_carrier(skc7)),
    inference(spr,[status(thm),theory(equality)],[100,16]),
    [iquote('0:SpR:100.0,16.0')] ).

cnf(117,plain,
    transitive(identity_on_carrier(skc7)),
    inference(spr,[status(thm),theory(equality)],[100,17]),
    [iquote('0:SpR:100.0,17.0')] ).

cnf(118,plain,
    symmetric(identity_on_carrier(skc7)),
    inference(spr,[status(thm),theory(equality)],[100,15]),
    [iquote('0:SpR:100.0,15.0')] ).

cnf(119,plain,
    reflexive(identity_on_carrier(skc7)),
    inference(spr,[status(thm),theory(equality)],[100,14]),
    [iquote('0:SpR:100.0,14.0')] ).

cnf(120,plain,
    relation(identity_on_carrier(skc7)),
    inference(spr,[status(thm),theory(equality)],[100,12]),
    [iquote('0:SpR:100.0,12.0')] ).

cnf(123,plain,
    v1_partfun1(identity_on_carrier(skc7),the_carrier(skc7),the_carrier(skc7)),
    inference(spr,[status(thm),theory(equality)],[100,92]),
    [iquote('0:SpR:100.0,92.0')] ).

cnf(139,plain,
    ~ empty(the_carrier(skc7)),
    inference(res,[status(thm),theory(equality)],[113,58]),
    [iquote('0:Res:113.0,58.1')] ).

cnf(188,plain,
    relation_of2(identity_on_carrier(skc7),the_carrier(skc7),the_carrier(skc7)),
    inference(res,[status(thm),theory(equality)],[99,67]),
    [iquote('0:Res:99.0,67.0')] ).

cnf(206,plain,
    ( ~ in(u,the_carrier(skc7))
    | equal(apply(identity_on_carrier(skc7),u),u) ),
    inference(spr,[status(thm),theory(equality)],[100,73]),
    [iquote('0:SpR:100.0,73.1')] ).

cnf(287,plain,
    ( ~ function(identity_on_carrier(skc7))
    | ~ reflexive(identity_on_carrier(skc7))
    | ~ relation_of2(identity_on_carrier(skc7),the_carrier(skc7),the_carrier(skc7))
    | one_to_one(identity_on_carrier(skc7)) ),
    inference(res,[status(thm),theory(equality)],[123,94]),
    [iquote('0:Res:123.0,94.2')] ).

cnf(293,plain,
    ( ~ relation_of2(identity_on_carrier(skc7),the_carrier(skc7),the_carrier(skc7))
    | one_to_one(identity_on_carrier(skc7)) ),
    inference(ssi,[status(thm)],[287,103,116,117,118,119,120]),
    [iquote('0:SSi:287.1,287.0,103.0,116.0,117.0,118.0,119.0,120.0,103.0,116.0,117.0,118.0,119.0,120.0')] ).

cnf(294,plain,
    one_to_one(identity_on_carrier(skc7)),
    inference(mrr,[status(thm)],[293,188]),
    [iquote('0:MRR:293.0,188.0')] ).

cnf(445,plain,
    ( ~ function(identity_on_carrier(skc7))
    | ~ element(skc8,the_carrier(skc7))
    | ~ quasi_total(identity_on_carrier(skc7),the_carrier(skc7),the_carrier(skc7))
    | ~ relation_of2(identity_on_carrier(skc7),the_carrier(skc7),the_carrier(skc7))
    | ~ equal(apply(identity_on_carrier(skc7),skc8),skc8)
    | empty(the_carrier(skc7)) ),
    inference(spl,[status(thm),theory(equality)],[90,74]),
    [iquote('0:SpL:90.5,74.0')] ).

cnf(446,plain,
    ( ~ element(skc8,the_carrier(skc7))
    | ~ quasi_total(identity_on_carrier(skc7),the_carrier(skc7),the_carrier(skc7))
    | ~ relation_of2(identity_on_carrier(skc7),the_carrier(skc7),the_carrier(skc7))
    | ~ equal(apply(identity_on_carrier(skc7),skc8),skc8)
    | empty(the_carrier(skc7)) ),
    inference(ssi,[status(thm)],[445,103,116,117,118,119,120,294]),
    [iquote('0:SSi:445.0,103.0,116.0,117.0,118.0,119.0,120.0,294.0')] ).

cnf(447,plain,
    ~ equal(apply(identity_on_carrier(skc7),skc8),skc8),
    inference(mrr,[status(thm)],[446,30,98,188,139]),
    [iquote('0:MRR:446.0,446.1,446.2,446.4,30.0,98.0,188.0,139.0')] ).

cnf(448,plain,
    ( ~ in(skc8,the_carrier(skc7))
    | ~ equal(skc8,skc8) ),
    inference(spl,[status(thm),theory(equality)],[206,447]),
    [iquote('0:SpL:206.1,447.0')] ).

cnf(449,plain,
    ~ in(skc8,the_carrier(skc7)),
    inference(obv,[status(thm),theory(equality)],[448]),
    [iquote('0:Obv:448.1')] ).

cnf(450,plain,
    $false,
    inference(mrr,[status(thm)],[449,113]),
    [iquote('0:MRR:449.0,113.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SEU353+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n025.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jun 20 11:56:29 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.47  
% 0.18/0.47  SPASS V 3.9 
% 0.18/0.47  SPASS beiseite: Proof found.
% 0.18/0.47  % SZS status Theorem
% 0.18/0.47  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.18/0.47  SPASS derived 281 clauses, backtracked 0 clauses, performed 0 splits and kept 247 clauses.
% 0.18/0.47  SPASS allocated 98010 KBytes.
% 0.18/0.47  SPASS spent	0:00:00.13 on the problem.
% 0.18/0.47  		0:00:00.04 for the input.
% 0.18/0.47  		0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.47  		0:00:00.01 for inferences.
% 0.18/0.47  		0:00:00.00 for the backtracking.
% 0.18/0.47  		0:00:00.02 for the reduction.
% 0.18/0.47  
% 0.18/0.47  
% 0.18/0.47  Here is a proof with depth 3, length 52 :
% 0.18/0.47  % SZS output start Refutation
% See solution above
% 0.18/0.48  Formulae used in the proof : t91_tmap_1 fc2_partfun1 dt_k6_partfun1 redefinition_k6_partfun1 dt_k7_grcat_1 t7_boole d11_grcat_1 fc1_struct_0 redefinition_m2_relset_1 t2_subset t35_funct_1 cc1_funct_2 cc4_funct_2 redefinition_k8_funct_2
% 0.18/0.48  
%------------------------------------------------------------------------------