TSTP Solution File: SWC245+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC245+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n008.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 22:02:46 EDT 2022

% Result   : Theorem 27.30s 27.51s
% Output   : Refutation 27.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   27
% Syntax   : Number of clauses     :   43 (  15 unt;   6 nHn;  43 RR)
%            Number of literals    :   97 (   0 equ;  54 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   13 (  12 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    ssList(skc5),
    file('SWC245+1.p',unknown),
    [] ).

cnf(7,axiom,
    ssList(nil),
    file('SWC245+1.p',unknown),
    [] ).

cnf(8,axiom,
    cyclefreeP(nil),
    file('SWC245+1.p',unknown),
    [] ).

cnf(9,axiom,
    totalorderP(nil),
    file('SWC245+1.p',unknown),
    [] ).

cnf(10,axiom,
    strictorderP(nil),
    file('SWC245+1.p',unknown),
    [] ).

cnf(11,axiom,
    totalorderedP(nil),
    file('SWC245+1.p',unknown),
    [] ).

cnf(12,axiom,
    strictorderedP(nil),
    file('SWC245+1.p',unknown),
    [] ).

cnf(13,axiom,
    duplicatefreeP(nil),
    file('SWC245+1.p',unknown),
    [] ).

cnf(14,axiom,
    equalelemsP(nil),
    file('SWC245+1.p',unknown),
    [] ).

cnf(53,axiom,
    ~ equal(skc5,nil),
    file('SWC245+1.p',unknown),
    [] ).

cnf(61,axiom,
    ssItem(skf44(u,v,w)),
    file('SWC245+1.p',unknown),
    [] ).

cnf(71,axiom,
    ( ~ ssItem(u)
    | ~ memberP(nil,u) ),
    file('SWC245+1.p',unknown),
    [] ).

cnf(72,axiom,
    ( ~ ssItem(u)
    | cyclefreeP(cons(u,nil)) ),
    file('SWC245+1.p',unknown),
    [] ).

cnf(73,axiom,
    ( ~ ssItem(u)
    | totalorderP(cons(u,nil)) ),
    file('SWC245+1.p',unknown),
    [] ).

cnf(74,axiom,
    ( ~ ssItem(u)
    | strictorderP(cons(u,nil)) ),
    file('SWC245+1.p',unknown),
    [] ).

cnf(75,axiom,
    ( ~ ssItem(u)
    | totalorderedP(cons(u,nil)) ),
    file('SWC245+1.p',unknown),
    [] ).

cnf(76,axiom,
    ( ~ ssItem(u)
    | strictorderedP(cons(u,nil)) ),
    file('SWC245+1.p',unknown),
    [] ).

cnf(77,axiom,
    ( ~ ssItem(u)
    | duplicatefreeP(cons(u,nil)) ),
    file('SWC245+1.p',unknown),
    [] ).

cnf(78,axiom,
    ( ~ ssItem(u)
    | equalelemsP(cons(u,nil)) ),
    file('SWC245+1.p',unknown),
    [] ).

cnf(80,axiom,
    ( ~ ssList(u)
    | equal(app(nil,u),u) ),
    file('SWC245+1.p',unknown),
    [] ).

cnf(84,axiom,
    ( ~ ssList(u)
    | ssItem(hd(u))
    | equal(nil,u) ),
    file('SWC245+1.p',unknown),
    [] ).

cnf(85,axiom,
    ( ~ ssList(u)
    | ssList(tl(u))
    | equal(nil,u) ),
    file('SWC245+1.p',unknown),
    [] ).

cnf(89,axiom,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ssList(cons(u,v)) ),
    file('SWC245+1.p',unknown),
    [] ).

cnf(116,axiom,
    ( ~ ssList(u)
    | equal(nil,u)
    | equal(cons(hd(u),tl(u)),u) ),
    file('SWC245+1.p',unknown),
    [] ).

cnf(119,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,nil),u)
    | singletonP(u) ),
    file('SWC245+1.p',unknown),
    [] ).

cnf(165,axiom,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | equal(app(cons(u,v),w),cons(u,app(v,w))) ),
    file('SWC245+1.p',unknown),
    [] ).

cnf(187,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssItem(w)
    | ~ equal(app(app(v,cons(w,nil)),u),skc5)
    | memberP(v,skf44(w,u,v)) ),
    file('SWC245+1.p',unknown),
    [] ).

cnf(254,plain,
    ( equal(skc5,nil)
    | equal(cons(hd(skc5),tl(skc5)),skc5) ),
    inference(res,[status(thm),theory(equality)],[3,116]),
    [iquote('0:Res:3.0,116.0')] ).

cnf(279,plain,
    ( equal(skc5,nil)
    | ssItem(hd(skc5)) ),
    inference(res,[status(thm),theory(equality)],[3,84]),
    [iquote('0:Res:3.0,84.0')] ).

cnf(280,plain,
    ( equal(skc5,nil)
    | ssList(tl(skc5)) ),
    inference(res,[status(thm),theory(equality)],[3,85]),
    [iquote('0:Res:3.0,85.0')] ).

cnf(568,plain,
    ssItem(hd(skc5)),
    inference(mrr,[status(thm)],[279,53]),
    [iquote('0:MRR:279.0,53.0')] ).

cnf(569,plain,
    ssList(tl(skc5)),
    inference(mrr,[status(thm)],[280,53]),
    [iquote('0:MRR:280.0,53.0')] ).

cnf(574,plain,
    equal(cons(hd(skc5),tl(skc5)),skc5),
    inference(mrr,[status(thm)],[254,53]),
    [iquote('0:MRR:254.0,53.0')] ).

cnf(1599,plain,
    ( ~ ssList(cons(u,nil))
    | ~ ssItem(u)
    | singletonP(cons(u,nil)) ),
    inference(eqr,[status(thm),theory(equality)],[119]),
    [iquote('0:EqR:119.2')] ).

cnf(1602,plain,
    ( ~ ssItem(u)
    | singletonP(cons(u,nil)) ),
    inference(ssi,[status(thm)],[1599,89,14,13,10,9,8,12,11,7,78,77,74,73,72,76,75]),
    [iquote('0:SSi:1599.0,89.1,14.1,13.1,10.1,9.1,8.1,12.1,11.0,7.0,78.0,77.0,74.0,73.0,72.0,76.0,75.2')] ).

cnf(7299,plain,
    ( ~ ssList(cons(u,nil))
    | ~ ssList(v)
    | ~ ssList(nil)
    | ~ ssItem(u)
    | ~ equal(app(cons(u,nil),v),skc5)
    | memberP(nil,skf44(u,v,nil)) ),
    inference(spl,[status(thm),theory(equality)],[80,187]),
    [iquote('0:SpL:80.1,187.3')] ).

cnf(7316,plain,
    ( ~ ssList(cons(u,nil))
    | ~ ssList(v)
    | ~ ssList(nil)
    | ~ ssItem(u)
    | ~ equal(cons(u,v),skc5)
    | memberP(nil,skf44(u,v,nil)) ),
    inference(rew,[status(thm),theory(equality)],[80,7299,165]),
    [iquote('0:Rew:80.1,7299.4,165.3,7299.4')] ).

cnf(7317,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,u),skc5)
    | memberP(nil,skf44(v,u,nil)) ),
    inference(ssi,[status(thm)],[7316,14,13,10,9,8,12,11,7,89,78,77,74,73,72,76,75,1602]),
    [iquote('0:SSi:7316.2,7316.0,14.1,13.1,10.1,9.1,8.1,12.1,11.1,7.1,89.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.2,78.0,77.0,74.0,73.0,72.0,76.0,75.0,1602.0')] ).

cnf(23291,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssItem(skf44(v,u,nil))
    | ~ equal(cons(v,u),skc5) ),
    inference(res,[status(thm),theory(equality)],[7317,71]),
    [iquote('0:Res:7317.3,71.1')] ).

cnf(23294,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,u),skc5) ),
    inference(ssi,[status(thm)],[23291,61,14,13,10,9,8,12,11,7]),
    [iquote('0:SSi:23291.2,61.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0')] ).

cnf(28505,plain,
    ( ~ ssList(tl(skc5))
    | ~ ssItem(hd(skc5))
    | ~ equal(skc5,skc5) ),
    inference(spl,[status(thm),theory(equality)],[574,23294]),
    [iquote('0:SpL:574.0,23294.2')] ).

cnf(28528,plain,
    ( ~ ssList(tl(skc5))
    | ~ ssItem(hd(skc5)) ),
    inference(obv,[status(thm),theory(equality)],[28505]),
    [iquote('0:Obv:28505.2')] ).

cnf(28529,plain,
    $false,
    inference(ssi,[status(thm)],[28528,568,569]),
    [iquote('0:SSi:28528.1,28528.0,568.0,569.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWC245+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n008.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 : Sun Jun 12 04:54:52 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 27.30/27.51  
% 27.30/27.51  SPASS V 3.9 
% 27.30/27.51  SPASS beiseite: Proof found.
% 27.30/27.51  % SZS status Theorem
% 27.30/27.51  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 27.30/27.51  SPASS derived 17692 clauses, backtracked 1639 clauses, performed 26 splits and kept 6379 clauses.
% 27.30/27.51  SPASS allocated 124340 KBytes.
% 27.30/27.51  SPASS spent	0:0:23.14 on the problem.
% 27.30/27.51  		0:00:00.04 for the input.
% 27.30/27.51  		0:00:00.07 for the FLOTTER CNF translation.
% 27.30/27.51  		0:00:00.32 for inferences.
% 27.30/27.51  		0:00:00.71 for the backtracking.
% 27.30/27.51  		0:0:21.72 for the reduction.
% 27.30/27.51  
% 27.30/27.51  
% 27.30/27.51  Here is a proof with depth 3, length 43 :
% 27.30/27.51  % SZS output start Refutation
% See solution above
% 27.30/27.51  Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax38 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax75 ax76 ax16 ax78 ax4 ax27
% 27.30/27.51  
%------------------------------------------------------------------------------