TSTP Solution File: SWC244+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC244+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n010.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 24.25s 24.45s
% Output   : Refutation 24.25s
% 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(2,axiom,
    ssList(skc4),
    file('SWC244+1.p',unknown),
    [] ).

cnf(6,axiom,
    ssList(nil),
    file('SWC244+1.p',unknown),
    [] ).

cnf(7,axiom,
    cyclefreeP(nil),
    file('SWC244+1.p',unknown),
    [] ).

cnf(8,axiom,
    totalorderP(nil),
    file('SWC244+1.p',unknown),
    [] ).

cnf(9,axiom,
    strictorderP(nil),
    file('SWC244+1.p',unknown),
    [] ).

cnf(10,axiom,
    totalorderedP(nil),
    file('SWC244+1.p',unknown),
    [] ).

cnf(11,axiom,
    strictorderedP(nil),
    file('SWC244+1.p',unknown),
    [] ).

cnf(12,axiom,
    duplicatefreeP(nil),
    file('SWC244+1.p',unknown),
    [] ).

cnf(13,axiom,
    equalelemsP(nil),
    file('SWC244+1.p',unknown),
    [] ).

cnf(53,axiom,
    ~ equal(skc4,nil),
    file('SWC244+1.p',unknown),
    [] ).

cnf(61,axiom,
    ssItem(skf44(u,v,w)),
    file('SWC244+1.p',unknown),
    [] ).

cnf(70,axiom,
    ( ~ ssItem(u)
    | ~ memberP(nil,u) ),
    file('SWC244+1.p',unknown),
    [] ).

cnf(71,axiom,
    ( ~ ssItem(u)
    | cyclefreeP(cons(u,nil)) ),
    file('SWC244+1.p',unknown),
    [] ).

cnf(72,axiom,
    ( ~ ssItem(u)
    | totalorderP(cons(u,nil)) ),
    file('SWC244+1.p',unknown),
    [] ).

cnf(73,axiom,
    ( ~ ssItem(u)
    | strictorderP(cons(u,nil)) ),
    file('SWC244+1.p',unknown),
    [] ).

cnf(74,axiom,
    ( ~ ssItem(u)
    | totalorderedP(cons(u,nil)) ),
    file('SWC244+1.p',unknown),
    [] ).

cnf(75,axiom,
    ( ~ ssItem(u)
    | strictorderedP(cons(u,nil)) ),
    file('SWC244+1.p',unknown),
    [] ).

cnf(76,axiom,
    ( ~ ssItem(u)
    | duplicatefreeP(cons(u,nil)) ),
    file('SWC244+1.p',unknown),
    [] ).

cnf(77,axiom,
    ( ~ ssItem(u)
    | equalelemsP(cons(u,nil)) ),
    file('SWC244+1.p',unknown),
    [] ).

cnf(79,axiom,
    ( ~ ssList(u)
    | equal(app(nil,u),u) ),
    file('SWC244+1.p',unknown),
    [] ).

cnf(83,axiom,
    ( ~ ssList(u)
    | ssItem(hd(u))
    | equal(nil,u) ),
    file('SWC244+1.p',unknown),
    [] ).

cnf(84,axiom,
    ( ~ ssList(u)
    | ssList(tl(u))
    | equal(nil,u) ),
    file('SWC244+1.p',unknown),
    [] ).

cnf(88,axiom,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ssList(cons(u,v)) ),
    file('SWC244+1.p',unknown),
    [] ).

cnf(115,axiom,
    ( ~ ssList(u)
    | equal(nil,u)
    | equal(cons(hd(u),tl(u)),u) ),
    file('SWC244+1.p',unknown),
    [] ).

cnf(118,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,nil),u)
    | singletonP(u) ),
    file('SWC244+1.p',unknown),
    [] ).

cnf(165,axiom,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | equal(app(cons(u,v),w),cons(u,app(v,w))) ),
    file('SWC244+1.p',unknown),
    [] ).

cnf(187,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssItem(w)
    | ~ equal(app(app(v,cons(w,nil)),u),skc4)
    | memberP(v,skf44(w,u,v)) ),
    file('SWC244+1.p',unknown),
    [] ).

cnf(254,plain,
    ( equal(skc4,nil)
    | equal(cons(hd(skc4),tl(skc4)),skc4) ),
    inference(res,[status(thm),theory(equality)],[2,115]),
    [iquote('0:Res:2.0,115.0')] ).

cnf(279,plain,
    ( equal(skc4,nil)
    | ssItem(hd(skc4)) ),
    inference(res,[status(thm),theory(equality)],[2,83]),
    [iquote('0:Res:2.0,83.0')] ).

cnf(280,plain,
    ( equal(skc4,nil)
    | ssList(tl(skc4)) ),
    inference(res,[status(thm),theory(equality)],[2,84]),
    [iquote('0:Res:2.0,84.0')] ).

cnf(565,plain,
    ssItem(hd(skc4)),
    inference(mrr,[status(thm)],[279,53]),
    [iquote('0:MRR:279.0,53.0')] ).

cnf(566,plain,
    ssList(tl(skc4)),
    inference(mrr,[status(thm)],[280,53]),
    [iquote('0:MRR:280.0,53.0')] ).

cnf(571,plain,
    equal(cons(hd(skc4),tl(skc4)),skc4),
    inference(mrr,[status(thm)],[254,53]),
    [iquote('0:MRR:254.0,53.0')] ).

cnf(1571,plain,
    ( ~ ssList(cons(u,nil))
    | ~ ssItem(u)
    | singletonP(cons(u,nil)) ),
    inference(eqr,[status(thm),theory(equality)],[118]),
    [iquote('0:EqR:118.2')] ).

cnf(1574,plain,
    ( ~ ssItem(u)
    | singletonP(cons(u,nil)) ),
    inference(ssi,[status(thm)],[1571,88,13,12,9,8,7,11,10,6,77,76,73,72,71,75,74]),
    [iquote('0:SSi:1571.0,88.1,13.1,12.1,9.1,8.1,7.1,11.1,10.0,6.0,77.0,76.0,73.0,72.0,71.0,75.0,74.2')] ).

cnf(6437,plain,
    ( ~ ssList(cons(u,nil))
    | ~ ssList(v)
    | ~ ssList(nil)
    | ~ ssItem(u)
    | ~ equal(app(cons(u,nil),v),skc4)
    | memberP(nil,skf44(u,v,nil)) ),
    inference(spl,[status(thm),theory(equality)],[79,187]),
    [iquote('0:SpL:79.1,187.3')] ).

cnf(6451,plain,
    ( ~ ssList(cons(u,nil))
    | ~ ssList(v)
    | ~ ssList(nil)
    | ~ ssItem(u)
    | ~ equal(cons(u,v),skc4)
    | memberP(nil,skf44(u,v,nil)) ),
    inference(rew,[status(thm),theory(equality)],[79,6437,165]),
    [iquote('0:Rew:79.1,6437.4,165.3,6437.4')] ).

cnf(6452,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,u),skc4)
    | memberP(nil,skf44(v,u,nil)) ),
    inference(ssi,[status(thm)],[6451,13,12,9,8,7,11,10,6,88,77,76,73,72,71,75,74,1574]),
    [iquote('0:SSi:6451.2,6451.0,13.1,12.1,9.1,8.1,7.1,11.1,10.1,6.1,88.0,13.0,12.0,9.0,8.0,7.0,11.0,10.0,6.2,77.0,76.0,73.0,72.0,71.0,75.0,74.0,1574.0')] ).

cnf(21498,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssItem(skf44(v,u,nil))
    | ~ equal(cons(v,u),skc4) ),
    inference(res,[status(thm),theory(equality)],[6452,70]),
    [iquote('0:Res:6452.3,70.1')] ).

cnf(21501,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,u),skc4) ),
    inference(ssi,[status(thm)],[21498,61,13,12,9,8,7,11,10,6]),
    [iquote('0:SSi:21498.2,61.0,13.0,12.0,9.0,8.0,7.0,11.0,10.0,6.0')] ).

cnf(26362,plain,
    ( ~ ssList(tl(skc4))
    | ~ ssItem(hd(skc4))
    | ~ equal(skc4,skc4) ),
    inference(spl,[status(thm),theory(equality)],[571,21501]),
    [iquote('0:SpL:571.0,21501.2')] ).

cnf(26385,plain,
    ( ~ ssList(tl(skc4))
    | ~ ssItem(hd(skc4)) ),
    inference(obv,[status(thm),theory(equality)],[26362]),
    [iquote('0:Obv:26362.2')] ).

cnf(26386,plain,
    $false,
    inference(ssi,[status(thm)],[26385,565,566]),
    [iquote('0:SSi:26385.1,26385.0,565.0,566.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SWC244+1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n010.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  : 600
% 0.12/0.34  % DateTime : Sun Jun 12 18:36:55 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 24.25/24.45  
% 24.25/24.45  SPASS V 3.9 
% 24.25/24.45  SPASS beiseite: Proof found.
% 24.25/24.45  % SZS status Theorem
% 24.25/24.45  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 24.25/24.45  SPASS derived 16320 clauses, backtracked 1648 clauses, performed 20 splits and kept 6014 clauses.
% 24.25/24.45  SPASS allocated 122364 KBytes.
% 24.25/24.45  SPASS spent	0:0:20.56 on the problem.
% 24.25/24.45  		0:00:00.04 for the input.
% 24.25/24.45  		0:00:00.07 for the FLOTTER CNF translation.
% 24.25/24.45  		0:00:00.27 for inferences.
% 24.25/24.45  		0:00:00.58 for the backtracking.
% 24.25/24.45  		0:0:19.27 for the reduction.
% 24.25/24.45  
% 24.25/24.45  
% 24.25/24.45  Here is a proof with depth 3, length 43 :
% 24.25/24.45  % SZS output start Refutation
% See solution above
% 24.25/24.45  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
% 24.25/24.45  
%------------------------------------------------------------------------------