TSTP Solution File: SWC046-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC046-1 : 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 22:01:20 EDT 2022

% Result   : Unsatisfiable 1.82s 2.06s
% Output   : Refutation 1.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   24
% Syntax   : Number of clauses     :   81 (  34 unt;   5 nHn;  81 RR)
%            Number of literals    :  155 (   0 equ;  80 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   13 (  12 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ssList(sk1),
    file('SWC046-1.p',unknown),
    [] ).

cnf(4,axiom,
    ssList(sk4),
    file('SWC046-1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(nil,sk2),
    file('SWC046-1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(sk2,sk4),
    file('SWC046-1.p',unknown),
    [] ).

cnf(7,axiom,
    equal(sk3,sk1),
    file('SWC046-1.p',unknown),
    [] ).

cnf(8,axiom,
    ~ equal(nil,sk1),
    file('SWC046-1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ ssItem(u)
    | ~ memberP(sk3,u)
    | memberP(sk4,u) ),
    file('SWC046-1.p',unknown),
    [] ).

cnf(24,axiom,
    ssItem(skaf83(u)),
    file('SWC046-1.p',unknown),
    [] ).

cnf(25,axiom,
    ssList(skaf82(u)),
    file('SWC046-1.p',unknown),
    [] ).

cnf(76,axiom,
    ( ~ ssItem(u)
    | equalelemsP(cons(u,nil)) ),
    file('SWC046-1.p',unknown),
    [] ).

cnf(77,axiom,
    ( ~ ssItem(u)
    | duplicatefreeP(cons(u,nil)) ),
    file('SWC046-1.p',unknown),
    [] ).

cnf(78,axiom,
    ( ~ ssItem(u)
    | strictorderedP(cons(u,nil)) ),
    file('SWC046-1.p',unknown),
    [] ).

cnf(79,axiom,
    ( ~ ssItem(u)
    | totalorderedP(cons(u,nil)) ),
    file('SWC046-1.p',unknown),
    [] ).

cnf(80,axiom,
    ( ~ ssItem(u)
    | strictorderP(cons(u,nil)) ),
    file('SWC046-1.p',unknown),
    [] ).

cnf(81,axiom,
    ( ~ ssItem(u)
    | totalorderP(cons(u,nil)) ),
    file('SWC046-1.p',unknown),
    [] ).

cnf(82,axiom,
    ( ~ ssItem(u)
    | cyclefreeP(cons(u,nil)) ),
    file('SWC046-1.p',unknown),
    [] ).

cnf(83,axiom,
    ( ~ ssItem(u)
    | ~ memberP(nil,u) ),
    file('SWC046-1.p',unknown),
    [] ).

cnf(84,axiom,
    ( ~ ssList(u)
    | ssItem(v)
    | duplicatefreeP(u) ),
    file('SWC046-1.p',unknown),
    [] ).

cnf(98,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ssList(cons(v,u)) ),
    file('SWC046-1.p',unknown),
    [] ).

cnf(109,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | equal(hd(cons(v,u)),v) ),
    file('SWC046-1.p',unknown),
    [] ).

cnf(113,axiom,
    ( ~ singletonP(u)
    | ~ ssList(u)
    | equal(cons(skaf44(u),nil),u) ),
    file('SWC046-1.p',unknown),
    [] ).

cnf(121,axiom,
    ( ~ ssList(u)
    | equal(cons(skaf83(u),skaf82(u)),u)
    | equal(nil,u) ),
    file('SWC046-1.p',unknown),
    [] ).

cnf(128,axiom,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ equal(cons(u,nil),v)
    | singletonP(v) ),
    file('SWC046-1.p',unknown),
    [] ).

cnf(150,axiom,
    ( ~ ssItem(u)
    | ~ ssItem(v)
    | ~ ssList(w)
    | ~ equal(u,v)
    | memberP(cons(v,w),u) ),
    file('SWC046-1.p',unknown),
    [] ).

cnf(200,plain,
    equal(nil,sk4),
    inference(rew,[status(thm),theory(equality)],[6,5]),
    [iquote('0:Rew:6.0,5.0')] ).

cnf(210,plain,
    ~ equal(sk4,sk1),
    inference(rew,[status(thm),theory(equality)],[200,8]),
    [iquote('0:Rew:200.0,8.0')] ).

cnf(214,plain,
    ( ~ ssItem(u)
    | ~ memberP(sk4,u) ),
    inference(rew,[status(thm),theory(equality)],[200,83]),
    [iquote('0:Rew:200.0,83.1')] ).

cnf(215,plain,
    ( ~ ssItem(u)
    | cyclefreeP(cons(u,sk4)) ),
    inference(rew,[status(thm),theory(equality)],[200,82]),
    [iquote('0:Rew:200.0,82.1')] ).

cnf(216,plain,
    ( ~ ssItem(u)
    | totalorderP(cons(u,sk4)) ),
    inference(rew,[status(thm),theory(equality)],[200,81]),
    [iquote('0:Rew:200.0,81.1')] ).

cnf(217,plain,
    ( ~ ssItem(u)
    | strictorderP(cons(u,sk4)) ),
    inference(rew,[status(thm),theory(equality)],[200,80]),
    [iquote('0:Rew:200.0,80.1')] ).

cnf(218,plain,
    ( ~ ssItem(u)
    | totalorderedP(cons(u,sk4)) ),
    inference(rew,[status(thm),theory(equality)],[200,79]),
    [iquote('0:Rew:200.0,79.1')] ).

cnf(219,plain,
    ( ~ ssItem(u)
    | strictorderedP(cons(u,sk4)) ),
    inference(rew,[status(thm),theory(equality)],[200,78]),
    [iquote('0:Rew:200.0,78.1')] ).

cnf(220,plain,
    ( ~ ssItem(u)
    | duplicatefreeP(cons(u,sk4)) ),
    inference(rew,[status(thm),theory(equality)],[200,77]),
    [iquote('0:Rew:200.0,77.1')] ).

cnf(221,plain,
    ( ~ ssItem(u)
    | equalelemsP(cons(u,sk4)) ),
    inference(rew,[status(thm),theory(equality)],[200,76]),
    [iquote('0:Rew:200.0,76.1')] ).

cnf(234,plain,
    ( ~ ssItem(u)
    | ~ memberP(sk1,u)
    | memberP(sk4,u) ),
    inference(rew,[status(thm),theory(equality)],[7,11]),
    [iquote('0:Rew:7.0,11.1')] ).

cnf(235,plain,
    ( ~ ssItem(u)
    | ~ memberP(sk1,u) ),
    inference(mrr,[status(thm)],[234,214]),
    [iquote('0:MRR:234.2,214.1')] ).

cnf(236,plain,
    ( ~ ssList(u)
    | ~ singletonP(u)
    | equal(cons(skaf44(u),sk4),u) ),
    inference(rew,[status(thm),theory(equality)],[200,113]),
    [iquote('0:Rew:200.0,113.2')] ).

cnf(238,plain,
    ( ~ ssList(u)
    | equal(sk4,u)
    | equal(cons(skaf83(u),skaf82(u)),u) ),
    inference(rew,[status(thm),theory(equality)],[200,121]),
    [iquote('0:Rew:200.0,121.2')] ).

cnf(240,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,sk4),u)
    | singletonP(u) ),
    inference(rew,[status(thm),theory(equality)],[200,128]),
    [iquote('0:Rew:200.0,128.2')] ).

cnf(393,plain,
    ( ~ ssItem(u)
    | equal(hd(cons(u,sk4)),u) ),
    inference(res,[status(thm),theory(equality)],[4,109]),
    [iquote('0:Res:4.0,109.1')] ).

cnf(398,plain,
    ( ~ ssItem(u)
    | ssList(cons(u,sk4)) ),
    inference(res,[status(thm),theory(equality)],[4,98]),
    [iquote('0:Res:4.0,98.1')] ).

cnf(490,plain,
    ( equal(cons(skaf83(sk1),skaf82(sk1)),sk1)
    | equal(sk4,sk1) ),
    inference(res,[status(thm),theory(equality)],[1,238]),
    [iquote('0:Res:1.0,238.0')] ).

cnf(513,plain,
    ( ssItem(u)
    | duplicatefreeP(sk1) ),
    inference(res,[status(thm),theory(equality)],[1,84]),
    [iquote('0:Res:1.0,84.0')] ).

cnf(614,plain,
    equal(cons(skaf83(sk1),skaf82(sk1)),sk1),
    inference(mrr,[status(thm)],[490,210]),
    [iquote('0:MRR:490.1,210.0')] ).

cnf(679,plain,
    ssItem(u),
    inference(spt,[spt(split,[position(s1)])],[84]),
    [iquote('1:Spt:84.1')] ).

cnf(693,plain,
    ~ memberP(sk1,u),
    inference(mrr,[status(thm)],[235,679]),
    [iquote('1:MRR:235.0,679.0')] ).

cnf(699,plain,
    equal(hd(cons(u,sk4)),u),
    inference(mrr,[status(thm)],[393,679]),
    [iquote('1:MRR:393.0,679.0')] ).

cnf(740,plain,
    ( ~ ssList(u)
    | ~ equal(v,w)
    | memberP(cons(w,u),v) ),
    inference(mrr,[status(thm)],[150,679]),
    [iquote('1:MRR:150.1,150.0,679.0')] ).

cnf(1202,plain,
    ( ~ ssList(skaf82(sk1))
    | ~ equal(u,skaf83(sk1))
    | memberP(sk1,u) ),
    inference(spr,[status(thm),theory(equality)],[614,740]),
    [iquote('1:SpR:614.0,740.2')] ).

cnf(1359,plain,
    ( ~ equal(u,skaf83(sk1))
    | memberP(sk1,u) ),
    inference(ssi,[status(thm)],[1202,25,1]),
    [iquote('1:SSi:1202.0,25.0,1.0')] ).

cnf(1360,plain,
    ~ equal(u,skaf83(sk1)),
    inference(mrr,[status(thm)],[1359,693]),
    [iquote('1:MRR:1359.1,693.0')] ).

cnf(1361,plain,
    $false,
    inference(unc,[status(thm)],[1360,699]),
    [iquote('1:UnC:1360.0,699.0')] ).

cnf(1364,plain,
    ( ~ ssList(u)
    | duplicatefreeP(u) ),
    inference(spt,[spt(split,[position(s2)])],[84]),
    [iquote('1:Spt:1361.0,84.0,84.2')] ).

cnf(1372,plain,
    ssItem(u),
    inference(spt,[spt(split,[position(s2s1)])],[513]),
    [iquote('2:Spt:513.0')] ).

cnf(1375,plain,
    ~ memberP(sk1,u),
    inference(mrr,[status(thm)],[235,1372]),
    [iquote('2:MRR:235.0,1372.0')] ).

cnf(1377,plain,
    equalelemsP(cons(u,sk4)),
    inference(mrr,[status(thm)],[221,1372]),
    [iquote('2:MRR:221.0,1372.0')] ).

cnf(1378,plain,
    duplicatefreeP(cons(u,sk4)),
    inference(mrr,[status(thm)],[220,1372]),
    [iquote('2:MRR:220.0,1372.0')] ).

cnf(1379,plain,
    strictorderedP(cons(u,sk4)),
    inference(mrr,[status(thm)],[219,1372]),
    [iquote('2:MRR:219.0,1372.0')] ).

cnf(1380,plain,
    totalorderedP(cons(u,sk4)),
    inference(mrr,[status(thm)],[218,1372]),
    [iquote('2:MRR:218.0,1372.0')] ).

cnf(1381,plain,
    strictorderP(cons(u,sk4)),
    inference(mrr,[status(thm)],[217,1372]),
    [iquote('2:MRR:217.0,1372.0')] ).

cnf(1382,plain,
    totalorderP(cons(u,sk4)),
    inference(mrr,[status(thm)],[216,1372]),
    [iquote('2:MRR:216.0,1372.0')] ).

cnf(1383,plain,
    cyclefreeP(cons(u,sk4)),
    inference(mrr,[status(thm)],[215,1372]),
    [iquote('2:MRR:215.0,1372.0')] ).

cnf(1385,plain,
    ssList(cons(u,sk4)),
    inference(mrr,[status(thm)],[398,1372]),
    [iquote('2:MRR:398.0,1372.0')] ).

cnf(1388,plain,
    equal(hd(cons(u,sk4)),u),
    inference(mrr,[status(thm)],[393,1372]),
    [iquote('2:MRR:393.0,1372.0')] ).

cnf(1434,plain,
    ( ~ ssList(u)
    | ~ equal(v,w)
    | memberP(cons(w,u),v) ),
    inference(mrr,[status(thm)],[150,1372]),
    [iquote('2:MRR:150.1,150.0,1372.0')] ).

cnf(1476,plain,
    ( ~ ssList(u)
    | ~ equal(cons(v,sk4),u)
    | singletonP(u) ),
    inference(mrr,[status(thm)],[240,1372]),
    [iquote('2:MRR:240.1,1372.0')] ).

cnf(1572,plain,
    ( ~ ssList(u)
    | ~ singletonP(u)
    | equal(hd(u),skaf44(u)) ),
    inference(spr,[status(thm),theory(equality)],[236,1388]),
    [iquote('2:SpR:236.2,1388.0')] ).

cnf(1751,plain,
    ( ~ ssList(cons(u,sk4))
    | singletonP(cons(u,sk4)) ),
    inference(eqr,[status(thm),theory(equality)],[1476]),
    [iquote('2:EqR:1476.1')] ).

cnf(1753,plain,
    singletonP(cons(u,sk4)),
    inference(ssi,[status(thm)],[1751,1377,1378,1379,1380,1381,1382,1383,1385]),
    [iquote('2:SSi:1751.0,1377.0,1378.0,1379.0,1380.0,1381.0,1382.0,1383.0,1385.0')] ).

cnf(1792,plain,
    ( ~ ssList(cons(u,sk4))
    | ~ singletonP(cons(u,sk4))
    | equal(skaf44(cons(u,sk4)),u) ),
    inference(spr,[status(thm),theory(equality)],[1572,1388]),
    [iquote('2:SpR:1572.2,1388.0')] ).

cnf(1800,plain,
    equal(skaf44(cons(u,sk4)),u),
    inference(ssi,[status(thm)],[1792,1377,1378,1379,1380,1381,1382,1383,1385,1753]),
    [iquote('2:SSi:1792.1,1792.0,1377.0,1378.0,1379.0,1380.0,1381.0,1382.0,1383.0,1385.0,1753.0,1377.0,1378.0,1379.0,1380.0,1381.0,1382.0,1383.0,1385.0,1753.0')] ).

cnf(1878,plain,
    ( ~ ssList(skaf82(sk1))
    | ~ equal(u,skaf83(sk1))
    | memberP(sk1,u) ),
    inference(spr,[status(thm),theory(equality)],[614,1434]),
    [iquote('2:SpR:614.0,1434.2')] ).

cnf(2006,plain,
    ( ~ equal(u,skaf83(sk1))
    | memberP(sk1,u) ),
    inference(ssi,[status(thm)],[1878,25,1]),
    [iquote('2:SSi:1878.0,25.0,1.0')] ).

cnf(2007,plain,
    ~ equal(u,skaf83(sk1)),
    inference(mrr,[status(thm)],[2006,1375]),
    [iquote('2:MRR:2006.1,1375.0')] ).

cnf(2008,plain,
    $false,
    inference(unc,[status(thm)],[2007,1800]),
    [iquote('2:UnC:2007.0,1800.0')] ).

cnf(2011,plain,
    duplicatefreeP(sk1),
    inference(spt,[spt(split,[position(s2s2)])],[513]),
    [iquote('2:Spt:2008.0,513.1')] ).

cnf(4199,plain,
    ( ~ ssItem(u)
    | ~ ssItem(skaf83(sk1))
    | ~ ssList(skaf82(sk1))
    | ~ equal(u,skaf83(sk1))
    | memberP(sk1,u) ),
    inference(spr,[status(thm),theory(equality)],[614,150]),
    [iquote('0:SpR:614.0,150.4')] ).

cnf(5782,plain,
    ( ~ ssItem(u)
    | ~ equal(u,skaf83(sk1))
    | memberP(sk1,u) ),
    inference(ssi,[status(thm)],[4199,25,1,2011,24]),
    [iquote('2:SSi:4199.2,4199.1,25.0,1.0,2011.0,24.0,1.0,2011.0')] ).

cnf(5783,plain,
    ( ~ ssItem(u)
    | ~ equal(u,skaf83(sk1)) ),
    inference(mrr,[status(thm)],[5782,235]),
    [iquote('2:MRR:5782.2,235.1')] ).

cnf(5981,plain,
    ~ ssItem(skaf83(sk1)),
    inference(eqr,[status(thm),theory(equality)],[5783]),
    [iquote('2:EqR:5783.1')] ).

cnf(6015,plain,
    $false,
    inference(ssi,[status(thm)],[5981,24,1,2011]),
    [iquote('2:SSi:5981.0,24.0,1.0,2011.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWC046-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n008.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 Jun 11 21:52:22 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.82/2.06  
% 1.82/2.06  SPASS V 3.9 
% 1.82/2.06  SPASS beiseite: Proof found.
% 1.82/2.06  % SZS status Theorem
% 1.82/2.06  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 1.82/2.06  SPASS derived 3701 clauses, backtracked 1364 clauses, performed 31 splits and kept 3045 clauses.
% 1.82/2.06  SPASS allocated 80794 KBytes.
% 1.82/2.06  SPASS spent	0:00:01.64 on the problem.
% 1.82/2.06  		0:00:00.04 for the input.
% 1.82/2.06  		0:00:00.00 for the FLOTTER CNF translation.
% 1.82/2.06  		0:00:00.04 for inferences.
% 1.82/2.06  		0:00:00.03 for the backtracking.
% 1.82/2.06  		0:00:01.34 for the reduction.
% 1.82/2.06  
% 1.82/2.06  
% 1.82/2.06  Here is a proof with depth 3, length 81 :
% 1.82/2.06  % SZS output start Refutation
% See solution above
% 1.82/2.06  Formulae used in the proof : co1_1 co1_4 co1_5 co1_6 co1_7 co1_8 co1_11 clause12 clause13 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause71 clause72 clause86 clause97 clause101 clause109 clause116 clause138
% 1.82/2.06  
%------------------------------------------------------------------------------