TSTP Solution File: SWC206-1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC206-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n011.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 22:02:28 EDT 2022

% Result   : Unsatisfiable 2.06s 2.26s
% Output   : Refutation 2.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   22
% Syntax   : Number of clauses     :   56 (  31 unt;   8 nHn;  56 RR)
%            Number of literals    :  106 (   0 equ;  46 neg)
%            Maximal clause size   :    7 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   13 (  12 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   8 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ssList(sk1),
    file('SWC206-1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(sk4,sk2),
    file('SWC206-1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(sk3,sk1),
    file('SWC206-1.p',unknown),
    [] ).

cnf(7,axiom,
    neq(sk2,nil),
    file('SWC206-1.p',unknown),
    [] ).

cnf(8,axiom,
    ~ neq(sk1,nil),
    file('SWC206-1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ neq(sk4,nil)
    | ssList(sk5) ),
    file('SWC206-1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ neq(sk4,nil)
    | neq(sk5,nil) ),
    file('SWC206-1.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ neq(sk4,nil)
    | segmentP(sk3,sk5) ),
    file('SWC206-1.p',unknown),
    [] ).

cnf(14,axiom,
    equalelemsP(nil),
    file('SWC206-1.p',unknown),
    [] ).

cnf(15,axiom,
    duplicatefreeP(nil),
    file('SWC206-1.p',unknown),
    [] ).

cnf(16,axiom,
    strictorderedP(nil),
    file('SWC206-1.p',unknown),
    [] ).

cnf(17,axiom,
    totalorderedP(nil),
    file('SWC206-1.p',unknown),
    [] ).

cnf(18,axiom,
    strictorderP(nil),
    file('SWC206-1.p',unknown),
    [] ).

cnf(19,axiom,
    totalorderP(nil),
    file('SWC206-1.p',unknown),
    [] ).

cnf(20,axiom,
    cyclefreeP(nil),
    file('SWC206-1.p',unknown),
    [] ).

cnf(21,axiom,
    ssList(nil),
    file('SWC206-1.p',unknown),
    [] ).

cnf(85,axiom,
    ( ~ ssList(u)
    | ssItem(v)
    | duplicatefreeP(u) ),
    file('SWC206-1.p',unknown),
    [] ).

cnf(93,axiom,
    ( ~ ssList(u)
    | ~ segmentP(nil,u)
    | equal(nil,u) ),
    file('SWC206-1.p',unknown),
    [] ).

cnf(113,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | equal(u,v)
    | neq(u,v) ),
    file('SWC206-1.p',unknown),
    [] ).

cnf(115,axiom,
    ( ~ ssItem(u)
    | ~ ssItem(v)
    | equal(u,v)
    | neq(u,v) ),
    file('SWC206-1.p',unknown),
    [] ).

cnf(130,axiom,
    ( ~ ssItem(u)
    | ~ ssItem(v)
    | ~ neq(u,v)
    | ~ equal(u,v) ),
    file('SWC206-1.p',unknown),
    [] ).

cnf(190,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ equal(hd(v),hd(u))
    | ~ equal(tl(v),tl(u))
    | equal(v,u)
    | equal(nil,v)
    | equal(nil,u) ),
    file('SWC206-1.p',unknown),
    [] ).

cnf(201,plain,
    ( ~ neq(sk2,nil)
    | ssList(sk5) ),
    inference(rew,[status(thm),theory(equality)],[5,10]),
    [iquote('0:Rew:5.0,10.0')] ).

cnf(202,plain,
    ssList(sk5),
    inference(mrr,[status(thm)],[201,7]),
    [iquote('0:MRR:201.0,7.0')] ).

cnf(203,plain,
    ( ~ neq(sk2,nil)
    | segmentP(sk1,sk5) ),
    inference(rew,[status(thm),theory(equality)],[6,13,5]),
    [iquote('0:Rew:6.0,13.1,5.0,13.0')] ).

cnf(204,plain,
    segmentP(sk1,sk5),
    inference(mrr,[status(thm)],[203,7]),
    [iquote('0:MRR:203.0,7.0')] ).

cnf(207,plain,
    ( ~ neq(sk2,nil)
    | neq(sk5,nil) ),
    inference(rew,[status(thm),theory(equality)],[5,11]),
    [iquote('0:Rew:5.0,11.0')] ).

cnf(208,plain,
    neq(sk5,nil),
    inference(mrr,[status(thm)],[207,7]),
    [iquote('0:MRR:207.0,7.0')] ).

cnf(481,plain,
    ( ~ ssList(u)
    | ~ equal(hd(u),hd(sk1))
    | ~ equal(tl(u),tl(sk1))
    | equal(u,sk1)
    | equal(nil,u)
    | equal(nil,sk1) ),
    inference(res,[status(thm),theory(equality)],[1,190]),
    [iquote('0:Res:1.0,190.1')] ).

cnf(520,plain,
    ( ~ ssList(u)
    | equal(sk1,u)
    | neq(sk1,u) ),
    inference(res,[status(thm),theory(equality)],[1,113]),
    [iquote('0:Res:1.0,113.1')] ).

cnf(565,plain,
    ssItem(u),
    inference(spt,[spt(split,[position(s1)])],[85]),
    [iquote('1:Spt:85.1')] ).

cnf(595,plain,
    ( equal(u,v)
    | neq(u,v) ),
    inference(mrr,[status(thm)],[115,565]),
    [iquote('1:MRR:115.1,115.0,565.0')] ).

cnf(605,plain,
    ( ~ neq(u,v)
    | ~ equal(u,v) ),
    inference(mrr,[status(thm)],[130,565]),
    [iquote('1:MRR:130.1,130.0,565.0')] ).

cnf(1774,plain,
    equal(nil,sk1),
    inference(res,[status(thm),theory(equality)],[595,8]),
    [iquote('1:Res:595.1,8.0')] ).

cnf(1785,plain,
    neq(sk5,sk1),
    inference(rew,[status(thm),theory(equality)],[1774,208]),
    [iquote('1:Rew:1774.0,208.0')] ).

cnf(1839,plain,
    ( ~ ssList(u)
    | ~ segmentP(nil,u)
    | equal(sk1,u) ),
    inference(rew,[status(thm),theory(equality)],[1774,93]),
    [iquote('1:Rew:1774.0,93.2')] ).

cnf(1911,plain,
    ( ~ ssList(u)
    | ~ segmentP(sk1,u)
    | equal(sk1,u) ),
    inference(rew,[status(thm),theory(equality)],[1774,1839]),
    [iquote('1:Rew:1774.0,1839.1')] ).

cnf(2210,plain,
    ~ equal(sk5,sk1),
    inference(res,[status(thm),theory(equality)],[1785,605]),
    [iquote('1:Res:1785.0,605.0')] ).

cnf(2294,plain,
    ( ~ ssList(sk5)
    | equal(sk5,sk1) ),
    inference(res,[status(thm),theory(equality)],[204,1911]),
    [iquote('1:Res:204.0,1911.1')] ).

cnf(2299,plain,
    equal(sk5,sk1),
    inference(ssi,[status(thm)],[2294,202]),
    [iquote('1:SSi:2294.0,202.0')] ).

cnf(2300,plain,
    $false,
    inference(mrr,[status(thm)],[2299,2210]),
    [iquote('1:MRR:2299.0,2210.0')] ).

cnf(2301,plain,
    ( ~ ssList(u)
    | duplicatefreeP(u) ),
    inference(spt,[spt(split,[position(s2)])],[85]),
    [iquote('1:Spt:2300.0,85.0,85.2')] ).

cnf(4690,plain,
    equal(nil,sk1),
    inference(spt,[spt(split,[position(s2s1)])],[481]),
    [iquote('2:Spt:481.5')] ).

cnf(4703,plain,
    neq(sk5,sk1),
    inference(rew,[status(thm),theory(equality)],[4690,208]),
    [iquote('2:Rew:4690.0,208.0')] ).

cnf(4708,plain,
    ~ neq(sk1,sk1),
    inference(rew,[status(thm),theory(equality)],[4690,8]),
    [iquote('2:Rew:4690.0,8.0')] ).

cnf(4734,plain,
    ( ~ ssList(u)
    | ~ segmentP(nil,u)
    | equal(sk1,u) ),
    inference(rew,[status(thm),theory(equality)],[4690,93]),
    [iquote('2:Rew:4690.0,93.2')] ).

cnf(4858,plain,
    ( ~ ssList(u)
    | ~ segmentP(sk1,u)
    | equal(sk1,u) ),
    inference(rew,[status(thm),theory(equality)],[4690,4734]),
    [iquote('2:Rew:4690.0,4734.1')] ).

cnf(5272,plain,
    ( ~ ssList(sk5)
    | equal(sk5,sk1) ),
    inference(res,[status(thm),theory(equality)],[204,4858]),
    [iquote('2:Res:204.0,4858.1')] ).

cnf(5277,plain,
    equal(sk5,sk1),
    inference(ssi,[status(thm)],[5272,202]),
    [iquote('2:SSi:5272.0,202.0')] ).

cnf(5280,plain,
    neq(sk1,sk1),
    inference(rew,[status(thm),theory(equality)],[5277,4703]),
    [iquote('2:Rew:5277.0,4703.0')] ).

cnf(5282,plain,
    $false,
    inference(mrr,[status(thm)],[5280,4708]),
    [iquote('2:MRR:5280.0,4708.0')] ).

cnf(5283,plain,
    ~ equal(nil,sk1),
    inference(spt,[spt(split,[position(s2sa)])],[5282,4690]),
    [iquote('2:Spt:5282.0,481.5,4690.0')] ).

cnf(5284,plain,
    ( ~ ssList(u)
    | ~ equal(hd(u),hd(sk1))
    | ~ equal(tl(u),tl(sk1))
    | equal(u,sk1)
    | equal(nil,u) ),
    inference(spt,[spt(split,[position(s2s2)])],[481]),
    [iquote('2:Spt:5282.0,481.0,481.1,481.2,481.3,481.4')] ).

cnf(5380,plain,
    ( ~ ssList(nil)
    | equal(nil,sk1) ),
    inference(res,[status(thm),theory(equality)],[520,8]),
    [iquote('0:Res:520.2,8.0')] ).

cnf(5381,plain,
    equal(nil,sk1),
    inference(ssi,[status(thm)],[5380,14,15,16,17,18,19,20,21]),
    [iquote('0:SSi:5380.0,14.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0')] ).

cnf(5382,plain,
    $false,
    inference(mrr,[status(thm)],[5381,5283]),
    [iquote('2:MRR:5381.0,5283.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWC206-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n011.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 18:11:48 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 2.06/2.26  
% 2.06/2.26  SPASS V 3.9 
% 2.06/2.26  SPASS beiseite: Proof found.
% 2.06/2.26  % SZS status Theorem
% 2.06/2.26  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 2.06/2.26  SPASS derived 3702 clauses, backtracked 3273 clauses, performed 83 splits and kept 5381 clauses.
% 2.06/2.26  SPASS allocated 79217 KBytes.
% 2.06/2.26  SPASS spent	0:00:01.84 on the problem.
% 2.06/2.26  		0:00:00.04 for the input.
% 2.06/2.26  		0:00:00.00 for the FLOTTER CNF translation.
% 2.06/2.26  		0:00:00.01 for inferences.
% 2.06/2.26  		0:00:00.02 for the backtracking.
% 2.06/2.26  		0:00:01.56 for the reduction.
% 2.06/2.26  
% 2.06/2.26  
% 2.06/2.26  Here is a proof with depth 2, length 56 :
% 2.06/2.26  % SZS output start Refutation
% See solution above
% 2.06/2.26  Formulae used in the proof : co1_1 co1_5 co1_6 co1_7 co1_8 co1_10 co1_11 co1_13 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause72 clause80 clause100 clause102 clause117 clause177
% 2.06/2.26  
%------------------------------------------------------------------------------