TSTP Solution File: SWC068+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC068+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n009.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 22:01:30 EDT 2022

% Result   : Theorem 25.54s 25.73s
% Output   : Refutation 25.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   21
% Syntax   : Number of clauses     :   57 (  29 unt;   7 nHn;  57 RR)
%            Number of literals    :  135 (   0 equ;  80 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   12 (  11 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ssList(skc5),
    file('SWC068+1.p',unknown),
    [] ).

cnf(2,axiom,
    ssList(skc4),
    file('SWC068+1.p',unknown),
    [] ).

cnf(5,axiom,
    ssList(nil),
    file('SWC068+1.p',unknown),
    [] ).

cnf(6,axiom,
    cyclefreeP(nil),
    file('SWC068+1.p',unknown),
    [] ).

cnf(7,axiom,
    totalorderP(nil),
    file('SWC068+1.p',unknown),
    [] ).

cnf(8,axiom,
    strictorderP(nil),
    file('SWC068+1.p',unknown),
    [] ).

cnf(9,axiom,
    totalorderedP(nil),
    file('SWC068+1.p',unknown),
    [] ).

cnf(10,axiom,
    strictorderedP(nil),
    file('SWC068+1.p',unknown),
    [] ).

cnf(11,axiom,
    duplicatefreeP(nil),
    file('SWC068+1.p',unknown),
    [] ).

cnf(12,axiom,
    equalelemsP(nil),
    file('SWC068+1.p',unknown),
    [] ).

cnf(58,axiom,
    equal(app(skc5,skc5),skc4),
    file('SWC068+1.p',unknown),
    [] ).

cnf(64,axiom,
    ( ~ ssList(u)
    | segmentP(u,u) ),
    file('SWC068+1.p',unknown),
    [] ).

cnf(76,axiom,
    ( ~ equal(skc4,nil)
    | ~ equal(skc5,nil) ),
    file('SWC068+1.p',unknown),
    [] ).

cnf(77,axiom,
    ( ~ ssList(u)
    | equal(app(nil,u),u) ),
    file('SWC068+1.p',unknown),
    [] ).

cnf(78,axiom,
    ( ~ ssList(u)
    | equal(app(u,nil),u) ),
    file('SWC068+1.p',unknown),
    [] ).

cnf(103,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | neq(v,u)
    | equal(v,u) ),
    file('SWC068+1.p',unknown),
    [] ).

cnf(123,axiom,
    ( ~ ssList(u)
    | ~ neq(u,nil)
    | ~ segmentP(skc4,u)
    | ~ segmentP(skc5,u) ),
    file('SWC068+1.p',unknown),
    [] ).

cnf(125,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ equal(app(v,u),nil)
    | equal(nil,u) ),
    file('SWC068+1.p',unknown),
    [] ).

cnf(155,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | equal(app(app(w,v),u),app(w,app(v,u))) ),
    file('SWC068+1.p',unknown),
    [] ).

cnf(176,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ ssList(x)
    | ~ segmentP(u,v)
    | segmentP(app(app(w,u),x),v) ),
    file('SWC068+1.p',unknown),
    [] ).

cnf(183,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ equal(tl(u),tl(v))
    | ~ equal(hd(u),hd(v))
    | equal(u,v)
    | equal(nil,v)
    | equal(nil,u) ),
    file('SWC068+1.p',unknown),
    [] ).

cnf(195,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ ssList(x)
    | ~ segmentP(x,w)
    | segmentP(app(v,app(x,u)),w) ),
    inference(rew,[status(thm),theory(equality)],[155,176]),
    [iquote('0:Rew:155.3,176.5')] ).

cnf(273,plain,
    equal(app(nil,skc4),skc4),
    inference(res,[status(thm),theory(equality)],[2,77]),
    [iquote('0:Res:2.0,77.0')] ).

cnf(281,plain,
    ( ~ ssList(u)
    | ~ equal(tl(skc4),tl(u))
    | ~ equal(hd(skc4),hd(u))
    | equal(nil,u)
    | equal(skc4,u)
    | equal(skc4,nil) ),
    inference(res,[status(thm),theory(equality)],[2,183]),
    [iquote('0:Res:2.0,183.1')] ).

cnf(420,plain,
    ( ~ ssList(u)
    | neq(skc5,u)
    | equal(skc5,u) ),
    inference(res,[status(thm),theory(equality)],[1,103]),
    [iquote('0:Res:1.0,103.0')] ).

cnf(446,plain,
    equal(app(skc5,nil),skc5),
    inference(res,[status(thm),theory(equality)],[1,78]),
    [iquote('0:Res:1.0,78.0')] ).

cnf(451,plain,
    segmentP(skc5,skc5),
    inference(res,[status(thm),theory(equality)],[1,64]),
    [iquote('0:Res:1.0,64.0')] ).

cnf(453,plain,
    ( ~ ssList(u)
    | ~ equal(tl(skc5),tl(u))
    | ~ equal(hd(skc5),hd(u))
    | equal(nil,u)
    | equal(skc5,u)
    | equal(skc5,nil) ),
    inference(res,[status(thm),theory(equality)],[1,183]),
    [iquote('0:Res:1.0,183.1')] ).

cnf(486,plain,
    ( ~ ssList(u)
    | ~ equal(app(u,skc5),nil)
    | equal(skc5,nil) ),
    inference(res,[status(thm),theory(equality)],[1,125]),
    [iquote('0:Res:1.0,125.1')] ).

cnf(551,plain,
    equal(skc4,nil),
    inference(spt,[spt(split,[position(s1)])],[281]),
    [iquote('1:Spt:281.5')] ).

cnf(558,plain,
    ( ~ equal(nil,nil)
    | ~ equal(skc5,nil) ),
    inference(rew,[status(thm),theory(equality)],[551,76]),
    [iquote('1:Rew:551.0,76.0')] ).

cnf(665,plain,
    equal(app(skc5,skc5),nil),
    inference(rew,[status(thm),theory(equality)],[551,58]),
    [iquote('1:Rew:551.0,58.0')] ).

cnf(717,plain,
    ~ equal(skc5,nil),
    inference(obv,[status(thm),theory(equality)],[558]),
    [iquote('1:Obv:558.0')] ).

cnf(725,plain,
    ( ~ ssList(u)
    | ~ equal(app(u,skc5),nil) ),
    inference(mrr,[status(thm)],[486,717]),
    [iquote('1:MRR:486.2,717.0')] ).

cnf(938,plain,
    ( ~ ssList(skc5)
    | ~ equal(nil,nil) ),
    inference(spl,[status(thm),theory(equality)],[665,725]),
    [iquote('1:SpL:665.0,725.1')] ).

cnf(1009,plain,
    ~ ssList(skc5),
    inference(obv,[status(thm),theory(equality)],[938]),
    [iquote('1:Obv:938.1')] ).

cnf(1010,plain,
    $false,
    inference(ssi,[status(thm)],[1009,1]),
    [iquote('1:SSi:1009.0,1.0')] ).

cnf(1018,plain,
    ~ equal(skc4,nil),
    inference(spt,[spt(split,[position(sa)])],[1010,551]),
    [iquote('1:Spt:1010.0,281.5,551.0')] ).

cnf(1019,plain,
    ( ~ ssList(u)
    | ~ equal(tl(skc4),tl(u))
    | ~ equal(hd(skc4),hd(u))
    | equal(nil,u)
    | equal(skc4,u) ),
    inference(spt,[spt(split,[position(s2)])],[281]),
    [iquote('1:Spt:1010.0,281.0,281.1,281.2,281.3,281.4')] ).

cnf(1039,plain,
    equal(skc5,nil),
    inference(spt,[spt(split,[position(s2s1)])],[453]),
    [iquote('2:Spt:453.5')] ).

cnf(1049,plain,
    equal(app(nil,nil),nil),
    inference(rew,[status(thm),theory(equality)],[1039,446]),
    [iquote('2:Rew:1039.0,446.0')] ).

cnf(1188,plain,
    equal(app(nil,nil),skc4),
    inference(rew,[status(thm),theory(equality)],[1039,58]),
    [iquote('2:Rew:1039.0,58.0')] ).

cnf(1195,plain,
    equal(skc4,nil),
    inference(rew,[status(thm),theory(equality)],[1049,1188]),
    [iquote('2:Rew:1049.0,1188.0')] ).

cnf(1196,plain,
    $false,
    inference(mrr,[status(thm)],[1195,1018]),
    [iquote('2:MRR:1195.0,1018.0')] ).

cnf(1298,plain,
    ~ equal(skc5,nil),
    inference(spt,[spt(split,[position(s2sa)])],[1196,1039]),
    [iquote('2:Spt:1196.0,453.5,1039.0')] ).

cnf(1299,plain,
    ( ~ ssList(u)
    | ~ equal(tl(skc5),tl(u))
    | ~ equal(hd(skc5),hd(u))
    | equal(nil,u)
    | equal(skc5,u) ),
    inference(spt,[spt(split,[position(s2s2)])],[453]),
    [iquote('2:Spt:1196.0,453.0,453.1,453.2,453.3,453.4')] ).

cnf(5803,plain,
    ( ~ ssList(skc5)
    | ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(skc5)
    | ~ segmentP(skc5,v)
    | segmentP(app(u,skc4),v) ),
    inference(spr,[status(thm),theory(equality)],[58,195]),
    [iquote('0:SpR:58.0,195.5')] ).

cnf(5835,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(skc5)
    | ~ segmentP(skc5,v)
    | segmentP(app(u,skc4),v) ),
    inference(obv,[status(thm),theory(equality)],[5803]),
    [iquote('0:Obv:5803.0')] ).

cnf(25276,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ segmentP(skc5,v)
    | segmentP(app(u,skc4),v) ),
    inference(ssi,[status(thm)],[5835,1]),
    [iquote('0:SSi:5835.2,1.0')] ).

cnf(26798,plain,
    ( ~ ssList(nil)
    | ~ ssList(u)
    | ~ segmentP(skc5,u)
    | segmentP(skc4,u) ),
    inference(spr,[status(thm),theory(equality)],[273,25276]),
    [iquote('0:SpR:273.0,25276.3')] ).

cnf(26815,plain,
    ( ~ ssList(u)
    | ~ segmentP(skc5,u)
    | segmentP(skc4,u) ),
    inference(ssi,[status(thm)],[26798,12,11,8,7,6,10,9,5]),
    [iquote('0:SSi:26798.0,12.0,11.0,8.0,7.0,6.0,10.0,9.0,5.0')] ).

cnf(26816,plain,
    ( ~ ssList(u)
    | ~ neq(u,nil)
    | ~ segmentP(skc5,u) ),
    inference(mrr,[status(thm)],[123,26815]),
    [iquote('0:MRR:123.2,26815.2')] ).

cnf(26850,plain,
    ( ~ ssList(skc5)
    | ~ neq(skc5,nil) ),
    inference(res,[status(thm),theory(equality)],[451,26816]),
    [iquote('0:Res:451.0,26816.2')] ).

cnf(27590,plain,
    ~ neq(skc5,nil),
    inference(ssi,[status(thm)],[26850,1]),
    [iquote('0:SSi:26850.0,1.0')] ).

cnf(27824,plain,
    ( ~ ssList(nil)
    | equal(skc5,nil) ),
    inference(res,[status(thm),theory(equality)],[420,27590]),
    [iquote('0:Res:420.1,27590.0')] ).

cnf(27827,plain,
    equal(skc5,nil),
    inference(ssi,[status(thm)],[27824,12,11,8,7,6,10,9,5]),
    [iquote('0:SSi:27824.0,12.0,11.0,8.0,7.0,6.0,10.0,9.0,5.0')] ).

cnf(27828,plain,
    $false,
    inference(mrr,[status(thm)],[27827,1298]),
    [iquote('2:MRR:27827.0,1298.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SWC068+1 : TPTP v8.1.0. Released v2.4.0.
% 0.10/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n009.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 : Sun Jun 12 12:51:53 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 25.54/25.73  
% 25.54/25.73  SPASS V 3.9 
% 25.54/25.73  SPASS beiseite: Proof found.
% 25.54/25.73  % SZS status Theorem
% 25.54/25.73  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 25.54/25.73  SPASS derived 16001 clauses, backtracked 7537 clauses, performed 102 splits and kept 10467 clauses.
% 25.54/25.73  SPASS allocated 120016 KBytes.
% 25.54/25.73  SPASS spent	0:0:22.77 on the problem.
% 25.54/25.73  		0:00:00.04 for the input.
% 25.54/25.73  		0:00:00.08 for the FLOTTER CNF translation.
% 25.54/25.73  		0:00:00.30 for inferences.
% 25.54/25.73  		0:00:00.61 for the backtracking.
% 25.54/25.73  		0:0:21.42 for the reduction.
% 25.54/25.73  
% 25.54/25.73  
% 25.54/25.73  Here is a proof with depth 3, length 57 :
% 25.54/25.73  % SZS output start Refutation
% See solution above
% 25.54/25.73  Formulae used in the proof : co1 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax55 ax28 ax84 ax15 ax83 ax82 ax56 ax77
% 25.54/25.73  
%------------------------------------------------------------------------------