TSTP Solution File: SWC090+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC090+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 22:01:38 EDT 2022

% Result   : Theorem 30.86s 31.09s
% Output   : Refutation 30.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   26
% Syntax   : Number of clauses     :   80 (  42 unt;   7 nHn;  80 RR)
%            Number of literals    :  172 (   0 equ;  96 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    :   12 (  12 usr;   9 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ssList(skc9),
    file('SWC090+1.p',unknown),
    [] ).

cnf(2,axiom,
    ssList(skc8),
    file('SWC090+1.p',unknown),
    [] ).

cnf(3,axiom,
    ssList(skc7),
    file('SWC090+1.p',unknown),
    [] ).

cnf(4,axiom,
    ssList(skc6),
    file('SWC090+1.p',unknown),
    [] ).

cnf(7,axiom,
    ssList(nil),
    file('SWC090+1.p',unknown),
    [] ).

cnf(8,axiom,
    cyclefreeP(nil),
    file('SWC090+1.p',unknown),
    [] ).

cnf(9,axiom,
    totalorderP(nil),
    file('SWC090+1.p',unknown),
    [] ).

cnf(10,axiom,
    strictorderP(nil),
    file('SWC090+1.p',unknown),
    [] ).

cnf(11,axiom,
    totalorderedP(nil),
    file('SWC090+1.p',unknown),
    [] ).

cnf(12,axiom,
    strictorderedP(nil),
    file('SWC090+1.p',unknown),
    [] ).

cnf(13,axiom,
    duplicatefreeP(nil),
    file('SWC090+1.p',unknown),
    [] ).

cnf(14,axiom,
    equalelemsP(nil),
    file('SWC090+1.p',unknown),
    [] ).

cnf(15,axiom,
    neq(skc7,nil),
    file('SWC090+1.p',unknown),
    [] ).

cnf(61,axiom,
    equal(app(skc8,skc9),skc7),
    file('SWC090+1.p',unknown),
    [] ).

cnf(62,axiom,
    equal(app(skc9,skc8),skc6),
    file('SWC090+1.p',unknown),
    [] ).

cnf(68,axiom,
    ( ~ ssList(u)
    | segmentP(u,u) ),
    file('SWC090+1.p',unknown),
    [] ).

cnf(69,axiom,
    ( ~ ssList(u)
    | segmentP(u,nil) ),
    file('SWC090+1.p',unknown),
    [] ).

cnf(80,axiom,
    ( ~ ssList(u)
    | equal(app(nil,u),u) ),
    file('SWC090+1.p',unknown),
    [] ).

cnf(81,axiom,
    ( ~ ssList(u)
    | equal(app(u,nil),u) ),
    file('SWC090+1.p',unknown),
    [] ).

cnf(90,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ssList(app(v,u)) ),
    file('SWC090+1.p',unknown),
    [] ).

cnf(106,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | neq(v,u)
    | equal(v,u) ),
    file('SWC090+1.p',unknown),
    [] ).

cnf(126,axiom,
    ( ~ ssList(u)
    | ~ neq(u,nil)
    | ~ segmentP(skc6,u)
    | ~ segmentP(skc7,u) ),
    file('SWC090+1.p',unknown),
    [] ).

cnf(132,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | equal(nil,v)
    | equal(hd(app(v,u)),hd(v)) ),
    file('SWC090+1.p',unknown),
    [] ).

cnf(158,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | equal(app(app(w,v),u),app(w,app(v,u))) ),
    file('SWC090+1.p',unknown),
    [] ).

cnf(184,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ ssList(x)
    | ~ equal(app(app(u,x),v),w)
    | segmentP(w,x) ),
    file('SWC090+1.p',unknown),
    [] ).

cnf(186,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('SWC090+1.p',unknown),
    [] ).

cnf(199,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ ssList(x)
    | ~ equal(app(x,app(u,w)),v)
    | segmentP(v,u) ),
    inference(rew,[status(thm),theory(equality)],[158,184]),
    [iquote('0:Rew:158.3,184.4')] ).

cnf(243,plain,
    ( ~ neq(skc6,nil)
    | ~ segmentP(skc7,skc6)
    | ~ segmentP(skc6,skc6) ),
    inference(res,[status(thm),theory(equality)],[4,126]),
    [iquote('0:Res:4.0,126.0')] ).

cnf(276,plain,
    equal(app(nil,skc6),skc6),
    inference(res,[status(thm),theory(equality)],[4,80]),
    [iquote('0:Res:4.0,80.0')] ).

cnf(277,plain,
    equal(app(skc6,nil),skc6),
    inference(res,[status(thm),theory(equality)],[4,81]),
    [iquote('0:Res:4.0,81.0')] ).

cnf(282,plain,
    segmentP(skc6,skc6),
    inference(res,[status(thm),theory(equality)],[4,68]),
    [iquote('0:Res:4.0,68.0')] ).

cnf(283,plain,
    segmentP(skc6,nil),
    inference(res,[status(thm),theory(equality)],[4,69]),
    [iquote('0:Res:4.0,69.0')] ).

cnf(324,plain,
    ( ~ ssList(u)
    | ssList(app(u,skc6)) ),
    inference(res,[status(thm),theory(equality)],[4,90]),
    [iquote('0:Res:4.0,90.1')] ).

cnf(415,plain,
    ( ~ neq(skc7,nil)
    | ~ segmentP(skc7,skc7)
    | ~ segmentP(skc6,skc7) ),
    inference(res,[status(thm),theory(equality)],[3,126]),
    [iquote('0:Res:3.0,126.0')] ).

cnf(449,plain,
    equal(app(skc7,nil),skc7),
    inference(res,[status(thm),theory(equality)],[3,81]),
    [iquote('0:Res:3.0,81.0')] ).

cnf(454,plain,
    segmentP(skc7,skc7),
    inference(res,[status(thm),theory(equality)],[3,68]),
    [iquote('0:Res:3.0,68.0')] ).

cnf(456,plain,
    ( ~ ssList(u)
    | ~ equal(tl(skc7),tl(u))
    | ~ equal(hd(skc7),hd(u))
    | equal(nil,u)
    | equal(skc7,u)
    | equal(skc7,nil) ),
    inference(res,[status(thm),theory(equality)],[3,186]),
    [iquote('0:Res:3.0,186.1')] ).

cnf(544,plain,
    ( ~ segmentP(skc7,skc6)
    | ~ neq(skc6,nil) ),
    inference(mrr,[status(thm)],[243,282]),
    [iquote('0:MRR:243.2,282.0')] ).

cnf(545,plain,
    ~ segmentP(skc6,skc7),
    inference(mrr,[status(thm)],[415,15,454]),
    [iquote('0:MRR:415.0,415.1,15.0,454.0')] ).

cnf(554,plain,
    equal(skc7,nil),
    inference(spt,[spt(split,[position(s1)])],[456]),
    [iquote('1:Spt:456.5')] ).

cnf(666,plain,
    ~ segmentP(skc6,nil),
    inference(rew,[status(thm),theory(equality)],[554,545]),
    [iquote('1:Rew:554.0,545.0')] ).

cnf(710,plain,
    $false,
    inference(mrr,[status(thm)],[666,283]),
    [iquote('1:MRR:666.0,283.0')] ).

cnf(830,plain,
    ~ equal(skc7,nil),
    inference(spt,[spt(split,[position(sa)])],[710,554]),
    [iquote('1:Spt:710.0,456.5,554.0')] ).

cnf(831,plain,
    ( ~ ssList(u)
    | ~ equal(tl(skc7),tl(u))
    | ~ equal(hd(skc7),hd(u))
    | equal(nil,u)
    | equal(skc7,u) ),
    inference(spt,[spt(split,[position(s2)])],[456]),
    [iquote('1:Spt:710.0,456.0,456.1,456.2,456.3,456.4')] ).

cnf(2796,plain,
    ( ~ ssList(skc8)
    | ~ ssList(skc9)
    | equal(skc9,nil)
    | equal(hd(skc9),hd(skc6)) ),
    inference(spr,[status(thm),theory(equality)],[62,132]),
    [iquote('0:SpR:62.0,132.3')] ).

cnf(2801,plain,
    ( equal(skc9,nil)
    | equal(hd(skc9),hd(skc6)) ),
    inference(ssi,[status(thm)],[2796,1,2]),
    [iquote('0:SSi:2796.1,2796.0,1.0,2.0')] ).

cnf(4802,plain,
    ( ~ ssList(u)
    | ~ ssList(skc9)
    | ~ ssList(skc8)
    | equal(app(skc8,app(skc9,u)),app(skc7,u)) ),
    inference(spr,[status(thm),theory(equality)],[61,158]),
    [iquote('0:SpR:61.0,158.3')] ).

cnf(4816,plain,
    ( ~ ssList(u)
    | equal(app(skc8,app(skc9,u)),app(skc7,u)) ),
    inference(ssi,[status(thm)],[4802,2,1]),
    [iquote('0:SSi:4802.2,4802.1,2.0,1.0')] ).

cnf(5922,plain,
    ( ~ ssList(u)
    | ~ ssList(app(v,app(u,w)))
    | ~ ssList(w)
    | ~ ssList(v)
    | segmentP(app(v,app(u,w)),u) ),
    inference(eqr,[status(thm),theory(equality)],[199]),
    [iquote('0:EqR:199.4')] ).

cnf(5937,plain,
    ( ~ ssList(skc9)
    | ~ ssList(u)
    | ~ ssList(skc8)
    | ~ ssList(v)
    | ~ equal(app(v,skc6),u)
    | segmentP(u,skc9) ),
    inference(spl,[status(thm),theory(equality)],[62,199]),
    [iquote('0:SpL:62.0,199.4')] ).

cnf(5955,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ equal(app(v,skc6),u)
    | segmentP(u,skc9) ),
    inference(ssi,[status(thm)],[5937,2,1]),
    [iquote('0:SSi:5937.2,5937.0,2.0,1.0')] ).

cnf(5959,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | segmentP(app(w,app(u,v)),u) ),
    inference(ssi,[status(thm)],[5922,90]),
    [iquote('0:SSi:5922.1,90.2,90.2')] ).

cnf(8324,plain,
    equal(skc9,nil),
    inference(spt,[spt(split,[position(s2s1)])],[2801]),
    [iquote('2:Spt:2801.0')] ).

cnf(8328,plain,
    equal(app(nil,skc8),skc6),
    inference(rew,[status(thm),theory(equality)],[8324,62]),
    [iquote('2:Rew:8324.0,62.0')] ).

cnf(8329,plain,
    equal(app(skc8,nil),skc7),
    inference(rew,[status(thm),theory(equality)],[8324,61]),
    [iquote('2:Rew:8324.0,61.0')] ).

cnf(8384,plain,
    ( ~ ssList(skc8)
    | equal(skc8,skc6) ),
    inference(spr,[status(thm),theory(equality)],[8328,80]),
    [iquote('2:SpR:8328.0,80.1')] ).

cnf(8407,plain,
    equal(skc8,skc6),
    inference(ssi,[status(thm)],[8384,2]),
    [iquote('2:SSi:8384.0,2.0')] ).

cnf(8428,plain,
    equal(app(skc6,nil),skc7),
    inference(rew,[status(thm),theory(equality)],[8407,8329]),
    [iquote('2:Rew:8407.0,8329.0')] ).

cnf(8434,plain,
    equal(skc7,skc6),
    inference(rew,[status(thm),theory(equality)],[277,8428]),
    [iquote('2:Rew:277.0,8428.0')] ).

cnf(8451,plain,
    neq(skc6,nil),
    inference(rew,[status(thm),theory(equality)],[8434,15]),
    [iquote('2:Rew:8434.0,15.0')] ).

cnf(8473,plain,
    ( ~ segmentP(skc6,skc6)
    | ~ neq(skc6,nil) ),
    inference(rew,[status(thm),theory(equality)],[8434,544]),
    [iquote('2:Rew:8434.0,544.0')] ).

cnf(8661,plain,
    ~ neq(skc6,nil),
    inference(mrr,[status(thm)],[8473,282]),
    [iquote('2:MRR:8473.0,282.0')] ).

cnf(8662,plain,
    $false,
    inference(mrr,[status(thm)],[8661,8451]),
    [iquote('2:MRR:8661.0,8451.0')] ).

cnf(8783,plain,
    ~ equal(skc9,nil),
    inference(spt,[spt(split,[position(s2sa)])],[8662,8324]),
    [iquote('2:Spt:8662.0,2801.0,8324.0')] ).

cnf(8784,plain,
    equal(hd(skc9),hd(skc6)),
    inference(spt,[spt(split,[position(s2s2)])],[2801]),
    [iquote('2:Spt:8662.0,2801.1')] ).

cnf(20924,plain,
    ( ~ ssList(app(u,skc6))
    | ~ ssList(u)
    | segmentP(app(u,skc6),skc9) ),
    inference(eqr,[status(thm),theory(equality)],[5955]),
    [iquote('0:EqR:5955.2')] ).

cnf(20939,plain,
    ( ~ ssList(u)
    | segmentP(app(u,skc6),skc9) ),
    inference(ssi,[status(thm)],[20924,324]),
    [iquote('0:SSi:20924.0,324.1')] ).

cnf(20956,plain,
    ( ~ ssList(nil)
    | segmentP(skc6,skc9) ),
    inference(spr,[status(thm),theory(equality)],[276,20939]),
    [iquote('0:SpR:276.0,20939.1')] ).

cnf(20965,plain,
    segmentP(skc6,skc9),
    inference(ssi,[status(thm)],[20956,14,13,10,9,8,12,11,7]),
    [iquote('0:SSi:20956.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0')] ).

cnf(25186,plain,
    ( ~ ssList(u)
    | ~ ssList(skc9)
    | ~ ssList(u)
    | ~ ssList(skc8)
    | segmentP(app(skc7,u),skc9) ),
    inference(spr,[status(thm),theory(equality)],[4816,5959]),
    [iquote('0:SpR:4816.1,5959.3')] ).

cnf(25223,plain,
    ( ~ ssList(skc9)
    | ~ ssList(u)
    | ~ ssList(skc8)
    | segmentP(app(skc7,u),skc9) ),
    inference(obv,[status(thm),theory(equality)],[25186]),
    [iquote('0:Obv:25186.0')] ).

cnf(28675,plain,
    ( ~ ssList(u)
    | segmentP(app(skc7,u),skc9) ),
    inference(ssi,[status(thm)],[25223,2,1]),
    [iquote('0:SSi:25223.2,25223.0,2.0,1.0')] ).

cnf(31984,plain,
    ( ~ ssList(nil)
    | segmentP(skc7,skc9) ),
    inference(spr,[status(thm),theory(equality)],[449,28675]),
    [iquote('0:SpR:449.0,28675.1')] ).

cnf(31996,plain,
    segmentP(skc7,skc9),
    inference(ssi,[status(thm)],[31984,14,13,10,9,8,12,11,7]),
    [iquote('0:SSi:31984.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0')] ).

cnf(32006,plain,
    ( ~ ssList(skc9)
    | ~ neq(skc9,nil)
    | ~ segmentP(skc6,skc9) ),
    inference(res,[status(thm),theory(equality)],[31996,126]),
    [iquote('0:Res:31996.0,126.3')] ).

cnf(32150,plain,
    ( ~ neq(skc9,nil)
    | ~ segmentP(skc6,skc9) ),
    inference(ssi,[status(thm)],[32006,1]),
    [iquote('0:SSi:32006.0,1.0')] ).

cnf(32151,plain,
    ~ neq(skc9,nil),
    inference(mrr,[status(thm)],[32150,20965]),
    [iquote('0:MRR:32150.1,20965.0')] ).

cnf(32394,plain,
    ( ~ ssList(nil)
    | ~ ssList(skc9)
    | equal(skc9,nil) ),
    inference(res,[status(thm),theory(equality)],[106,32151]),
    [iquote('0:Res:106.2,32151.0')] ).

cnf(32396,plain,
    equal(skc9,nil),
    inference(ssi,[status(thm)],[32394,1,14,13,10,9,8,12,11,7]),
    [iquote('0:SSi:32394.1,32394.0,1.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0')] ).

cnf(32397,plain,
    $false,
    inference(mrr,[status(thm)],[32396,8783]),
    [iquote('2:MRR:32396.0,8783.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SWC090+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n009.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 : Sat Jun 11 22:25:23 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 30.86/31.09  
% 30.86/31.09  SPASS V 3.9 
% 30.86/31.09  SPASS beiseite: Proof found.
% 30.86/31.09  % SZS status Theorem
% 30.86/31.09  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 30.86/31.09  SPASS derived 20149 clauses, backtracked 4856 clauses, performed 46 splits and kept 10853 clauses.
% 30.86/31.09  SPASS allocated 127790 KBytes.
% 30.86/31.09  SPASS spent	0:0:26.68 on the problem.
% 30.86/31.09  		0:00:00.04 for the input.
% 30.86/31.09  		0:00:00.07 for the FLOTTER CNF translation.
% 30.86/31.09  		0:00:00.33 for inferences.
% 30.86/31.09  		0:00:00.98 for the backtracking.
% 30.86/31.09  		0:0:24.91 for the reduction.
% 30.86/31.09  
% 30.86/31.09  
% 30.86/31.09  Here is a proof with depth 5, length 80 :
% 30.86/31.09  % SZS output start Refutation
% See solution above
% 30.86/31.09  Formulae used in the proof : co1 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax55 ax57 ax28 ax84 ax26 ax15 ax85 ax82 ax7 ax77
% 30.86/31.09  
%------------------------------------------------------------------------------