TSTP Solution File: SWC117+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC117+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 22:01:50 EDT 2022

% Result   : Theorem 101.94s 102.11s
% Output   : Refutation 101.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   38
% Syntax   : Number of clauses     :   87 (  25 unt;  10 nHn;  87 RR)
%            Number of literals    :  218 (   0 equ; 137 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   15 (  14 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ssList(skc5),
    file('SWC117+1.p',unknown),
    [] ).

cnf(2,axiom,
    ssList(skc4),
    file('SWC117+1.p',unknown),
    [] ).

cnf(3,axiom,
    equalelemsP(skc4),
    file('SWC117+1.p',unknown),
    [] ).

cnf(6,axiom,
    ssList(nil),
    file('SWC117+1.p',unknown),
    [] ).

cnf(7,axiom,
    cyclefreeP(nil),
    file('SWC117+1.p',unknown),
    [] ).

cnf(8,axiom,
    totalorderP(nil),
    file('SWC117+1.p',unknown),
    [] ).

cnf(9,axiom,
    strictorderP(nil),
    file('SWC117+1.p',unknown),
    [] ).

cnf(10,axiom,
    totalorderedP(nil),
    file('SWC117+1.p',unknown),
    [] ).

cnf(11,axiom,
    strictorderedP(nil),
    file('SWC117+1.p',unknown),
    [] ).

cnf(12,axiom,
    duplicatefreeP(nil),
    file('SWC117+1.p',unknown),
    [] ).

cnf(13,axiom,
    equalelemsP(nil),
    file('SWC117+1.p',unknown),
    [] ).

cnf(14,axiom,
    segmentP(skc5,skc4),
    file('SWC117+1.p',unknown),
    [] ).

cnf(56,axiom,
    ssList(skf46(u,v)),
    file('SWC117+1.p',unknown),
    [] ).

cnf(66,axiom,
    ( ~ ssList(u)
    | segmentP(u,nil) ),
    file('SWC117+1.p',unknown),
    [] ).

cnf(69,axiom,
    ( ~ ssItem(u)
    | cyclefreeP(cons(u,nil)) ),
    file('SWC117+1.p',unknown),
    [] ).

cnf(70,axiom,
    ( ~ ssItem(u)
    | totalorderP(cons(u,nil)) ),
    file('SWC117+1.p',unknown),
    [] ).

cnf(71,axiom,
    ( ~ ssItem(u)
    | strictorderP(cons(u,nil)) ),
    file('SWC117+1.p',unknown),
    [] ).

cnf(72,axiom,
    ( ~ ssItem(u)
    | totalorderedP(cons(u,nil)) ),
    file('SWC117+1.p',unknown),
    [] ).

cnf(73,axiom,
    ( ~ ssItem(u)
    | strictorderedP(cons(u,nil)) ),
    file('SWC117+1.p',unknown),
    [] ).

cnf(74,axiom,
    ( ~ ssItem(u)
    | duplicatefreeP(cons(u,nil)) ),
    file('SWC117+1.p',unknown),
    [] ).

cnf(75,axiom,
    ( ~ ssItem(u)
    | equalelemsP(cons(u,nil)) ),
    file('SWC117+1.p',unknown),
    [] ).

cnf(77,axiom,
    ( ~ equal(skc4,nil)
    | ~ equal(skc5,nil) ),
    file('SWC117+1.p',unknown),
    [] ).

cnf(78,axiom,
    ( ~ neq(skc4,nil)
    | ~ segmentP(skc5,skc4) ),
    file('SWC117+1.p',unknown),
    [] ).

cnf(79,axiom,
    ( ~ ssList(u)
    | equal(app(nil,u),u) ),
    file('SWC117+1.p',unknown),
    [] ).

cnf(83,axiom,
    ( ~ ssList(u)
    | ssItem(hd(u))
    | equal(nil,u) ),
    file('SWC117+1.p',unknown),
    [] ).

cnf(84,axiom,
    ( ~ ssList(u)
    | ssList(tl(u))
    | equal(nil,u) ),
    file('SWC117+1.p',unknown),
    [] ).

cnf(88,axiom,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ssList(cons(u,v)) ),
    file('SWC117+1.p',unknown),
    [] ).

cnf(89,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ssList(app(v,u)) ),
    file('SWC117+1.p',unknown),
    [] ).

cnf(105,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | neq(v,u)
    | equal(v,u) ),
    file('SWC117+1.p',unknown),
    [] ).

cnf(107,axiom,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ equal(cons(u,v),nil) ),
    file('SWC117+1.p',unknown),
    [] ).

cnf(115,axiom,
    ( ~ ssList(u)
    | equal(nil,u)
    | equal(cons(hd(u),tl(u)),u) ),
    file('SWC117+1.p',unknown),
    [] ).

cnf(118,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,nil),u)
    | singletonP(u) ),
    file('SWC117+1.p',unknown),
    [] ).

cnf(125,axiom,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | equal(app(cons(u,nil),v),cons(u,v)) ),
    file('SWC117+1.p',unknown),
    [] ).

cnf(133,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ frontsegP(v,u)
    | equal(app(u,skf46(v,u)),v) ),
    file('SWC117+1.p',unknown),
    [] ).

cnf(140,axiom,
    ( ~ equalelemsP(u)
    | ~ ssList(u)
    | ~ segmentP(u,skc4)
    | ~ neq(skc4,u)
    | ~ segmentP(skc5,u) ),
    file('SWC117+1.p',unknown),
    [] ).

cnf(141,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ equal(app(u,w),v)
    | frontsegP(v,u) ),
    file('SWC117+1.p',unknown),
    [] ).

cnf(157,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | equal(app(app(w,v),u),app(w,app(v,u))) ),
    file('SWC117+1.p',unknown),
    [] ).

cnf(183,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ ssList(x)
    | ~ equal(app(app(u,x),v),w)
    | segmentP(w,x) ),
    file('SWC117+1.p',unknown),
    [] ).

cnf(194,plain,
    ~ neq(skc4,nil),
    inference(mrr,[status(thm)],[78,14]),
    [iquote('0:MRR:78.1,14.0')] ).

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)],[157,183]),
    [iquote('0:Rew:157.3,183.4')] ).

cnf(253,plain,
    ( ~ ssList(u)
    | neq(skc4,u)
    | equal(skc4,u) ),
    inference(res,[status(thm),theory(equality)],[2,105]),
    [iquote('0:Res:2.0,105.0')] ).

cnf(255,plain,
    ( ~ ssItem(u)
    | ~ equal(cons(u,skc4),nil) ),
    inference(res,[status(thm),theory(equality)],[2,107]),
    [iquote('0:Res:2.0,107.0')] ).

cnf(268,plain,
    ( ~ ssItem(u)
    | ssList(cons(u,skc4)) ),
    inference(res,[status(thm),theory(equality)],[2,88]),
    [iquote('0:Res:2.0,88.0')] ).

cnf(412,plain,
    ( ~ ssList(u)
    | ~ frontsegP(skc5,u)
    | equal(app(u,skf46(skc5,u)),skc5) ),
    inference(res,[status(thm),theory(equality)],[1,133]),
    [iquote('0:Res:1.0,133.0')] ).

cnf(423,plain,
    ( equal(skc5,nil)
    | equal(cons(hd(skc5),tl(skc5)),skc5) ),
    inference(res,[status(thm),theory(equality)],[1,115]),
    [iquote('0:Res:1.0,115.0')] ).

cnf(448,plain,
    ( ssItem(hd(skc5))
    | equal(skc5,nil) ),
    inference(res,[status(thm),theory(equality)],[1,83]),
    [iquote('0:Res:1.0,83.0')] ).

cnf(449,plain,
    ( ssList(tl(skc5))
    | equal(skc5,nil) ),
    inference(res,[status(thm),theory(equality)],[1,84]),
    [iquote('0:Res:1.0,84.0')] ).

cnf(2250,plain,
    ( ~ ssList(cons(u,nil))
    | ~ ssItem(u)
    | singletonP(cons(u,nil)) ),
    inference(eqr,[status(thm),theory(equality)],[118]),
    [iquote('0:EqR:118.2')] ).

cnf(2511,plain,
    ( ~ ssItem(u)
    | singletonP(cons(u,nil)) ),
    inference(ssi,[status(thm)],[2250,88,13,12,9,8,7,11,10,6,75,74,71,70,69,73,72]),
    [iquote('0:SSi:2250.0,88.1,13.1,12.1,9.1,8.1,7.1,11.1,10.0,6.0,75.0,74.0,71.0,70.0,69.0,73.0,72.2')] ).

cnf(2835,plain,
    ( ~ ssList(nil)
    | ~ ssList(skc4)
    | equal(skc4,nil) ),
    inference(res,[status(thm),theory(equality)],[105,194]),
    [iquote('0:Res:105.2,194.0')] ).

cnf(2866,plain,
    equal(skc4,nil),
    inference(ssi,[status(thm)],[2835,2,3,13,12,9,8,7,11,10,6]),
    [iquote('0:SSi:2835.1,2835.0,2.0,3.0,13.0,12.0,9.0,8.0,7.0,11.0,10.0,6.0')] ).

cnf(2900,plain,
    ( ~ ssItem(u)
    | ssList(cons(u,nil)) ),
    inference(rew,[status(thm),theory(equality)],[2866,268]),
    [iquote('0:Rew:2866.0,268.1')] ).

cnf(2901,plain,
    ( ~ ssItem(u)
    | ~ equal(cons(u,nil),nil) ),
    inference(rew,[status(thm),theory(equality)],[2866,255]),
    [iquote('0:Rew:2866.0,255.1')] ).

cnf(2919,plain,
    ( ~ equalelemsP(u)
    | ~ ssList(u)
    | ~ segmentP(u,skc4)
    | ~ neq(nil,u)
    | ~ segmentP(skc5,u) ),
    inference(rew,[status(thm),theory(equality)],[2866,140]),
    [iquote('0:Rew:2866.0,140.3')] ).

cnf(2921,plain,
    ( ~ ssList(u)
    | neq(nil,u)
    | equal(skc4,u) ),
    inference(rew,[status(thm),theory(equality)],[2866,253]),
    [iquote('0:Rew:2866.0,253.1')] ).

cnf(3020,plain,
    ( ~ equal(nil,nil)
    | ~ equal(skc5,nil) ),
    inference(rew,[status(thm),theory(equality)],[2866,77]),
    [iquote('0:Rew:2866.0,77.0')] ).

cnf(3021,plain,
    ~ equal(skc5,nil),
    inference(obv,[status(thm),theory(equality)],[3020]),
    [iquote('0:Obv:3020.0')] ).

cnf(3022,plain,
    ssItem(hd(skc5)),
    inference(mrr,[status(thm)],[448,3021]),
    [iquote('0:MRR:448.1,3021.0')] ).

cnf(3023,plain,
    ssList(tl(skc5)),
    inference(mrr,[status(thm)],[449,3021]),
    [iquote('0:MRR:449.1,3021.0')] ).

cnf(3032,plain,
    ( ~ ssList(u)
    | neq(nil,u)
    | equal(nil,u) ),
    inference(rew,[status(thm),theory(equality)],[2866,2921]),
    [iquote('0:Rew:2866.0,2921.2')] ).

cnf(3034,plain,
    equal(cons(hd(skc5),tl(skc5)),skc5),
    inference(mrr,[status(thm)],[423,3021]),
    [iquote('0:MRR:423.0,3021.0')] ).

cnf(3118,plain,
    ( ~ equalelemsP(u)
    | ~ ssList(u)
    | ~ segmentP(u,nil)
    | ~ neq(nil,u)
    | ~ segmentP(skc5,u) ),
    inference(rew,[status(thm),theory(equality)],[2866,2919]),
    [iquote('0:Rew:2866.0,2919.2')] ).

cnf(3119,plain,
    ( ~ equalelemsP(u)
    | ~ ssList(u)
    | ~ neq(nil,u)
    | ~ segmentP(skc5,u) ),
    inference(mrr,[status(thm)],[3118,66]),
    [iquote('0:MRR:3118.2,66.1')] ).

cnf(4487,plain,
    ( ~ ssList(u)
    | ~ ssList(app(u,v))
    | ~ ssList(v)
    | frontsegP(app(u,v),u) ),
    inference(eqr,[status(thm),theory(equality)],[141]),
    [iquote('0:EqR:141.3')] ).

cnf(4501,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | frontsegP(app(u,v),u) ),
    inference(ssi,[status(thm)],[4487,89]),
    [iquote('0:SSi:4487.1,89.2')] ).

cnf(5665,plain,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ ssList(cons(u,nil))
    | ~ ssList(v)
    | frontsegP(cons(u,v),cons(u,nil)) ),
    inference(spr,[status(thm),theory(equality)],[125,4501]),
    [iquote('0:SpR:125.2,4501.2')] ).

cnf(5684,plain,
    ( ~ ssItem(u)
    | ~ ssList(cons(u,nil))
    | ~ ssList(v)
    | frontsegP(cons(u,v),cons(u,nil)) ),
    inference(obv,[status(thm),theory(equality)],[5665]),
    [iquote('0:Obv:5665.1')] ).

cnf(5685,plain,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | frontsegP(cons(u,v),cons(u,nil)) ),
    inference(ssi,[status(thm)],[5684,75,74,71,70,69,73,72,2511,2900]),
    [iquote('0:SSi:5684.1,75.1,74.1,71.1,70.1,69.1,73.1,72.1,2511.1,2900.1')] ).

cnf(6418,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(6454,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | segmentP(app(w,app(u,v)),u) ),
    inference(ssi,[status(thm)],[6418,89]),
    [iquote('0:SSi:6418.1,89.2,89.2')] ).

cnf(11004,plain,
    ( ~ ssItem(hd(skc5))
    | ~ ssList(tl(skc5))
    | frontsegP(skc5,cons(hd(skc5),nil)) ),
    inference(spr,[status(thm),theory(equality)],[3034,5685]),
    [iquote('0:SpR:3034.0,5685.2')] ).

cnf(15672,plain,
    ( ~ ssList(app(u,v))
    | ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(nil)
    | segmentP(app(u,v),u) ),
    inference(spr,[status(thm),theory(equality)],[79,6454]),
    [iquote('0:SpR:79.1,6454.3')] ).

cnf(15685,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | segmentP(app(u,v),u) ),
    inference(ssi,[status(thm)],[15672,13,12,9,8,7,11,10,6,89]),
    [iquote('0:SSi:15672.3,15672.0,13.2,12.0,9.0,8.0,7.0,11.0,10.0,6.0,89.0')] ).

cnf(17979,plain,
    ( ~ ssList(u)
    | ~ ssList(u)
    | ~ ssList(skf46(skc5,u))
    | ~ frontsegP(skc5,u)
    | segmentP(skc5,u) ),
    inference(spr,[status(thm),theory(equality)],[412,15685]),
    [iquote('0:SpR:412.2,15685.2')] ).

cnf(18007,plain,
    ( ~ ssList(u)
    | ~ ssList(skf46(skc5,u))
    | ~ frontsegP(skc5,u)
    | segmentP(skc5,u) ),
    inference(obv,[status(thm),theory(equality)],[17979]),
    [iquote('0:Obv:17979.0')] ).

cnf(28174,plain,
    ( ~ ssItem(hd(skc5))
    | frontsegP(skc5,cons(hd(skc5),nil)) ),
    inference(ssi,[status(thm)],[11004,3023]),
    [iquote('0:SSi:11004.1,3023.0')] ).

cnf(28175,plain,
    frontsegP(skc5,cons(hd(skc5),nil)),
    inference(mrr,[status(thm)],[28174,3022]),
    [iquote('0:MRR:28174.0,3022.0')] ).

cnf(47520,plain,
    ( ~ ssList(u)
    | ~ frontsegP(skc5,u)
    | segmentP(skc5,u) ),
    inference(ssi,[status(thm)],[18007,56,1]),
    [iquote('0:SSi:18007.1,56.0,1.0')] ).

cnf(52625,plain,
    ( ~ ssList(cons(hd(skc5),nil))
    | segmentP(skc5,cons(hd(skc5),nil)) ),
    inference(res,[status(thm),theory(equality)],[28175,47520]),
    [iquote('0:Res:28175.0,47520.1')] ).

cnf(52633,plain,
    segmentP(skc5,cons(hd(skc5),nil)),
    inference(ssi,[status(thm)],[52625,75,3022,74,71,70,69,73,72,2511,2900]),
    [iquote('0:SSi:52625.0,75.0,3022.1,74.0,3022.1,71.0,3022.1,70.0,3022.1,69.0,3022.1,73.0,3022.1,72.0,3022.1,2511.0,3022.1,2900.0,3022.1')] ).

cnf(52702,plain,
    ( ~ equalelemsP(cons(hd(skc5),nil))
    | ~ ssList(cons(hd(skc5),nil))
    | ~ neq(nil,cons(hd(skc5),nil)) ),
    inference(res,[status(thm),theory(equality)],[52633,3119]),
    [iquote('0:Res:52633.0,3119.3')] ).

cnf(52707,plain,
    ~ neq(nil,cons(hd(skc5),nil)),
    inference(ssi,[status(thm)],[52702,75,3022,74,71,70,69,73,72,2511,2900]),
    [iquote('0:SSi:52702.1,52702.0,75.0,3022.1,74.0,3022.1,71.0,3022.1,70.0,3022.1,69.0,3022.1,73.0,3022.1,72.0,3022.1,2511.0,3022.1,2900.0,3022.1,75.0,3022.1,74.0,3022.1,71.0,3022.1,70.0,3022.1,69.0,3022.1,73.0,3022.1,72.0,3022.1,2511.0,3022.1,2900.0,3022.1')] ).

cnf(52714,plain,
    ( ~ ssList(cons(hd(skc5),nil))
    | equal(cons(hd(skc5),nil),nil) ),
    inference(res,[status(thm),theory(equality)],[3032,52707]),
    [iquote('0:Res:3032.1,52707.0')] ).

cnf(52715,plain,
    equal(cons(hd(skc5),nil),nil),
    inference(ssi,[status(thm)],[52714,75,3022,74,71,70,69,73,72,2511,2900]),
    [iquote('0:SSi:52714.0,75.0,3022.1,74.0,3022.1,71.0,3022.1,70.0,3022.1,69.0,3022.1,73.0,3022.1,72.0,3022.1,2511.0,3022.1,2900.0,3022.1')] ).

cnf(52775,plain,
    ( ~ ssItem(hd(skc5))
    | ~ equal(nil,nil) ),
    inference(spl,[status(thm),theory(equality)],[52715,2901]),
    [iquote('0:SpL:52715.0,2901.1')] ).

cnf(52844,plain,
    ~ ssItem(hd(skc5)),
    inference(obv,[status(thm),theory(equality)],[52775]),
    [iquote('0:Obv:52775.1')] ).

cnf(52845,plain,
    $false,
    inference(ssi,[status(thm)],[52844,3022]),
    [iquote('0:SSi:52844.0,3022.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWC117+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.14/0.34  % Computer : n009.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Sun Jun 12 05:15:53 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 101.94/102.11  
% 101.94/102.11  SPASS V 3.9 
% 101.94/102.11  SPASS beiseite: Proof found.
% 101.94/102.11  % SZS status Theorem
% 101.94/102.11  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 101.94/102.11  SPASS derived 30968 clauses, backtracked 10333 clauses, performed 107 splits and kept 17040 clauses.
% 101.94/102.11  SPASS allocated 144416 KBytes.
% 101.94/102.11  SPASS spent	0:1:27.89 on the problem.
% 101.94/102.11  		0:00:00.04 for the input.
% 101.94/102.11  		0:00:00.06 for the FLOTTER CNF translation.
% 101.94/102.11  		0:00:00.61 for inferences.
% 101.94/102.11  		0:00:02.41 for the backtracking.
% 101.94/102.11  		0:1:24.19 for the reduction.
% 101.94/102.11  
% 101.94/102.11  
% 101.94/102.11  Here is a proof with depth 7, length 87 :
% 101.94/102.11  % SZS output start Refutation
% See solution above
% 101.94/102.11  Formulae used in the proof : co1 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax5 ax57 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax75 ax76 ax16 ax26 ax15 ax21 ax78 ax4 ax2 ax81 ax82 ax7
% 101.94/102.11  
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