TSTP Solution File: SWC012-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC012-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n019.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 22:01:04 EDT 2022

% Result   : Unsatisfiable 37.52s 37.71s
% Output   : Refutation 37.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   30
% Syntax   : Number of clauses     :   66 (  28 unt;   2 nHn;  66 RR)
%            Number of literals    :  157 (   0 equ; 105 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   13 (  12 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;  11 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ssList(sk1),
    file('SWC012-1.p',unknown),
    [] ).

cnf(2,axiom,
    ssList(sk2),
    file('SWC012-1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(sk4,sk2),
    file('SWC012-1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(sk3,sk1),
    file('SWC012-1.p',unknown),
    [] ).

cnf(7,axiom,
    ( neq(sk2,nil)
    | neq(sk2,nil) ),
    file('SWC012-1.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ equal(app(app(v,cons(u,nil)),w),sk2)
    | ~ equal(app(v,w),sk1)
    | ~ neq(sk4,nil) ),
    file('SWC012-1.p',unknown),
    [] ).

cnf(14,axiom,
    ( ~ neq(sk4,nil)
    | equal(app(sk3,cons(sk5,nil)),sk4) ),
    file('SWC012-1.p',unknown),
    [] ).

cnf(15,axiom,
    equalelemsP(nil),
    file('SWC012-1.p',unknown),
    [] ).

cnf(16,axiom,
    duplicatefreeP(nil),
    file('SWC012-1.p',unknown),
    [] ).

cnf(17,axiom,
    strictorderedP(nil),
    file('SWC012-1.p',unknown),
    [] ).

cnf(18,axiom,
    totalorderedP(nil),
    file('SWC012-1.p',unknown),
    [] ).

cnf(19,axiom,
    strictorderP(nil),
    file('SWC012-1.p',unknown),
    [] ).

cnf(20,axiom,
    totalorderP(nil),
    file('SWC012-1.p',unknown),
    [] ).

cnf(21,axiom,
    cyclefreeP(nil),
    file('SWC012-1.p',unknown),
    [] ).

cnf(22,axiom,
    ssList(nil),
    file('SWC012-1.p',unknown),
    [] ).

cnf(61,axiom,
    ssItem(skaf44(u)),
    file('SWC012-1.p',unknown),
    [] ).

cnf(78,axiom,
    ( ~ ssItem(u)
    | equalelemsP(cons(u,nil)) ),
    file('SWC012-1.p',unknown),
    [] ).

cnf(79,axiom,
    ( ~ ssItem(u)
    | duplicatefreeP(cons(u,nil)) ),
    file('SWC012-1.p',unknown),
    [] ).

cnf(80,axiom,
    ( ~ ssItem(u)
    | strictorderedP(cons(u,nil)) ),
    file('SWC012-1.p',unknown),
    [] ).

cnf(81,axiom,
    ( ~ ssItem(u)
    | totalorderedP(cons(u,nil)) ),
    file('SWC012-1.p',unknown),
    [] ).

cnf(82,axiom,
    ( ~ ssItem(u)
    | strictorderP(cons(u,nil)) ),
    file('SWC012-1.p',unknown),
    [] ).

cnf(83,axiom,
    ( ~ ssItem(u)
    | totalorderP(cons(u,nil)) ),
    file('SWC012-1.p',unknown),
    [] ).

cnf(84,axiom,
    ( ~ ssItem(u)
    | cyclefreeP(cons(u,nil)) ),
    file('SWC012-1.p',unknown),
    [] ).

cnf(86,axiom,
    ( ~ ssList(u)
    | ssItem(v)
    | duplicatefreeP(u) ),
    file('SWC012-1.p',unknown),
    [] ).

cnf(87,axiom,
    ( ~ ssList(u)
    | equal(app(u,nil),u) ),
    file('SWC012-1.p',unknown),
    [] ).

cnf(99,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ssList(app(u,v)) ),
    file('SWC012-1.p',unknown),
    [] ).

cnf(100,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ssList(cons(v,u)) ),
    file('SWC012-1.p',unknown),
    [] ).

cnf(130,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,nil),u)
    | singletonP(u) ),
    file('SWC012-1.p',unknown),
    [] ).

cnf(171,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssItem(w)
    | equal(app(cons(w,v),u),cons(w,app(v,u))) ),
    file('SWC012-1.p',unknown),
    [] ).

cnf(193,axiom,
    ( ~ ssList(u)
    | ~ duplicatefreeP(u)
    | ~ ssItem(v)
    | ~ ssList(w)
    | ~ ssList(x)
    | ~ ssList(y)
    | ~ equal(app(app(w,cons(v,x)),cons(v,y)),u) ),
    file('SWC012-1.p',unknown),
    [] ).

cnf(204,plain,
    neq(sk2,nil),
    inference(obv,[status(thm),theory(equality)],[7]),
    [iquote('0:Obv:7.0')] ).

cnf(205,plain,
    ( ~ neq(sk2,nil)
    | equal(app(sk1,cons(sk5,nil)),sk2) ),
    inference(rew,[status(thm),theory(equality)],[6,14,5]),
    [iquote('0:Rew:6.0,14.1,5.0,14.1,5.0,14.0')] ).

cnf(206,plain,
    equal(app(sk1,cons(sk5,nil)),sk2),
    inference(mrr,[status(thm)],[205,204]),
    [iquote('0:MRR:205.0,204.0')] ).

cnf(211,plain,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ equal(app(app(v,cons(u,nil)),w),sk2)
    | ~ equal(app(v,w),sk1)
    | ~ neq(sk2,nil) ),
    inference(rew,[status(thm),theory(equality)],[5,12]),
    [iquote('0:Rew:5.0,12.5')] ).

cnf(212,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssItem(w)
    | ~ equal(app(v,u),sk1)
    | ~ equal(app(app(v,cons(w,nil)),u),sk2) ),
    inference(mrr,[status(thm)],[211,204]),
    [iquote('0:MRR:211.5,204.0')] ).

cnf(351,plain,
    ( ~ ssItem(u)
    | ssList(cons(u,sk2)) ),
    inference(res,[status(thm),theory(equality)],[2,100]),
    [iquote('0:Res:2.0,100.1')] ).

cnf(563,plain,
    ssItem(u),
    inference(spt,[spt(split,[position(s1)])],[86]),
    [iquote('1:Spt:86.1')] ).

cnf(569,plain,
    cyclefreeP(cons(u,nil)),
    inference(mrr,[status(thm)],[84,563]),
    [iquote('1:MRR:84.0,563.0')] ).

cnf(570,plain,
    totalorderP(cons(u,nil)),
    inference(mrr,[status(thm)],[83,563]),
    [iquote('1:MRR:83.0,563.0')] ).

cnf(571,plain,
    strictorderP(cons(u,nil)),
    inference(mrr,[status(thm)],[82,563]),
    [iquote('1:MRR:82.0,563.0')] ).

cnf(572,plain,
    totalorderedP(cons(u,nil)),
    inference(mrr,[status(thm)],[81,563]),
    [iquote('1:MRR:81.0,563.0')] ).

cnf(573,plain,
    strictorderedP(cons(u,nil)),
    inference(mrr,[status(thm)],[80,563]),
    [iquote('1:MRR:80.0,563.0')] ).

cnf(574,plain,
    duplicatefreeP(cons(u,nil)),
    inference(mrr,[status(thm)],[79,563]),
    [iquote('1:MRR:79.0,563.0')] ).

cnf(575,plain,
    equalelemsP(cons(u,nil)),
    inference(mrr,[status(thm)],[78,563]),
    [iquote('1:MRR:78.0,563.0')] ).

cnf(688,plain,
    ( ~ ssList(u)
    | ssList(cons(v,u)) ),
    inference(mrr,[status(thm)],[100,563]),
    [iquote('1:MRR:100.1,563.0')] ).

cnf(693,plain,
    ( ~ ssList(u)
    | ~ equal(cons(v,nil),u)
    | singletonP(u) ),
    inference(mrr,[status(thm)],[130,563]),
    [iquote('1:MRR:130.1,563.0')] ).

cnf(763,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ equal(app(v,u),sk1)
    | ~ equal(app(app(v,cons(w,nil)),u),sk2) ),
    inference(mrr,[status(thm)],[212,563]),
    [iquote('1:MRR:212.2,563.0')] ).

cnf(3181,plain,
    ( ~ ssList(cons(u,nil))
    | singletonP(cons(u,nil)) ),
    inference(eqr,[status(thm),theory(equality)],[693]),
    [iquote('1:EqR:693.1')] ).

cnf(3182,plain,
    singletonP(cons(u,nil)),
    inference(ssi,[status(thm)],[3181,688,22,21,20,19,18,17,16,15,569,570,571,572,573,574,575]),
    [iquote('1:SSi:3181.0,688.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0,569.0,570.0,571.0,572.0,573.0,574.0,575.1')] ).

cnf(6498,plain,
    ( ~ ssList(app(u,cons(v,nil)))
    | ~ ssList(nil)
    | ~ ssList(u)
    | ~ equal(app(u,nil),sk1)
    | ~ equal(app(u,cons(v,nil)),sk2) ),
    inference(spl,[status(thm),theory(equality)],[87,763]),
    [iquote('1:SpL:87.1,763.3')] ).

cnf(6507,plain,
    ( ~ ssList(app(u,cons(v,nil)))
    | ~ ssList(nil)
    | ~ ssList(u)
    | ~ equal(u,sk1)
    | ~ equal(app(u,cons(v,nil)),sk2) ),
    inference(rew,[status(thm),theory(equality)],[87,6498]),
    [iquote('1:Rew:87.1,6498.3')] ).

cnf(6508,plain,
    ( ~ ssList(u)
    | ~ equal(u,sk1)
    | ~ equal(app(u,cons(v,nil)),sk2) ),
    inference(ssi,[status(thm)],[6507,22,21,20,19,18,17,16,15,99,688,569,570,571,572,573,574,575,3182]),
    [iquote('1:SSi:6507.1,6507.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0,99.0,688.0,22.0,21.0,20.0,19.0,18.0,17.0,16.1,15.2,569.0,570.0,571.0,572.0,573.0,574.0,575.0,3182.0')] ).

cnf(13665,plain,
    ( ~ ssList(sk1)
    | ~ equal(sk1,sk1)
    | ~ equal(sk2,sk2) ),
    inference(spl,[status(thm),theory(equality)],[206,6508]),
    [iquote('1:SpL:206.0,6508.2')] ).

cnf(14823,plain,
    ~ ssList(sk1),
    inference(obv,[status(thm),theory(equality)],[13665]),
    [iquote('1:Obv:13665.2')] ).

cnf(14824,plain,
    $false,
    inference(ssi,[status(thm)],[14823,1]),
    [iquote('1:SSi:14823.0,1.0')] ).

cnf(15022,plain,
    ( ~ ssList(u)
    | duplicatefreeP(u) ),
    inference(spt,[spt(split,[position(s2)])],[86]),
    [iquote('1:Spt:14824.0,86.0,86.2')] ).

cnf(15085,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(w)
    | ~ ssList(x)
    | ~ ssList(y)
    | ~ equal(app(app(w,cons(v,x)),cons(v,y)),u) ),
    inference(mrr,[status(thm)],[193,15022]),
    [iquote('1:MRR:193.1,15022.1')] ).

cnf(41521,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssItem(w)
    | ~ ssList(cons(w,v))
    | ~ ssList(u)
    | ssList(cons(w,app(v,u))) ),
    inference(spr,[status(thm),theory(equality)],[171,99]),
    [iquote('0:SpR:171.3,99.2')] ).

cnf(41569,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(cons(v,u))
    | ~ ssList(w)
    | ssList(cons(v,app(u,w))) ),
    inference(obv,[status(thm),theory(equality)],[41521]),
    [iquote('0:Obv:41521.0')] ).

cnf(41570,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(w)
    | ssList(cons(v,app(u,w))) ),
    inference(ssi,[status(thm)],[41569,100]),
    [iquote('0:SSi:41569.2,100.2')] ).

cnf(42656,plain,
    ( ~ ssList(app(app(u,cons(v,w)),cons(v,x)))
    | ~ ssItem(v)
    | ~ ssList(u)
    | ~ ssList(w)
    | ~ ssList(x) ),
    inference(eqr,[status(thm),theory(equality)],[15085]),
    [iquote('1:EqR:15085.5')] ).

cnf(42688,plain,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ ssList(x) ),
    inference(ssi,[status(thm)],[42656,99,100]),
    [iquote('1:SSi:42656.0,99.2,99.2,100.2,100.2')] ).

cnf(42689,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(w) ),
    inference(mrr,[status(thm)],[41570,42688]),
    [iquote('1:MRR:41570.3,42688.1')] ).

cnf(42692,plain,
    ( ~ ssList(u)
    | ~ ssItem(v) ),
    inference(con,[status(thm)],[42689]),
    [iquote('1:Con:42689.2')] ).

cnf(42694,plain,
    ~ ssItem(u),
    inference(mrr,[status(thm)],[351,42692]),
    [iquote('1:MRR:351.1,42692.0')] ).

cnf(42696,plain,
    $false,
    inference(unc,[status(thm)],[42694,61]),
    [iquote('1:UnC:42694.0,61.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWC012-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n019.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 08:04:10 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 37.52/37.71  
% 37.52/37.71  SPASS V 3.9 
% 37.52/37.71  SPASS beiseite: Proof found.
% 37.52/37.71  % SZS status Theorem
% 37.52/37.71  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 37.52/37.71  SPASS derived 26130 clauses, backtracked 15497 clauses, performed 119 splits and kept 24565 clauses.
% 37.52/37.71  SPASS allocated 105882 KBytes.
% 37.52/37.71  SPASS spent	0:0:29.11 on the problem.
% 37.52/37.71  		0:00:00.04 for the input.
% 37.52/37.71  		0:00:00.00 for the FLOTTER CNF translation.
% 37.52/37.71  		0:00:00.33 for inferences.
% 37.52/37.71  		0:00:01.06 for the backtracking.
% 37.52/37.71  		0:0:27.17 for the reduction.
% 37.52/37.71  
% 37.52/37.71  
% 37.52/37.71  Here is a proof with depth 2, length 66 :
% 37.52/37.71  % SZS output start Refutation
% See solution above
% 37.52/37.71  Formulae used in the proof : co1_1 co1_2 co1_5 co1_6 co1_7 co1_12 co1_14 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause47 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause72 clause73 clause85 clause86 clause116 clause157 clause179
% 37.52/37.71  
%------------------------------------------------------------------------------