TSTP Solution File: SWC419-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC419-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n024.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 22:03:57 EDT 2022

% Result   : Unsatisfiable 41.32s 41.53s
% Output   : Refutation 41.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   34
% Syntax   : Number of clauses     :   84 (  30 unt;   1 nHn;  84 RR)
%            Number of literals    :  199 (   0 equ; 131 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    :   15 (  15 usr;  12 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ssList(sk1),
    file('SWC419-1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(sk4,sk2),
    file('SWC419-1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(sk3,sk1),
    file('SWC419-1.p',unknown),
    [] ).

cnf(7,axiom,
    neq(sk2,nil),
    file('SWC419-1.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssItem(w)
    | ~ equal(app(app(u,cons(w,nil)),v),sk1)
    | ~ equal(app(app(v,cons(w,nil)),u),sk2) ),
    file('SWC419-1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ neq(sk4,nil)
    | ssList(sk6) ),
    file('SWC419-1.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ neq(sk4,nil)
    | equal(app(cons(sk5,nil),sk6),sk4) ),
    file('SWC419-1.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ neq(sk4,nil)
    | equal(app(sk6,cons(sk5,nil)),sk3) ),
    file('SWC419-1.p',unknown),
    [] ).

cnf(14,axiom,
    equalelemsP(nil),
    file('SWC419-1.p',unknown),
    [] ).

cnf(15,axiom,
    duplicatefreeP(nil),
    file('SWC419-1.p',unknown),
    [] ).

cnf(16,axiom,
    strictorderedP(nil),
    file('SWC419-1.p',unknown),
    [] ).

cnf(17,axiom,
    totalorderedP(nil),
    file('SWC419-1.p',unknown),
    [] ).

cnf(18,axiom,
    strictorderP(nil),
    file('SWC419-1.p',unknown),
    [] ).

cnf(19,axiom,
    totalorderP(nil),
    file('SWC419-1.p',unknown),
    [] ).

cnf(20,axiom,
    cyclefreeP(nil),
    file('SWC419-1.p',unknown),
    [] ).

cnf(21,axiom,
    ssList(nil),
    file('SWC419-1.p',unknown),
    [] ).

cnf(60,axiom,
    ssItem(skaf44(u)),
    file('SWC419-1.p',unknown),
    [] ).

cnf(77,axiom,
    ( ~ ssItem(u)
    | equalelemsP(cons(u,nil)) ),
    file('SWC419-1.p',unknown),
    [] ).

cnf(78,axiom,
    ( ~ ssItem(u)
    | duplicatefreeP(cons(u,nil)) ),
    file('SWC419-1.p',unknown),
    [] ).

cnf(79,axiom,
    ( ~ ssItem(u)
    | strictorderedP(cons(u,nil)) ),
    file('SWC419-1.p',unknown),
    [] ).

cnf(80,axiom,
    ( ~ ssItem(u)
    | totalorderedP(cons(u,nil)) ),
    file('SWC419-1.p',unknown),
    [] ).

cnf(81,axiom,
    ( ~ ssItem(u)
    | strictorderP(cons(u,nil)) ),
    file('SWC419-1.p',unknown),
    [] ).

cnf(82,axiom,
    ( ~ ssItem(u)
    | totalorderP(cons(u,nil)) ),
    file('SWC419-1.p',unknown),
    [] ).

cnf(83,axiom,
    ( ~ ssItem(u)
    | cyclefreeP(cons(u,nil)) ),
    file('SWC419-1.p',unknown),
    [] ).

cnf(85,axiom,
    ( ~ ssList(u)
    | ssItem(v)
    | duplicatefreeP(u) ),
    file('SWC419-1.p',unknown),
    [] ).

cnf(86,axiom,
    ( ~ ssList(u)
    | equal(app(u,nil),u) ),
    file('SWC419-1.p',unknown),
    [] ).

cnf(87,axiom,
    ( ~ ssList(u)
    | equal(app(nil,u),u) ),
    file('SWC419-1.p',unknown),
    [] ).

cnf(98,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ssList(app(u,v)) ),
    file('SWC419-1.p',unknown),
    [] ).

cnf(99,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ssList(cons(v,u)) ),
    file('SWC419-1.p',unknown),
    [] ).

cnf(129,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,nil),u)
    | singletonP(u) ),
    file('SWC419-1.p',unknown),
    [] ).

cnf(133,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | equal(app(cons(v,nil),u),cons(v,u)) ),
    file('SWC419-1.p',unknown),
    [] ).

cnf(162,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | equal(app(app(u,v),w),app(u,app(v,w))) ),
    file('SWC419-1.p',unknown),
    [] ).

cnf(170,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssItem(w)
    | equal(app(cons(w,v),u),cons(w,app(v,u))) ),
    file('SWC419-1.p',unknown),
    [] ).

cnf(192,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('SWC419-1.p',unknown),
    [] ).

cnf(201,plain,
    ( ~ neq(sk2,nil)
    | ssList(sk6) ),
    inference(rew,[status(thm),theory(equality)],[5,11]),
    [iquote('0:Rew:5.0,11.0')] ).

cnf(202,plain,
    ssList(sk6),
    inference(mrr,[status(thm)],[201,7]),
    [iquote('0:MRR:201.0,7.0')] ).

cnf(206,plain,
    ( ~ neq(sk2,nil)
    | equal(app(sk6,cons(sk5,nil)),sk1) ),
    inference(rew,[status(thm),theory(equality)],[6,13,5]),
    [iquote('0:Rew:6.0,13.1,5.0,13.0')] ).

cnf(207,plain,
    equal(app(sk6,cons(sk5,nil)),sk1),
    inference(mrr,[status(thm)],[206,7]),
    [iquote('0:MRR:206.0,7.0')] ).

cnf(208,plain,
    ( ~ neq(sk2,nil)
    | equal(app(cons(sk5,nil),sk6),sk2) ),
    inference(rew,[status(thm),theory(equality)],[5,12]),
    [iquote('0:Rew:5.0,12.1,5.0,12.0')] ).

cnf(209,plain,
    equal(app(cons(sk5,nil),sk6),sk2),
    inference(mrr,[status(thm)],[208,7]),
    [iquote('0:MRR:208.0,7.0')] ).

cnf(525,plain,
    ( ~ ssItem(u)
    | ssList(cons(u,sk1)) ),
    inference(res,[status(thm),theory(equality)],[1,99]),
    [iquote('0:Res:1.0,99.1')] ).

cnf(569,plain,
    ssItem(u),
    inference(spt,[spt(split,[position(s1)])],[85]),
    [iquote('1:Spt:85.1')] ).

cnf(575,plain,
    cyclefreeP(cons(u,nil)),
    inference(mrr,[status(thm)],[83,569]),
    [iquote('1:MRR:83.0,569.0')] ).

cnf(576,plain,
    totalorderP(cons(u,nil)),
    inference(mrr,[status(thm)],[82,569]),
    [iquote('1:MRR:82.0,569.0')] ).

cnf(577,plain,
    strictorderP(cons(u,nil)),
    inference(mrr,[status(thm)],[81,569]),
    [iquote('1:MRR:81.0,569.0')] ).

cnf(578,plain,
    totalorderedP(cons(u,nil)),
    inference(mrr,[status(thm)],[80,569]),
    [iquote('1:MRR:80.0,569.0')] ).

cnf(579,plain,
    strictorderedP(cons(u,nil)),
    inference(mrr,[status(thm)],[79,569]),
    [iquote('1:MRR:79.0,569.0')] ).

cnf(580,plain,
    duplicatefreeP(cons(u,nil)),
    inference(mrr,[status(thm)],[78,569]),
    [iquote('1:MRR:78.0,569.0')] ).

cnf(581,plain,
    equalelemsP(cons(u,nil)),
    inference(mrr,[status(thm)],[77,569]),
    [iquote('1:MRR:77.0,569.0')] ).

cnf(694,plain,
    ( ~ ssList(u)
    | ssList(cons(v,u)) ),
    inference(mrr,[status(thm)],[99,569]),
    [iquote('1:MRR:99.1,569.0')] ).

cnf(699,plain,
    ( ~ ssList(u)
    | ~ equal(cons(v,nil),u)
    | singletonP(u) ),
    inference(mrr,[status(thm)],[129,569]),
    [iquote('1:MRR:129.1,569.0')] ).

cnf(700,plain,
    ( ~ ssList(u)
    | equal(app(cons(v,nil),u),cons(v,u)) ),
    inference(mrr,[status(thm)],[133,569]),
    [iquote('1:MRR:133.1,569.0')] ).

cnf(766,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | equal(app(cons(w,v),u),cons(w,app(v,u))) ),
    inference(mrr,[status(thm)],[170,569]),
    [iquote('1:MRR:170.2,569.0')] ).

cnf(769,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ equal(app(app(u,cons(w,nil)),v),sk1)
    | ~ equal(app(app(v,cons(w,nil)),u),sk2) ),
    inference(mrr,[status(thm)],[8,569]),
    [iquote('1:MRR:8.2,569.0')] ).

cnf(1779,plain,
    ( ~ ssList(cons(u,nil))
    | singletonP(cons(u,nil)) ),
    inference(eqr,[status(thm),theory(equality)],[699]),
    [iquote('1:EqR:699.1')] ).

cnf(1780,plain,
    singletonP(cons(u,nil)),
    inference(ssi,[status(thm)],[1779,694,14,15,16,17,18,19,20,21,581,580,579,578,577,576,575]),
    [iquote('1:SSi:1779.0,694.0,14.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,581.0,580.0,579.0,578.0,577.0,576.0,575.1')] ).

cnf(1890,plain,
    ( ~ ssList(sk6)
    | equal(cons(sk5,sk6),sk2) ),
    inference(spr,[status(thm),theory(equality)],[700,209]),
    [iquote('1:SpR:700.1,209.0')] ).

cnf(1901,plain,
    equal(cons(sk5,sk6),sk2),
    inference(ssi,[status(thm)],[1890,202]),
    [iquote('1:SSi:1890.0,202.0')] ).

cnf(4029,plain,
    ( ~ ssList(u)
    | ~ ssList(nil)
    | ~ ssList(u)
    | ~ ssList(v)
    | equal(app(nil,app(u,v)),app(u,v)) ),
    inference(spr,[status(thm),theory(equality)],[87,162]),
    [iquote('0:SpR:87.1,162.3')] ).

cnf(4056,plain,
    ( ~ ssList(nil)
    | ~ ssList(u)
    | ~ ssList(v)
    | equal(app(nil,app(u,v)),app(u,v)) ),
    inference(obv,[status(thm),theory(equality)],[4029]),
    [iquote('0:Obv:4029.0')] ).

cnf(4057,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | equal(app(nil,app(u,v)),app(u,v)) ),
    inference(ssi,[status(thm)],[4056,14,15,16,17,18,19,20,21]),
    [iquote('0:SSi:4056.0,14.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0')] ).

cnf(10860,plain,
    ( ~ ssList(u)
    | ~ ssList(cons(v,nil))
    | ~ ssList(u)
    | equal(app(nil,cons(v,u)),cons(v,u)) ),
    inference(spr,[status(thm),theory(equality)],[700,4057]),
    [iquote('1:SpR:700.1,4057.2')] ).

cnf(10908,plain,
    ( ~ ssList(cons(u,nil))
    | ~ ssList(v)
    | equal(app(nil,cons(u,v)),cons(u,v)) ),
    inference(obv,[status(thm),theory(equality)],[10860]),
    [iquote('1:Obv:10860.0')] ).

cnf(14274,plain,
    ( ~ ssList(u)
    | equal(app(nil,cons(v,u)),cons(v,u)) ),
    inference(ssi,[status(thm)],[10908,694,14,15,16,17,18,19,20,21,581,580,579,578,577,576,575,1780]),
    [iquote('1:SSi:10908.0,694.0,14.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,581.0,580.0,579.0,578.0,577.0,576.0,575.0,1780.1')] ).

cnf(15247,plain,
    ( ~ ssList(app(u,cons(v,nil)))
    | ~ ssList(u)
    | ~ ssList(nil)
    | ~ equal(app(u,cons(v,nil)),sk1)
    | ~ equal(app(app(nil,cons(v,nil)),u),sk2) ),
    inference(spl,[status(thm),theory(equality)],[86,769]),
    [iquote('1:SpL:86.1,769.2')] ).

cnf(15256,plain,
    ( ~ ssList(app(u,cons(v,nil)))
    | ~ ssList(u)
    | ~ ssList(nil)
    | ~ equal(app(u,cons(v,nil)),sk1)
    | ~ equal(app(cons(v,nil),u),sk2) ),
    inference(rew,[status(thm),theory(equality)],[14274,15247]),
    [iquote('1:Rew:14274.1,15247.4')] ).

cnf(15257,plain,
    ( ~ ssList(app(u,cons(v,nil)))
    | ~ ssList(u)
    | ~ ssList(nil)
    | ~ equal(app(u,cons(v,nil)),sk1)
    | ~ equal(cons(v,u),sk2) ),
    inference(rew,[status(thm),theory(equality)],[87,15256,766]),
    [iquote('1:Rew:87.1,15256.4,766.2,15256.4')] ).

cnf(15258,plain,
    ( ~ ssList(u)
    | ~ equal(app(u,cons(v,nil)),sk1)
    | ~ equal(cons(v,u),sk2) ),
    inference(ssi,[status(thm)],[15257,14,15,16,17,18,19,20,21,98,694,581,580,579,578,577,576,575,1780]),
    [iquote('1:SSi:15257.2,15257.0,14.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,98.0,694.0,14.0,15.0,16.0,17.0,18.0,19.0,20.1,21.2,581.0,580.0,579.0,578.0,577.0,576.0,575.0,1780.0')] ).

cnf(23966,plain,
    ( ~ ssList(sk6)
    | ~ equal(sk1,sk1)
    | ~ equal(cons(sk5,sk6),sk2) ),
    inference(spl,[status(thm),theory(equality)],[207,15258]),
    [iquote('1:SpL:207.0,15258.1')] ).

cnf(24727,plain,
    ( ~ ssList(sk6)
    | ~ equal(cons(sk5,sk6),sk2) ),
    inference(obv,[status(thm),theory(equality)],[23966]),
    [iquote('1:Obv:23966.1')] ).

cnf(24728,plain,
    ( ~ ssList(sk6)
    | ~ equal(sk2,sk2) ),
    inference(rew,[status(thm),theory(equality)],[1901,24727]),
    [iquote('1:Rew:1901.0,24727.1')] ).

cnf(24729,plain,
    ~ ssList(sk6),
    inference(obv,[status(thm),theory(equality)],[24728]),
    [iquote('1:Obv:24728.1')] ).

cnf(24730,plain,
    $false,
    inference(ssi,[status(thm)],[24729,202]),
    [iquote('1:SSi:24729.0,202.0')] ).

cnf(25137,plain,
    ( ~ ssList(u)
    | duplicatefreeP(u) ),
    inference(spt,[spt(split,[position(s2)])],[85]),
    [iquote('1:Spt:24730.0,85.0,85.2')] ).

cnf(25351,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)],[192,25137]),
    [iquote('1:MRR:192.1,25137.1')] ).

cnf(44650,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)],[170,98]),
    [iquote('0:SpR:170.3,98.2')] ).

cnf(44696,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(cons(v,u))
    | ~ ssList(w)
    | ssList(cons(v,app(u,w))) ),
    inference(obv,[status(thm),theory(equality)],[44650]),
    [iquote('0:Obv:44650.0')] ).

cnf(44697,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(w)
    | ssList(cons(v,app(u,w))) ),
    inference(ssi,[status(thm)],[44696,99]),
    [iquote('0:SSi:44696.2,99.2')] ).

cnf(45958,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)],[25351]),
    [iquote('1:EqR:25351.5')] ).

cnf(45983,plain,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ ssList(x) ),
    inference(ssi,[status(thm)],[45958,98,99]),
    [iquote('1:SSi:45958.0,98.2,98.2,99.2,99.2')] ).

cnf(45984,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(w) ),
    inference(mrr,[status(thm)],[44697,45983]),
    [iquote('1:MRR:44697.3,45983.1')] ).

cnf(45990,plain,
    ( ~ ssList(u)
    | ~ ssItem(v) ),
    inference(con,[status(thm)],[45984]),
    [iquote('1:Con:45984.2')] ).

cnf(45991,plain,
    ~ ssItem(u),
    inference(mrr,[status(thm)],[525,45990]),
    [iquote('1:MRR:525.1,45990.0')] ).

cnf(45994,plain,
    $false,
    inference(unc,[status(thm)],[45991,60]),
    [iquote('1:UnC:45991.0,60.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SWC419-1 : TPTP v8.1.0. Released v2.4.0.
% 0.08/0.14  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n024.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Sun Jun 12 18:40:18 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 41.32/41.53  
% 41.32/41.53  SPASS V 3.9 
% 41.32/41.53  SPASS beiseite: Proof found.
% 41.32/41.53  % SZS status Theorem
% 41.32/41.53  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 41.32/41.53  SPASS derived 28986 clauses, backtracked 9841 clauses, performed 91 splits and kept 19083 clauses.
% 41.32/41.53  SPASS allocated 110061 KBytes.
% 41.32/41.53  SPASS spent	0:0:31.51 on the problem.
% 41.32/41.53  		0:00:00.04 for the input.
% 41.32/41.53  		0:00:00.00 for the FLOTTER CNF translation.
% 41.32/41.53  		0:00:00.36 for inferences.
% 41.32/41.53  		0:00:01.75 for the backtracking.
% 41.32/41.53  		0:0:28.95 for the reduction.
% 41.32/41.53  
% 41.32/41.53  
% 41.32/41.53  Here is a proof with depth 2, length 84 :
% 41.32/41.53  % SZS output start Refutation
% See solution above
% 41.32/41.54  Formulae used in the proof : co1_1 co1_5 co1_6 co1_7 co1_8 co1_11 co1_12 co1_13 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause47 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause72 clause73 clause74 clause85 clause86 clause116 clause120 clause149 clause157 clause179
% 41.32/41.54  
%------------------------------------------------------------------------------