TSTP Solution File: SWC422-1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC422-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n012.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 22:03:58 EDT 2022

% Result   : Unsatisfiable 36.46s 36.69s
% Output   : Refutation 36.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   17
% Syntax   : Number of clauses     :   47 (  13 unt;   4 nHn;  47 RR)
%            Number of literals    :  127 (   0 equ;  91 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;  13 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ssList(sk1),
    file('SWC422-1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(sk4,sk2),
    file('SWC422-1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(sk3,sk1),
    file('SWC422-1.p',unknown),
    [] ).

cnf(7,axiom,
    ( neq(sk2,nil)
    | neq(sk2,nil) ),
    file('SWC422-1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ssList(sk6)
    | neq(sk2,nil) ),
    file('SWC422-1.p',unknown),
    [] ).

cnf(12,axiom,
    ( ssList(sk7)
    | neq(sk2,nil) ),
    file('SWC422-1.p',unknown),
    [] ).

cnf(15,axiom,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ equal(app(app(v,cons(u,nil)),w),sk2)
    | ~ equal(app(app(w,cons(u,nil)),v),sk1)
    | ~ neq(sk4,nil) ),
    file('SWC422-1.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ neq(sk4,nil)
    | ssList(sk6) ),
    file('SWC422-1.p',unknown),
    [] ).

cnf(18,axiom,
    ( ~ neq(sk4,nil)
    | ssList(sk7) ),
    file('SWC422-1.p',unknown),
    [] ).

cnf(19,axiom,
    ( ~ neq(sk4,nil)
    | equal(app(app(sk6,cons(sk5,nil)),sk7),sk4) ),
    file('SWC422-1.p',unknown),
    [] ).

cnf(20,axiom,
    ( ~ neq(sk4,nil)
    | equal(app(app(sk7,cons(sk5,nil)),sk6),sk3) ),
    file('SWC422-1.p',unknown),
    [] ).

cnf(67,axiom,
    ssItem(skaf44(u)),
    file('SWC422-1.p',unknown),
    [] ).

cnf(92,axiom,
    ( ~ ssList(u)
    | ssItem(v)
    | duplicatefreeP(u) ),
    file('SWC422-1.p',unknown),
    [] ).

cnf(105,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ssList(app(u,v)) ),
    file('SWC422-1.p',unknown),
    [] ).

cnf(106,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ssList(cons(v,u)) ),
    file('SWC422-1.p',unknown),
    [] ).

cnf(177,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssItem(w)
    | equal(app(cons(w,v),u),cons(w,app(v,u))) ),
    file('SWC422-1.p',unknown),
    [] ).

cnf(199,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('SWC422-1.p',unknown),
    [] ).

cnf(208,plain,
    ( ~ neq(sk2,nil)
    | ssList(sk7) ),
    inference(rew,[status(thm),theory(equality)],[5,18]),
    [iquote('0:Rew:5.0,18.0')] ).

cnf(209,plain,
    ssList(sk7),
    inference(mrr,[status(thm)],[208,12]),
    [iquote('0:MRR:208.0,12.1')] ).

cnf(210,plain,
    ( ~ neq(sk2,nil)
    | ssList(sk6) ),
    inference(rew,[status(thm),theory(equality)],[5,17]),
    [iquote('0:Rew:5.0,17.0')] ).

cnf(211,plain,
    ssList(sk6),
    inference(mrr,[status(thm)],[210,11]),
    [iquote('0:MRR:210.0,11.1')] ).

cnf(214,plain,
    neq(sk2,nil),
    inference(obv,[status(thm),theory(equality)],[7]),
    [iquote('0:Obv:7.0')] ).

cnf(215,plain,
    ( ~ neq(sk2,nil)
    | equal(app(app(sk7,cons(sk5,nil)),sk6),sk1) ),
    inference(rew,[status(thm),theory(equality)],[6,20,5]),
    [iquote('0:Rew:6.0,20.1,5.0,20.0')] ).

cnf(216,plain,
    equal(app(app(sk7,cons(sk5,nil)),sk6),sk1),
    inference(mrr,[status(thm)],[215,214]),
    [iquote('0:MRR:215.0,214.0')] ).

cnf(217,plain,
    ( ~ neq(sk2,nil)
    | equal(app(app(sk6,cons(sk5,nil)),sk7),sk2) ),
    inference(rew,[status(thm),theory(equality)],[5,19]),
    [iquote('0:Rew:5.0,19.1,5.0,19.0')] ).

cnf(218,plain,
    equal(app(app(sk6,cons(sk5,nil)),sk7),sk2),
    inference(mrr,[status(thm)],[217,214]),
    [iquote('0:MRR:217.0,214.0')] ).

cnf(223,plain,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ equal(app(app(v,cons(u,nil)),w),sk2)
    | ~ equal(app(app(w,cons(u,nil)),v),sk1)
    | ~ neq(sk2,nil) ),
    inference(rew,[status(thm),theory(equality)],[5,15]),
    [iquote('0:Rew:5.0,15.5')] ).

cnf(224,plain,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssItem(w)
    | ~ equal(app(app(u,cons(w,nil)),v),sk1)
    | ~ equal(app(app(v,cons(w,nil)),u),sk2) ),
    inference(mrr,[status(thm)],[223,214]),
    [iquote('0:MRR:223.5,214.0')] ).

cnf(536,plain,
    ( ~ ssItem(u)
    | ssList(cons(u,sk1)) ),
    inference(res,[status(thm),theory(equality)],[1,106]),
    [iquote('0:Res:1.0,106.1')] ).

cnf(575,plain,
    ssItem(u),
    inference(spt,[spt(split,[position(s1)])],[92]),
    [iquote('1:Spt:92.1')] ).

cnf(775,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)],[224,575]),
    [iquote('1:MRR:224.2,575.0')] ).

cnf(17688,plain,
    ( ~ ssList(sk7)
    | ~ ssList(sk6)
    | ~ equal(sk1,sk1)
    | ~ equal(app(app(sk6,cons(sk5,nil)),sk7),sk2) ),
    inference(spl,[status(thm),theory(equality)],[216,775]),
    [iquote('1:SpL:216.0,775.2')] ).

cnf(17690,plain,
    ( ~ ssList(sk7)
    | ~ ssList(sk6)
    | ~ equal(app(app(sk6,cons(sk5,nil)),sk7),sk2) ),
    inference(obv,[status(thm),theory(equality)],[17688]),
    [iquote('1:Obv:17688.2')] ).

cnf(17691,plain,
    ( ~ ssList(sk7)
    | ~ ssList(sk6)
    | ~ equal(sk2,sk2) ),
    inference(rew,[status(thm),theory(equality)],[218,17690]),
    [iquote('1:Rew:218.0,17690.2')] ).

cnf(17692,plain,
    ( ~ ssList(sk7)
    | ~ ssList(sk6) ),
    inference(obv,[status(thm),theory(equality)],[17691]),
    [iquote('1:Obv:17691.2')] ).

cnf(17693,plain,
    $false,
    inference(ssi,[status(thm)],[17692,211,209]),
    [iquote('1:SSi:17692.1,17692.0,211.0,209.0')] ).

cnf(17730,plain,
    ( ~ ssList(u)
    | duplicatefreeP(u) ),
    inference(spt,[spt(split,[position(s2)])],[92]),
    [iquote('1:Spt:17693.0,92.0,92.2')] ).

cnf(17866,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)],[199,17730]),
    [iquote('1:MRR:199.1,17730.1')] ).

cnf(43017,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)],[177,105]),
    [iquote('0:SpR:177.3,105.2')] ).

cnf(43081,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(cons(v,u))
    | ~ ssList(w)
    | ssList(cons(v,app(u,w))) ),
    inference(obv,[status(thm),theory(equality)],[43017]),
    [iquote('0:Obv:43017.0')] ).

cnf(43082,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(w)
    | ssList(cons(v,app(u,w))) ),
    inference(ssi,[status(thm)],[43081,106]),
    [iquote('0:SSi:43081.2,106.2')] ).

cnf(45539,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)],[17866]),
    [iquote('1:EqR:17866.5')] ).

cnf(45564,plain,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ ssList(x) ),
    inference(ssi,[status(thm)],[45539,105,106]),
    [iquote('1:SSi:45539.0,105.2,105.2,106.2,106.2')] ).

cnf(45565,plain,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ ssList(w) ),
    inference(mrr,[status(thm)],[43082,45564]),
    [iquote('1:MRR:43082.3,45564.1')] ).

cnf(45568,plain,
    ( ~ ssList(u)
    | ~ ssItem(v) ),
    inference(con,[status(thm)],[45565]),
    [iquote('1:Con:45565.2')] ).

cnf(45569,plain,
    ~ ssItem(u),
    inference(mrr,[status(thm)],[536,45568]),
    [iquote('1:MRR:536.1,45568.0')] ).

cnf(45570,plain,
    $false,
    inference(unc,[status(thm)],[45569,67]),
    [iquote('1:UnC:45569.0,67.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWC422-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n012.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 17:37:26 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 36.46/36.69  
% 36.46/36.69  SPASS V 3.9 
% 36.46/36.69  SPASS beiseite: Proof found.
% 36.46/36.69  % SZS status Theorem
% 36.46/36.69  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 36.46/36.69  SPASS derived 30262 clauses, backtracked 11298 clauses, performed 119 splits and kept 23818 clauses.
% 36.46/36.69  SPASS allocated 108317 KBytes.
% 36.46/36.69  SPASS spent	0:0:27.14 on the problem.
% 36.46/36.69  		0:00:00.04 for the input.
% 36.46/36.69  		0:00:00.00 for the FLOTTER CNF translation.
% 36.46/36.69  		0:00:00.32 for inferences.
% 36.46/36.69  		0:00:01.41 for the backtracking.
% 36.46/36.69  		0:0:24.99 for the reduction.
% 36.46/36.69  
% 36.46/36.69  
% 36.46/36.69  Here is a proof with depth 1, length 47 :
% 36.46/36.69  % SZS output start Refutation
% See solution above
% 36.46/36.69  Formulae used in the proof : co1_1 co1_5 co1_6 co1_7 co1_11 co1_12 co1_15 co1_17 co1_18 co1_19 co1_20 clause47 clause72 clause85 clause86 clause157 clause179
% 36.46/36.69  
%------------------------------------------------------------------------------