TSTP Solution File: SWC191+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC191+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n013.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 22:02:22 EDT 2022

% Result   : Theorem 19.85s 20.02s
% Output   : Refutation 19.85s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   29
% Syntax   : Number of clauses     :   44 (  22 unt;   0 nHn;  44 RR)
%            Number of literals    :   95 (   0 equ;  54 neg)
%            Maximal clause size   :    8 (   2 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :   12 (  11 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;  11 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ssList(skc13),
    file('SWC191+1.p',unknown),
    [] ).

cnf(2,axiom,
    ssList(skc12),
    file('SWC191+1.p',unknown),
    [] ).

cnf(3,axiom,
    ssItem(skc11),
    file('SWC191+1.p',unknown),
    [] ).

cnf(4,axiom,
    ssItem(skc10),
    file('SWC191+1.p',unknown),
    [] ).

cnf(6,axiom,
    ssList(skc8),
    file('SWC191+1.p',unknown),
    [] ).

cnf(7,axiom,
    equalelemsP(skc8),
    file('SWC191+1.p',unknown),
    [] ).

cnf(10,axiom,
    ssList(nil),
    file('SWC191+1.p',unknown),
    [] ).

cnf(11,axiom,
    cyclefreeP(nil),
    file('SWC191+1.p',unknown),
    [] ).

cnf(12,axiom,
    totalorderP(nil),
    file('SWC191+1.p',unknown),
    [] ).

cnf(13,axiom,
    strictorderP(nil),
    file('SWC191+1.p',unknown),
    [] ).

cnf(14,axiom,
    totalorderedP(nil),
    file('SWC191+1.p',unknown),
    [] ).

cnf(15,axiom,
    strictorderedP(nil),
    file('SWC191+1.p',unknown),
    [] ).

cnf(16,axiom,
    duplicatefreeP(nil),
    file('SWC191+1.p',unknown),
    [] ).

cnf(17,axiom,
    equalelemsP(nil),
    file('SWC191+1.p',unknown),
    [] ).

cnf(57,axiom,
    ~ equal(skc11,skc10),
    file('SWC191+1.p',unknown),
    [] ).

cnf(74,axiom,
    ( ~ ssItem(u)
    | cyclefreeP(cons(u,nil)) ),
    file('SWC191+1.p',unknown),
    [] ).

cnf(75,axiom,
    ( ~ ssItem(u)
    | totalorderP(cons(u,nil)) ),
    file('SWC191+1.p',unknown),
    [] ).

cnf(76,axiom,
    ( ~ ssItem(u)
    | strictorderP(cons(u,nil)) ),
    file('SWC191+1.p',unknown),
    [] ).

cnf(77,axiom,
    ( ~ ssItem(u)
    | totalorderedP(cons(u,nil)) ),
    file('SWC191+1.p',unknown),
    [] ).

cnf(78,axiom,
    ( ~ ssItem(u)
    | strictorderedP(cons(u,nil)) ),
    file('SWC191+1.p',unknown),
    [] ).

cnf(79,axiom,
    ( ~ ssItem(u)
    | duplicatefreeP(cons(u,nil)) ),
    file('SWC191+1.p',unknown),
    [] ).

cnf(80,axiom,
    ( ~ ssItem(u)
    | equalelemsP(cons(u,nil)) ),
    file('SWC191+1.p',unknown),
    [] ).

cnf(91,axiom,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | ssList(cons(u,v)) ),
    file('SWC191+1.p',unknown),
    [] ).

cnf(92,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ssList(app(v,u)) ),
    file('SWC191+1.p',unknown),
    [] ).

cnf(113,axiom,
    equal(app(app(app(skc12,cons(skc10,nil)),cons(skc11,nil)),skc13),skc8),
    file('SWC191+1.p',unknown),
    [] ).

cnf(122,axiom,
    ( ~ ssList(u)
    | ~ ssItem(v)
    | ~ equal(cons(v,nil),u)
    | singletonP(u) ),
    file('SWC191+1.p',unknown),
    [] ).

cnf(129,axiom,
    ( ~ ssItem(u)
    | ~ ssList(v)
    | equal(app(cons(u,nil),v),cons(u,v)) ),
    file('SWC191+1.p',unknown),
    [] ).

cnf(161,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | equal(app(app(w,v),u),app(w,app(v,u))) ),
    file('SWC191+1.p',unknown),
    [] ).

cnf(191,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ ssList(w)
    | ~ ssItem(x)
    | ~ ssItem(y)
    | ~ equalelemsP(u)
    | ~ equal(app(w,cons(y,cons(x,v))),u)
    | equal(y,x) ),
    file('SWC191+1.p',unknown),
    [] ).

cnf(2449,plain,
    ( ~ ssList(cons(u,nil))
    | ~ ssItem(u)
    | singletonP(cons(u,nil)) ),
    inference(eqr,[status(thm),theory(equality)],[122]),
    [iquote('0:EqR:122.2')] ).

cnf(2452,plain,
    ( ~ ssItem(u)
    | singletonP(cons(u,nil)) ),
    inference(ssi,[status(thm)],[2449,91,17,16,13,12,11,15,14,10,80,79,76,75,74,78,77]),
    [iquote('0:SSi:2449.0,91.1,17.1,16.1,13.1,12.1,11.1,15.1,14.0,10.0,80.0,79.0,76.0,75.0,74.0,78.0,77.2')] ).

cnf(4366,plain,
    ( ~ ssList(skc13)
    | ~ ssList(cons(skc11,nil))
    | ~ ssList(app(skc12,cons(skc10,nil)))
    | equal(app(app(skc12,cons(skc10,nil)),app(cons(skc11,nil),skc13)),skc8) ),
    inference(spr,[status(thm),theory(equality)],[161,113]),
    [iquote('0:SpR:161.3,113.0')] ).

cnf(4414,plain,
    equal(app(app(skc12,cons(skc10,nil)),app(cons(skc11,nil),skc13)),skc8),
    inference(ssi,[status(thm)],[4366,92,2,91,4,17,16,13,12,11,15,14,10,80,79,76,75,74,78,77,2452,3,1]),
    [iquote('0:SSi:4366.2,4366.1,4366.0,92.0,2.0,91.1,4.0,17.1,16.0,13.1,12.0,11.1,15.0,14.1,10.0,80.1,4.0,79.1,4.0,76.1,4.0,75.0,4.0,74.0,4.0,78.0,4.0,77.0,4.0,2452.2,4.0,91.1,3.0,17.1,16.0,13.1,12.0,11.1,15.0,14.1,10.0,80.1,3.0,79.1,3.0,76.1,3.0,75.0,3.0,74.0,3.0,78.0,3.0,77.0,3.0,2452.2,3.0,1.2')] ).

cnf(9057,plain,
    ( ~ ssItem(skc11)
    | ~ ssList(skc13)
    | equal(app(app(skc12,cons(skc10,nil)),cons(skc11,skc13)),skc8) ),
    inference(spr,[status(thm),theory(equality)],[129,4414]),
    [iquote('0:SpR:129.2,4414.0')] ).

cnf(9071,plain,
    equal(app(app(skc12,cons(skc10,nil)),cons(skc11,skc13)),skc8),
    inference(ssi,[status(thm)],[9057,1,3]),
    [iquote('0:SSi:9057.1,9057.0,1.0,3.0')] ).

cnf(9270,plain,
    ( ~ ssList(cons(skc11,skc13))
    | ~ ssList(cons(skc10,nil))
    | ~ ssList(skc12)
    | equal(app(skc12,app(cons(skc10,nil),cons(skc11,skc13))),skc8) ),
    inference(spr,[status(thm),theory(equality)],[9071,161]),
    [iquote('0:SpR:9071.0,161.3')] ).

cnf(9302,plain,
    equal(app(skc12,app(cons(skc10,nil),cons(skc11,skc13))),skc8),
    inference(ssi,[status(thm)],[9270,2,91,4,17,16,13,12,11,15,14,10,80,79,76,75,74,78,77,2452,3,1]),
    [iquote('0:SSi:9270.2,9270.1,9270.0,2.0,91.0,4.2,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,80.0,4.1,79.0,4.1,76.0,4.1,75.0,4.1,74.0,4.0,78.0,4.0,77.0,4.0,2452.0,4.0,91.0,3.2,1.0')] ).

cnf(25044,plain,
    ( ~ ssItem(skc10)
    | ~ ssList(cons(skc11,skc13))
    | equal(app(skc12,cons(skc10,cons(skc11,skc13))),skc8) ),
    inference(spr,[status(thm),theory(equality)],[129,9302]),
    [iquote('0:SpR:129.2,9302.0')] ).

cnf(25062,plain,
    equal(app(skc12,cons(skc10,cons(skc11,skc13))),skc8),
    inference(ssi,[status(thm)],[25044,91,3,1,4]),
    [iquote('0:SSi:25044.1,25044.0,91.0,3.0,1.0,4.2')] ).

cnf(27316,plain,
    ( ~ ssList(u)
    | ~ ssList(skc13)
    | ~ ssList(skc12)
    | ~ ssItem(skc11)
    | ~ ssItem(skc10)
    | ~ equalelemsP(u)
    | ~ equal(skc8,u)
    | equal(skc11,skc10) ),
    inference(spl,[status(thm),theory(equality)],[25062,191]),
    [iquote('0:SpL:25062.0,191.6')] ).

cnf(27327,plain,
    ( ~ ssList(u)
    | ~ equalelemsP(u)
    | ~ equal(skc8,u)
    | equal(skc11,skc10) ),
    inference(ssi,[status(thm)],[27316,4,3,2,1]),
    [iquote('0:SSi:27316.4,27316.3,27316.2,27316.1,4.0,3.0,2.0,1.0')] ).

cnf(27328,plain,
    ( ~ ssList(u)
    | ~ equalelemsP(u)
    | ~ equal(skc8,u) ),
    inference(mrr,[status(thm)],[27327,57]),
    [iquote('0:MRR:27327.3,57.0')] ).

cnf(27955,plain,
    ~ equal(skc8,skc8),
    inference(ems,[status(thm)],[27328,6,7]),
    [iquote('0:EmS:27328.0,27328.1,6.0,7.0')] ).

cnf(27958,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[27955]),
    [iquote('0:Obv:27955.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWC191+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n013.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 : Sun Jun 12 10:23:44 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 19.85/20.02  
% 19.85/20.02  SPASS V 3.9 
% 19.85/20.02  SPASS beiseite: Proof found.
% 19.85/20.02  % SZS status Theorem
% 19.85/20.02  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 19.85/20.02  SPASS derived 18995 clauses, backtracked 3237 clauses, performed 33 splits and kept 9285 clauses.
% 19.85/20.02  SPASS allocated 121587 KBytes.
% 19.85/20.02  SPASS spent	0:0:17.30 on the problem.
% 19.85/20.02  		0:00:00.04 for the input.
% 19.85/20.02  		0:00:00.07 for the FLOTTER CNF translation.
% 19.85/20.02  		0:00:00.24 for inferences.
% 19.85/20.02  		0:00:00.44 for the backtracking.
% 19.85/20.02  		0:0:16.17 for the reduction.
% 19.85/20.02  
% 19.85/20.02  
% 19.85/20.02  Here is a proof with depth 6, length 44 :
% 19.85/20.02  % SZS output start Refutation
% See solution above
% 19.85/20.02  Formulae used in the proof : co1 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax16 ax26 ax4 ax2 ax81 ax82 ax14
% 19.85/20.02  
%------------------------------------------------------------------------------