TSTP Solution File: NUN056+2 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUN056+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n022.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 : Mon Jul 18 16:38:42 EDT 2022

% Result   : Theorem 18.31s 18.48s
% Output   : Refutation 18.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   14
% Syntax   : Number of clauses     :   43 (  27 unt;   3 nHn;  43 RR)
%            Number of literals    :   93 (   0 equ;  58 neg)
%            Maximal clause size   :   10 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   1 prp; 0-4 aty)
%            Number of functors    :   17 (  17 usr;  10 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    r1(skf22(u)),
    file('NUN056+2.p',unknown),
    [] ).

cnf(5,axiom,
    r2(u,skf17(v,u)),
    file('NUN056+2.p',unknown),
    [] ).

cnf(6,axiom,
    r2(u,skf20(v,u)),
    file('NUN056+2.p',unknown),
    [] ).

cnf(7,axiom,
    r3(u,skf22(u),u),
    file('NUN056+2.p',unknown),
    [] ).

cnf(8,axiom,
    ( equal(u,skc1)
    | skP0(skc1,u) ),
    file('NUN056+2.p',unknown),
    [] ).

cnf(9,axiom,
    r3(u,v,skf18(v,u)),
    file('NUN056+2.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ r1(u)
    | ~ skP0(v,u) ),
    file('NUN056+2.p',unknown),
    [] ).

cnf(14,axiom,
    r2(skf18(u,v),skf16(v,u)),
    file('NUN056+2.p',unknown),
    [] ).

cnf(18,axiom,
    r3(u,skf17(u,v),skf16(u,v)),
    file('NUN056+2.p',unknown),
    [] ).

cnf(21,axiom,
    ( equal(u,skf13(v))
    | skP1(skf13(v),u,v) ),
    file('NUN056+2.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ r2(u,v)
    | ~ skP1(w,v,u) ),
    file('NUN056+2.p',unknown),
    [] ).

cnf(27,axiom,
    ( ~ r3(u,v,w)
    | ~ skP2(x,w,v,u) ),
    file('NUN056+2.p',unknown),
    [] ).

cnf(31,axiom,
    ( equal(u,skf14(v,w))
    | skP2(skf14(v,w),u,w,v) ),
    file('NUN056+2.p',unknown),
    [] ).

cnf(33,axiom,
    ( ~ r1(u)
    | ~ r1(v)
    | ~ r1(w)
    | ~ r2(u,x)
    | ~ r2(y,z)
    | ~ r2(x,x1)
    | ~ r2(v,x2)
    | ~ r2(x3,y)
    | ~ r2(w,x3)
    | ~ r3(x2,x1,z) ),
    file('NUN056+2.p',unknown),
    [] ).

cnf(50,plain,
    ( ~ r1(u)
    | ~ r1(v)
    | ~ r1(w)
    | ~ r2(u,x)
    | ~ r2(x,y)
    | ~ r2(v,z)
    | ~ r2(w,x1)
    | ~ r2(skf20(x2,x1),x3)
    | ~ r3(z,y,x3) ),
    inference(res,[status(thm),theory(equality)],[6,33]),
    [iquote('0:Res:6.0,33.5')] ).

cnf(65,plain,
    ( ~ r1(u)
    | equal(u,skc1) ),
    inference(res,[status(thm),theory(equality)],[8,13]),
    [iquote('0:Res:8.1,13.1')] ).

cnf(67,plain,
    equal(skf22(u),skc1),
    inference(ems,[status(thm)],[65,1]),
    [iquote('0:EmS:65.0,1.0')] ).

cnf(70,plain,
    r1(skc1),
    inference(rew,[status(thm),theory(equality)],[67,1]),
    [iquote('0:Rew:67.0,1.0')] ).

cnf(71,plain,
    r3(u,skc1,u),
    inference(rew,[status(thm),theory(equality)],[67,7]),
    [iquote('0:Rew:67.0,7.0')] ).

cnf(106,plain,
    ( ~ r2(u,v)
    | equal(v,skf13(u)) ),
    inference(res,[status(thm),theory(equality)],[21,22]),
    [iquote('0:Res:21.1,22.1')] ).

cnf(107,plain,
    equal(skf20(u,v),skf13(v)),
    inference(res,[status(thm),theory(equality)],[6,106]),
    [iquote('0:Res:6.0,106.0')] ).

cnf(108,plain,
    equal(skf17(u,v),skf13(v)),
    inference(res,[status(thm),theory(equality)],[5,106]),
    [iquote('0:Res:5.0,106.0')] ).

cnf(111,plain,
    equal(skf13(skf18(u,v)),skf16(v,u)),
    inference(res,[status(thm),theory(equality)],[14,106]),
    [iquote('0:Res:14.0,106.0')] ).

cnf(114,plain,
    r2(u,skf13(u)),
    inference(rew,[status(thm),theory(equality)],[107,6]),
    [iquote('0:Rew:107.0,6.0')] ).

cnf(116,plain,
    ( ~ r1(u)
    | ~ r1(v)
    | ~ r1(w)
    | ~ r2(u,x)
    | ~ r2(x,y)
    | ~ r2(v,z)
    | ~ r2(w,x1)
    | ~ r2(skf13(x1),x2)
    | ~ r3(z,y,x2) ),
    inference(rew,[status(thm),theory(equality)],[107,50]),
    [iquote('0:Rew:107.0,50.7')] ).

cnf(122,plain,
    r3(u,skf13(v),skf16(u,v)),
    inference(rew,[status(thm),theory(equality)],[108,18]),
    [iquote('0:Rew:108.0,18.0')] ).

cnf(406,plain,
    ( ~ r3(u,v,w)
    | equal(w,skf14(u,v)) ),
    inference(res,[status(thm),theory(equality)],[31,27]),
    [iquote('0:Res:31.1,27.1')] ).

cnf(441,plain,
    equal(skf18(u,v),skf14(v,u)),
    inference(res,[status(thm),theory(equality)],[9,406]),
    [iquote('0:Res:9.0,406.0')] ).

cnf(442,plain,
    equal(skf14(u,skc1),u),
    inference(res,[status(thm),theory(equality)],[71,406]),
    [iquote('0:Res:71.0,406.0')] ).

cnf(443,plain,
    equal(skf14(u,skf13(v)),skf16(u,v)),
    inference(res,[status(thm),theory(equality)],[122,406]),
    [iquote('0:Res:122.0,406.0')] ).

cnf(451,plain,
    r2(skf14(u,v),skf16(u,v)),
    inference(rew,[status(thm),theory(equality)],[441,14]),
    [iquote('0:Rew:441.0,14.0')] ).

cnf(452,plain,
    equal(skf13(skf14(u,v)),skf16(u,v)),
    inference(rew,[status(thm),theory(equality)],[441,111]),
    [iquote('0:Rew:441.0,111.0')] ).

cnf(487,plain,
    r2(u,skf16(u,skc1)),
    inference(spr,[status(thm),theory(equality)],[442,451]),
    [iquote('0:SpR:442.0,451.0')] ).

cnf(494,plain,
    equal(skf16(u,skc1),skf13(u)),
    inference(res,[status(thm),theory(equality)],[487,106]),
    [iquote('0:Res:487.0,106.0')] ).

cnf(578,plain,
    equal(skf16(u,skf13(v)),skf13(skf16(u,v))),
    inference(spr,[status(thm),theory(equality)],[443,452]),
    [iquote('0:SpR:443.0,452.0')] ).

cnf(721,plain,
    r3(u,skf13(skf13(v)),skf13(skf16(u,v))),
    inference(spr,[status(thm),theory(equality)],[578,122]),
    [iquote('0:SpR:578.0,122.0')] ).

cnf(742,plain,
    r3(u,skf13(skf13(skc1)),skf13(skf13(u))),
    inference(spr,[status(thm),theory(equality)],[494,721]),
    [iquote('0:SpR:494.0,721.0')] ).

cnf(805,plain,
    ( ~ r1(u)
    | ~ r1(v)
    | ~ r1(w)
    | ~ r2(u,x)
    | ~ r2(x,y)
    | ~ r2(v,z)
    | ~ r2(w,x1)
    | ~ r3(z,y,skf13(skf13(x1))) ),
    inference(res,[status(thm),theory(equality)],[114,116]),
    [iquote('0:Res:114.0,116.7')] ).

cnf(3169,plain,
    ( ~ r1(u)
    | ~ r1(v)
    | ~ r1(w)
    | ~ r2(u,x)
    | ~ r2(x,skf13(skf13(skc1)))
    | ~ r2(v,y)
    | ~ r2(w,y) ),
    inference(res,[status(thm),theory(equality)],[742,805]),
    [iquote('0:Res:742.0,805.7')] ).

cnf(3176,plain,
    ( ~ r1(u)
    | ~ r2(u,v)
    | ~ r2(v,skf13(skf13(skc1))) ),
    inference(con,[status(thm)],[3169]),
    [iquote('0:Con:3169.1')] ).

cnf(16288,plain,
    ( ~ r1(u)
    | ~ r2(u,skf13(skc1)) ),
    inference(res,[status(thm),theory(equality)],[114,3176]),
    [iquote('0:Res:114.0,3176.2')] ).

cnf(16322,plain,
    ~ r1(skc1),
    inference(res,[status(thm),theory(equality)],[114,16288]),
    [iquote('0:Res:114.0,16288.1')] ).

cnf(16331,plain,
    $false,
    inference(ssi,[status(thm)],[16322,70]),
    [iquote('0:SSi:16322.0,70.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUN056+2 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n022.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Thu Jun  2 03:07:21 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 18.31/18.48  
% 18.31/18.48  SPASS V 3.9 
% 18.31/18.48  SPASS beiseite: Proof found.
% 18.31/18.48  % SZS status Theorem
% 18.31/18.48  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 18.31/18.48  SPASS derived 12404 clauses, backtracked 0 clauses, performed 0 splits and kept 5106 clauses.
% 18.31/18.48  SPASS allocated 114753 KBytes.
% 18.31/18.48  SPASS spent	0:0:17.90 on the problem.
% 18.31/18.48  		0:00:00.03 for the input.
% 18.31/18.48  		0:00:00.04 for the FLOTTER CNF translation.
% 18.31/18.48  		0:00:00.19 for inferences.
% 18.31/18.48  		0:00:00.00 for the backtracking.
% 18.31/18.48  		0:0:17.51 for the reduction.
% 18.31/18.48  
% 18.31/18.48  
% 18.31/18.48  Here is a proof with depth 8, length 43 :
% 18.31/18.48  % SZS output start Refutation
% See solution above
% 18.31/18.48  Formulae used in the proof : axiom_4a axiom_1a axiom_2a axiom_1 axiom_2 axiom_3 oneplustwoeqthree
% 18.31/18.48  
%------------------------------------------------------------------------------