TSTP Solution File: NUM478+2 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM478+2 : TPTP v8.1.0. Released v4.0.0.
% 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 : Mon Jul 18 14:26:37 EDT 2022

% Result   : Theorem 1.31s 1.51s
% Output   : Refutation 1.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   13
% Syntax   : Number of clauses     :   34 (  13 unt;   7 nHn;  34 RR)
%            Number of literals    :   94 (   0 equ;  60 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    aNaturalNumber0(xl),
    file('NUM478+2.p',unknown),
    [] ).

cnf(4,axiom,
    aNaturalNumber0(xm),
    file('NUM478+2.p',unknown),
    [] ).

cnf(5,axiom,
    aNaturalNumber0(skc1),
    file('NUM478+2.p',unknown),
    [] ).

cnf(6,axiom,
    aNaturalNumber0(xn),
    file('NUM478+2.p',unknown),
    [] ).

cnf(8,axiom,
    aNaturalNumber0(sdtsldt0(xm,xl)),
    file('NUM478+2.p',unknown),
    [] ).

cnf(12,axiom,
    ~ equal(xl,sz00),
    file('NUM478+2.p',unknown),
    [] ).

cnf(13,axiom,
    equal(sdtasdt0(xl,skc1),xm),
    file('NUM478+2.p',unknown),
    [] ).

cnf(15,axiom,
    equal(sdtasdt0(xl,sdtsldt0(xm,xl)),xm),
    file('NUM478+2.p',unknown),
    [] ).

cnf(24,axiom,
    ~ equal(sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),sdtasdt0(xn,xm)),
    file('NUM478+2.p',unknown),
    [] ).

cnf(29,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | equal(sdtasdt0(v,u),sdtasdt0(u,v)) ),
    file('NUM478+2.p',unknown),
    [] ).

cnf(43,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | ~ equal(u,sdtasdt0(v,w))
    | doDivides0(v,u) ),
    file('NUM478+2.p',unknown),
    [] ).

cnf(48,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | equal(sdtasdt0(sdtasdt0(w,v),u),sdtasdt0(w,sdtasdt0(v,u))) ),
    file('NUM478+2.p',unknown),
    [] ).

cnf(66,axiom,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | ~ doDivides0(v,w)
    | ~ equal(w,sdtasdt0(v,u))
    | equal(u,sdtsldt0(w,v))
    | equal(v,sz00) ),
    file('NUM478+2.p',unknown),
    [] ).

cnf(70,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(v)
    | ~ aNaturalNumber0(w)
    | ~ equal(u,sdtasdt0(v,w))
    | equal(v,sz00)
    | equal(w,sdtsldt0(u,v)) ),
    inference(mrr,[status(thm)],[66,43]),
    [iquote('0:MRR:66.3,43.4')] ).

cnf(1073,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(skc1)
    | ~ aNaturalNumber0(xl)
    | equal(sdtasdt0(xl,sdtasdt0(skc1,u)),sdtasdt0(xm,u)) ),
    inference(spr,[status(thm),theory(equality)],[13,48]),
    [iquote('0:SpR:13.0,48.3')] ).

cnf(1077,plain,
    ( ~ aNaturalNumber0(u)
    | equal(sdtasdt0(xl,sdtasdt0(skc1,u)),sdtasdt0(xm,u)) ),
    inference(ssi,[status(thm)],[1073,3,5]),
    [iquote('0:SSi:1073.2,1073.1,3.0,5.0')] ).

cnf(1191,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(skc1)
    | ~ aNaturalNumber0(u)
    | equal(sdtasdt0(xl,sdtasdt0(u,skc1)),sdtasdt0(xm,u)) ),
    inference(spr,[status(thm),theory(equality)],[29,1077]),
    [iquote('0:SpR:29.2,1077.1')] ).

cnf(1204,plain,
    ( ~ aNaturalNumber0(skc1)
    | ~ aNaturalNumber0(u)
    | equal(sdtasdt0(xl,sdtasdt0(u,skc1)),sdtasdt0(xm,u)) ),
    inference(obv,[status(thm),theory(equality)],[1191]),
    [iquote('0:Obv:1191.0')] ).

cnf(1205,plain,
    ( ~ aNaturalNumber0(u)
    | equal(sdtasdt0(xl,sdtasdt0(u,skc1)),sdtasdt0(xm,u)) ),
    inference(ssi,[status(thm)],[1204,5]),
    [iquote('0:SSi:1204.0,5.0')] ).

cnf(2237,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(skc1)
    | ~ equal(u,xm)
    | equal(xl,sz00)
    | equal(sdtsldt0(u,xl),skc1) ),
    inference(spl,[status(thm),theory(equality)],[13,70]),
    [iquote('0:SpL:13.0,70.3')] ).

cnf(2238,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(sdtsldt0(xm,xl))
    | ~ equal(u,xm)
    | equal(xl,sz00)
    | equal(sdtsldt0(xm,xl),sdtsldt0(u,xl)) ),
    inference(spl,[status(thm),theory(equality)],[15,70]),
    [iquote('0:SpL:15.0,70.3')] ).

cnf(2255,plain,
    ( ~ aNaturalNumber0(u)
    | ~ equal(u,xm)
    | equal(xl,sz00)
    | equal(sdtsldt0(u,xl),skc1) ),
    inference(ssi,[status(thm)],[2237,5,3]),
    [iquote('0:SSi:2237.2,2237.1,5.0,3.0')] ).

cnf(2256,plain,
    ( ~ aNaturalNumber0(u)
    | ~ equal(u,xm)
    | equal(sdtsldt0(u,xl),skc1) ),
    inference(mrr,[status(thm)],[2255,12]),
    [iquote('0:MRR:2255.2,12.0')] ).

cnf(2265,plain,
    ( ~ aNaturalNumber0(u)
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(sdtsldt0(xm,xl))
    | ~ equal(u,xm)
    | equal(xl,sz00)
    | equal(sdtsldt0(xm,xl),skc1) ),
    inference(rew,[status(thm),theory(equality)],[2256,2238]),
    [iquote('0:Rew:2256.2,2238.5')] ).

cnf(2266,plain,
    ( ~ aNaturalNumber0(u)
    | ~ equal(u,xm)
    | equal(xl,sz00)
    | equal(sdtsldt0(xm,xl),skc1) ),
    inference(ssi,[status(thm)],[2265,8,3]),
    [iquote('0:SSi:2265.2,2265.1,8.0,3.0')] ).

cnf(2267,plain,
    ( ~ aNaturalNumber0(u)
    | ~ equal(u,xm)
    | equal(sdtsldt0(xm,xl),skc1) ),
    inference(mrr,[status(thm)],[2266,12]),
    [iquote('0:MRR:2266.2,12.0')] ).

cnf(4027,plain,
    ( ~ aNaturalNumber0(xm)
    | equal(sdtsldt0(xm,xl),skc1) ),
    inference(eqr,[status(thm),theory(equality)],[2267]),
    [iquote('0:EqR:2267.1')] ).

cnf(4028,plain,
    equal(sdtsldt0(xm,xl),skc1),
    inference(ssi,[status(thm)],[4027,4]),
    [iquote('0:SSi:4027.0,4.0')] ).

cnf(4038,plain,
    ~ equal(sdtasdt0(xl,sdtasdt0(xn,skc1)),sdtasdt0(xn,xm)),
    inference(rew,[status(thm),theory(equality)],[4028,24]),
    [iquote('0:Rew:4028.0,24.0')] ).

cnf(5544,plain,
    ( ~ aNaturalNumber0(xn)
    | ~ equal(sdtasdt0(xn,xm),sdtasdt0(xm,xn)) ),
    inference(spl,[status(thm),theory(equality)],[1205,4038]),
    [iquote('0:SpL:1205.1,4038.0')] ).

cnf(5555,plain,
    ~ equal(sdtasdt0(xn,xm),sdtasdt0(xm,xn)),
    inference(ssi,[status(thm)],[5544,6]),
    [iquote('0:SSi:5544.0,6.0')] ).

cnf(5755,plain,
    ( ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm)
    | ~ equal(sdtasdt0(xm,xn),sdtasdt0(xm,xn)) ),
    inference(spl,[status(thm),theory(equality)],[29,5555]),
    [iquote('0:SpL:29.2,5555.0')] ).

cnf(5758,plain,
    ( ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm) ),
    inference(obv,[status(thm),theory(equality)],[5755]),
    [iquote('0:Obv:5755.2')] ).

cnf(5759,plain,
    $false,
    inference(ssi,[status(thm)],[5758,4,6]),
    [iquote('0:SSi:5758.1,5758.0,4.0,6.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : NUM478+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n012.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 : Tue Jul  5 10:21:45 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.31/1.51  
% 1.31/1.51  SPASS V 3.9 
% 1.31/1.51  SPASS beiseite: Proof found.
% 1.31/1.51  % SZS status Theorem
% 1.31/1.51  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 1.31/1.51  SPASS derived 3501 clauses, backtracked 357 clauses, performed 9 splits and kept 1464 clauses.
% 1.31/1.51  SPASS allocated 102130 KBytes.
% 1.31/1.51  SPASS spent	0:00:01.04 on the problem.
% 1.31/1.51  		0:00:00.04 for the input.
% 1.31/1.51  		0:00:00.04 for the FLOTTER CNF translation.
% 1.31/1.51  		0:00:00.04 for inferences.
% 1.31/1.51  		0:00:00.01 for the backtracking.
% 1.31/1.51  		0:00:00.87 for the reduction.
% 1.31/1.51  
% 1.31/1.51  
% 1.31/1.51  Here is a proof with depth 4, length 34 :
% 1.31/1.51  % SZS output start Refutation
% See solution above
% 1.31/1.51  Formulae used in the proof : m__1524 m__1524_04 m__1553 m__ mMulComm mDefDiv mMulAsso mDefQuot
% 1.31/1.51  
%------------------------------------------------------------------------------