TSTP Solution File: NUM543+2 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM543+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n005.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 14:27:19 EDT 2022

% Result   : Theorem 0.74s 0.95s
% Output   : Refutation 0.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   16
% Syntax   : Number of clauses     :   41 (   9 unt;   8 nHn;  41 RR)
%            Number of literals    :  120 (   0 equ;  81 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(4,axiom,
    aSet0(xS),
    file('NUM543+2.p',unknown),
    [] ).

cnf(5,axiom,
    isFinite0(xS),
    file('NUM543+2.p',unknown),
    [] ).

cnf(7,axiom,
    aSubsetOf0(xS,szNzAzT0),
    file('NUM543+2.p',unknown),
    [] ).

cnf(8,axiom,
    aElementOf0(skf10(u),xS),
    file('NUM543+2.p',unknown),
    [] ).

cnf(21,axiom,
    ( ~ aElementOf0(u,xS)
    | aElementOf0(u,szNzAzT0) ),
    file('NUM543+2.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ aElementOf0(u,v)
    | ~ equal(v,slcrc0) ),
    file('NUM543+2.p',unknown),
    [] ).

cnf(24,axiom,
    ( ~ aElementOf0(u,szNzAzT0)
    | aElementOf0(szszuzczcdt0(u),szNzAzT0) ),
    file('NUM543+2.p',unknown),
    [] ).

cnf(35,axiom,
    ( ~ aElementOf0(u,szNzAzT0)
    | ~ aElementOf0(skf10(u),slbdtrb0(u)) ),
    file('NUM543+2.p',unknown),
    [] ).

cnf(45,axiom,
    ( ~ aElementOf0(u,szNzAzT0)
    | ~ aElementOf0(v,slbdtrb0(u))
    | aElementOf0(v,szNzAzT0) ),
    file('NUM543+2.p',unknown),
    [] ).

cnf(60,axiom,
    ( ~ aElementOf0(u,szNzAzT0)
    | ~ aElementOf0(v,szNzAzT0)
    | sdtlseqdt0(v,u)
    | sdtlseqdt0(szszuzczcdt0(u),v) ),
    file('NUM543+2.p',unknown),
    [] ).

cnf(65,axiom,
    ( ~ aElementOf0(u,szNzAzT0)
    | ~ aElementOf0(v,szNzAzT0)
    | ~ sdtlseqdt0(szszuzczcdt0(v),u)
    | aElementOf0(v,slbdtrb0(u)) ),
    file('NUM543+2.p',unknown),
    [] ).

cnf(71,axiom,
    ( ~ equal(u,v)
    | ~ aElementOf0(v,szNzAzT0)
    | ~ aElementOf0(u,szNzAzT0)
    | aElementOf0(u,slbdtrb0(szszuzczcdt0(v))) ),
    file('NUM543+2.p',unknown),
    [] ).

cnf(75,axiom,
    ( ~ isFinite0(u)
    | ~ aSubsetOf0(u,szNzAzT0)
    | ~ equal(v,szmzazxdt0(u))
    | aElementOf0(v,u)
    | equal(u,slcrc0) ),
    file('NUM543+2.p',unknown),
    [] ).

cnf(76,axiom,
    ( ~ aElementOf0(u,slbdtrb0(v))
    | ~ aElementOf0(u,szNzAzT0)
    | ~ aElementOf0(v,szNzAzT0)
    | aElementOf0(u,slbdtrb0(szszuzczcdt0(v))) ),
    file('NUM543+2.p',unknown),
    [] ).

cnf(77,axiom,
    ( ~ sdtlseqdt0(u,v)
    | ~ sdtlseqdt0(v,u)
    | ~ aElementOf0(u,szNzAzT0)
    | ~ aElementOf0(v,szNzAzT0)
    | equal(v,u) ),
    file('NUM543+2.p',unknown),
    [] ).

cnf(93,axiom,
    ( ~ isFinite0(u)
    | ~ equal(v,szmzazxdt0(u))
    | ~ aSubsetOf0(u,szNzAzT0)
    | ~ aElementOf0(w,u)
    | sdtlseqdt0(w,v)
    | equal(u,slcrc0) ),
    file('NUM543+2.p',unknown),
    [] ).

cnf(105,plain,
    ( ~ aElementOf0(u,szNzAzT0)
    | ~ aElementOf0(v,slbdtrb0(u))
    | aElementOf0(v,slbdtrb0(szszuzczcdt0(u))) ),
    inference(mrr,[status(thm)],[76,45]),
    [iquote('0:MRR:76.1,45.2')] ).

cnf(110,plain,
    ( ~ isFinite0(u)
    | ~ aElementOf0(v,u)
    | ~ aSubsetOf0(u,szNzAzT0)
    | ~ equal(w,szmzazxdt0(u))
    | sdtlseqdt0(v,w) ),
    inference(mrr,[status(thm)],[93,22]),
    [iquote('0:MRR:93.5,22.1')] ).

cnf(114,plain,
    aElementOf0(skf10(u),szNzAzT0),
    inference(res,[status(thm),theory(equality)],[8,21]),
    [iquote('0:Res:8.0,21.0')] ).

cnf(122,plain,
    ~ equal(xS,slcrc0),
    inference(res,[status(thm),theory(equality)],[8,22]),
    [iquote('0:Res:8.0,22.0')] ).

cnf(128,plain,
    ( ~ isFinite0(xS)
    | ~ equal(u,szmzazxdt0(xS))
    | ~ aSubsetOf0(xS,szNzAzT0)
    | sdtlseqdt0(skf10(v),u) ),
    inference(res,[status(thm),theory(equality)],[8,110]),
    [iquote('0:Res:8.0,110.3')] ).

cnf(159,plain,
    ( ~ equal(u,szmzazxdt0(xS))
    | sdtlseqdt0(skf10(v),u) ),
    inference(mrr,[status(thm)],[128,5,7]),
    [iquote('0:MRR:128.0,128.2,5.0,7.0')] ).

cnf(420,plain,
    ( ~ aElementOf0(u,szNzAzT0)
    | ~ aElementOf0(skf10(szszuzczcdt0(u)),slbdtrb0(u))
    | ~ aElementOf0(szszuzczcdt0(u),szNzAzT0) ),
    inference(res,[status(thm),theory(equality)],[105,35]),
    [iquote('0:Res:105.2,35.1')] ).

cnf(424,plain,
    ( ~ aElementOf0(u,szNzAzT0)
    | ~ aElementOf0(skf10(szszuzczcdt0(u)),slbdtrb0(u)) ),
    inference(mrr,[status(thm)],[420,24]),
    [iquote('0:MRR:420.2,24.1')] ).

cnf(1065,plain,
    ( ~ equal(skf10(szszuzczcdt0(u)),u)
    | ~ aElementOf0(u,szNzAzT0)
    | ~ aElementOf0(skf10(szszuzczcdt0(u)),szNzAzT0)
    | ~ aElementOf0(szszuzczcdt0(u),szNzAzT0) ),
    inference(res,[status(thm),theory(equality)],[71,35]),
    [iquote('0:Res:71.3,35.1')] ).

cnf(1077,plain,
    ( ~ equal(skf10(szszuzczcdt0(u)),u)
    | ~ aElementOf0(u,szNzAzT0) ),
    inference(mrr,[status(thm)],[1065,114,24]),
    [iquote('0:MRR:1065.2,1065.3,114.0,24.1')] ).

cnf(1107,plain,
    ( ~ aElementOf0(u,szNzAzT0)
    | ~ aElementOf0(v,szNzAzT0)
    | ~ aElementOf0(v,szNzAzT0)
    | ~ aElementOf0(u,szNzAzT0)
    | sdtlseqdt0(v,u)
    | aElementOf0(u,slbdtrb0(v)) ),
    inference(res,[status(thm),theory(equality)],[60,65]),
    [iquote('0:Res:60.3,65.2')] ).

cnf(1115,plain,
    ( ~ aElementOf0(u,szNzAzT0)
    | ~ aElementOf0(v,szNzAzT0)
    | sdtlseqdt0(u,v)
    | aElementOf0(v,slbdtrb0(u)) ),
    inference(obv,[status(thm),theory(equality)],[1107]),
    [iquote('0:Obv:1107.1')] ).

cnf(1352,plain,
    ( ~ isFinite0(u)
    | ~ aSubsetOf0(u,szNzAzT0)
    | aElementOf0(szmzazxdt0(u),u)
    | equal(u,slcrc0) ),
    inference(eqr,[status(thm),theory(equality)],[75]),
    [iquote('0:EqR:75.2')] ).

cnf(2369,plain,
    ( ~ isFinite0(xS)
    | ~ aSubsetOf0(xS,szNzAzT0)
    | equal(xS,slcrc0)
    | aElementOf0(szmzazxdt0(xS),szNzAzT0) ),
    inference(res,[status(thm),theory(equality)],[1352,21]),
    [iquote('0:Res:1352.2,21.0')] ).

cnf(2378,plain,
    ( ~ aSubsetOf0(xS,szNzAzT0)
    | equal(xS,slcrc0)
    | aElementOf0(szmzazxdt0(xS),szNzAzT0) ),
    inference(ssi,[status(thm)],[2369,5,4]),
    [iquote('0:SSi:2369.0,5.0,4.0')] ).

cnf(2379,plain,
    aElementOf0(szmzazxdt0(xS),szNzAzT0),
    inference(mrr,[status(thm)],[2378,7,122]),
    [iquote('0:MRR:2378.0,2378.1,7.0,122.0')] ).

cnf(2591,plain,
    ( ~ aElementOf0(u,szNzAzT0)
    | ~ aElementOf0(skf10(szszuzczcdt0(u)),szNzAzT0)
    | ~ aElementOf0(u,szNzAzT0)
    | sdtlseqdt0(u,skf10(szszuzczcdt0(u))) ),
    inference(res,[status(thm),theory(equality)],[1115,424]),
    [iquote('0:Res:1115.3,424.1')] ).

cnf(2609,plain,
    ( ~ aElementOf0(skf10(szszuzczcdt0(u)),szNzAzT0)
    | ~ aElementOf0(u,szNzAzT0)
    | sdtlseqdt0(u,skf10(szszuzczcdt0(u))) ),
    inference(obv,[status(thm),theory(equality)],[2591]),
    [iquote('0:Obv:2591.0')] ).

cnf(2610,plain,
    ( ~ aElementOf0(u,szNzAzT0)
    | sdtlseqdt0(u,skf10(szszuzczcdt0(u))) ),
    inference(mrr,[status(thm)],[2609,114]),
    [iquote('0:MRR:2609.0,114.0')] ).

cnf(2639,plain,
    ( ~ aElementOf0(u,szNzAzT0)
    | ~ sdtlseqdt0(skf10(szszuzczcdt0(u)),u)
    | ~ aElementOf0(u,szNzAzT0)
    | ~ aElementOf0(skf10(szszuzczcdt0(u)),szNzAzT0)
    | equal(skf10(szszuzczcdt0(u)),u) ),
    inference(res,[status(thm),theory(equality)],[2610,77]),
    [iquote('0:Res:2610.1,77.0')] ).

cnf(2642,plain,
    ( ~ sdtlseqdt0(skf10(szszuzczcdt0(u)),u)
    | ~ aElementOf0(u,szNzAzT0)
    | ~ aElementOf0(skf10(szszuzczcdt0(u)),szNzAzT0)
    | equal(skf10(szszuzczcdt0(u)),u) ),
    inference(obv,[status(thm),theory(equality)],[2639]),
    [iquote('0:Obv:2639.0')] ).

cnf(2643,plain,
    ( ~ sdtlseqdt0(skf10(szszuzczcdt0(u)),u)
    | ~ aElementOf0(u,szNzAzT0) ),
    inference(mrr,[status(thm)],[2642,114,1077]),
    [iquote('0:MRR:2642.2,2642.3,114.0,1077.0')] ).

cnf(2677,plain,
    ( ~ equal(u,szmzazxdt0(xS))
    | ~ aElementOf0(u,szNzAzT0) ),
    inference(res,[status(thm),theory(equality)],[159,2643]),
    [iquote('0:Res:159.1,2643.0')] ).

cnf(2696,plain,
    ~ equal(szmzazxdt0(xS),szmzazxdt0(xS)),
    inference(res,[status(thm),theory(equality)],[2379,2677]),
    [iquote('0:Res:2379.0,2677.1')] ).

cnf(2714,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[2696]),
    [iquote('0:Obv:2696.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM543+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n005.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 : Thu Jul  7 07:55:37 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.74/0.95  
% 0.74/0.95  SPASS V 3.9 
% 0.74/0.95  SPASS beiseite: Proof found.
% 0.74/0.95  % SZS status Theorem
% 0.74/0.95  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.74/0.95  SPASS derived 1910 clauses, backtracked 123 clauses, performed 2 splits and kept 1060 clauses.
% 0.74/0.95  SPASS allocated 99944 KBytes.
% 0.74/0.95  SPASS spent	0:00:00.59 on the problem.
% 0.74/0.95  		0:00:00.04 for the input.
% 0.74/0.95  		0:00:00.12 for the FLOTTER CNF translation.
% 0.74/0.95  		0:00:00.03 for inferences.
% 0.74/0.95  		0:00:00.00 for the backtracking.
% 0.74/0.95  		0:00:00.37 for the reduction.
% 0.74/0.95  
% 0.74/0.95  
% 0.74/0.95  Here is a proof with depth 5, length 41 :
% 0.74/0.95  % SZS output start Refutation
% See solution above
% 0.74/0.95  Formulae used in the proof : m__1986 m__ mZeroNum mDefEmp mSuccNum mLessTotal mSegSucc mDefMax mLessASymm
% 0.74/0.95  
%------------------------------------------------------------------------------