TSTP Solution File: SEU298+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU298+1 : TPTP v8.1.0. Released v3.3.0.
% 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 14:35:59 EDT 2022

% Result   : Theorem 0.35s 0.53s
% Output   : Refutation 0.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   49 (  13 unt;   8 nHn;  49 RR)
%            Number of literals    :  129 (   0 equ;  83 neg)
%            Maximal clause size   :    5 (   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;   7 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ordinal(skc14),
    file('SEU298+1.p',unknown),
    [] ).

cnf(65,axiom,
    element(skc15,powerset(powerset(succ(skc14)))),
    file('SEU298+1.p',unknown),
    [] ).

cnf(73,axiom,
    ( in(skf11(u),u)
    | in(skf12(v),skc15) ),
    file('SEU298+1.p',unknown),
    [] ).

cnf(81,axiom,
    ( in(skf11(u),u)
    | in(skf11(u),powerset(skc14)) ),
    file('SEU298+1.p',unknown),
    [] ).

cnf(93,axiom,
    ( ~ equal(skf22(u,v),skf22(u,v))
    | skP0(w,x) ),
    file('SEU298+1.p',unknown),
    [] ).

cnf(94,axiom,
    ( in(skf11(u),u)
    | equal(set_difference(skf12(u),singleton(skc14)),skf11(u)) ),
    file('SEU298+1.p',unknown),
    [] ).

cnf(97,axiom,
    ( ~ in(u,v)
    | ~ in(w,powerset(x))
    | ~ equal(w,set_difference(u,singleton(x)))
    | in(w,skf20(v,x)) ),
    file('SEU298+1.p',unknown),
    [] ).

cnf(98,axiom,
    ( ~ in(u,skc15)
    | ~ in(skf11(v),v)
    | ~ in(skf11(v),powerset(skc14))
    | ~ equal(skf11(v),set_difference(u,singleton(skc14))) ),
    file('SEU298+1.p',unknown),
    [] ).

cnf(99,axiom,
    ( ~ ordinal(u)
    | ~ skP0(u,v)
    | ~ in(w,skf20(v,u))
    | ~ element(v,powerset(powerset(succ(u))))
    | in(w,powerset(u)) ),
    file('SEU298+1.p',unknown),
    [] ).

cnf(100,axiom,
    ( ~ ordinal(u)
    | ~ skP0(u,v)
    | ~ in(w,skf20(v,u))
    | ~ element(v,powerset(powerset(succ(u))))
    | in(skf21(v,x,y),v) ),
    file('SEU298+1.p',unknown),
    [] ).

cnf(101,axiom,
    ( ~ ordinal(u)
    | ~ skP0(u,v)
    | ~ in(w,skf20(v,u))
    | ~ element(v,powerset(powerset(succ(u))))
    | equal(set_difference(skf21(v,u,w),singleton(u)),w) ),
    file('SEU298+1.p',unknown),
    [] ).

cnf(103,plain,
    skP0(u,v),
    inference(obv,[status(thm),theory(equality)],[93]),
    [iquote('0:Obv:93.0')] ).

cnf(105,plain,
    ( ~ ordinal(u)
    | ~ element(v,powerset(powerset(succ(u))))
    | ~ in(w,skf20(v,u))
    | in(w,powerset(u)) ),
    inference(mrr,[status(thm)],[99,103]),
    [iquote('0:MRR:99.1,103.0')] ).

cnf(106,plain,
    ( ~ ordinal(u)
    | ~ element(v,powerset(powerset(succ(u))))
    | ~ in(w,skf20(v,u))
    | in(skf21(v,x,y),v) ),
    inference(mrr,[status(thm)],[100,103]),
    [iquote('0:MRR:100.1,103.0')] ).

cnf(107,plain,
    ( ~ ordinal(u)
    | ~ element(v,powerset(powerset(succ(u))))
    | ~ in(w,skf20(v,u))
    | equal(set_difference(skf21(v,u,w),singleton(u)),w) ),
    inference(mrr,[status(thm)],[101,103]),
    [iquote('0:MRR:101.1,103.0')] ).

cnf(121,plain,
    ( ~ ordinal(skc14)
    | ~ in(u,skf20(skc15,skc14))
    | equal(set_difference(skf21(skc15,skc14,u),singleton(skc14)),u) ),
    inference(res,[status(thm),theory(equality)],[65,107]),
    [iquote('0:Res:65.0,107.2')] ).

cnf(122,plain,
    ( ~ ordinal(skc14)
    | ~ in(u,skf20(skc15,skc14))
    | in(skf21(skc15,v,w),skc15) ),
    inference(res,[status(thm),theory(equality)],[65,106]),
    [iquote('0:Res:65.0,106.2')] ).

cnf(123,plain,
    ( ~ ordinal(skc14)
    | ~ in(u,skf20(skc15,skc14))
    | in(u,powerset(skc14)) ),
    inference(res,[status(thm),theory(equality)],[65,105]),
    [iquote('0:Res:65.0,105.2')] ).

cnf(127,plain,
    ( ~ in(u,skf20(skc15,skc14))
    | in(u,powerset(skc14)) ),
    inference(mrr,[status(thm)],[123,1]),
    [iquote('0:MRR:123.0,1.0')] ).

cnf(128,plain,
    ( ~ in(u,skf20(skc15,skc14))
    | in(skf21(skc15,v,w),skc15) ),
    inference(mrr,[status(thm)],[122,1]),
    [iquote('0:MRR:122.0,1.0')] ).

cnf(129,plain,
    ( ~ in(u,skf20(skc15,skc14))
    | equal(set_difference(skf21(skc15,skc14,u),singleton(skc14)),u) ),
    inference(mrr,[status(thm)],[121,1]),
    [iquote('0:MRR:121.0,1.0')] ).

cnf(133,plain,
    in(skf11(u),u),
    inference(spt,[spt(split,[position(s1)])],[73]),
    [iquote('1:Spt:73.0')] ).

cnf(134,plain,
    ( ~ in(u,skc15)
    | ~ in(skf11(v),powerset(skc14))
    | ~ equal(skf11(v),set_difference(u,singleton(skc14))) ),
    inference(mrr,[status(thm)],[98,133]),
    [iquote('1:MRR:98.1,133.0')] ).

cnf(182,plain,
    in(skf11(skf20(skc15,skc14)),powerset(skc14)),
    inference(res,[status(thm),theory(equality)],[133,127]),
    [iquote('1:Res:133.0,127.0')] ).

cnf(207,plain,
    ( ~ in(u,v)
    | ~ in(set_difference(u,singleton(w)),powerset(w))
    | in(set_difference(u,singleton(w)),skf20(v,w)) ),
    inference(eqr,[status(thm),theory(equality)],[97]),
    [iquote('0:EqR:97.2')] ).

cnf(249,plain,
    in(skf21(skc15,u,v),skc15),
    inference(res,[status(thm),theory(equality)],[133,128]),
    [iquote('1:Res:133.0,128.0')] ).

cnf(279,plain,
    ( ~ in(u,skf20(skc15,skc14))
    | ~ in(skf21(skc15,skc14,u),skc15)
    | ~ in(skf11(v),powerset(skc14))
    | ~ equal(skf11(v),u) ),
    inference(spl,[status(thm),theory(equality)],[129,134]),
    [iquote('1:SpL:129.1,134.2')] ).

cnf(281,plain,
    ( ~ in(u,skf20(skc15,skc14))
    | ~ in(skf11(v),powerset(skc14))
    | ~ equal(skf11(v),u) ),
    inference(mrr,[status(thm)],[279,249]),
    [iquote('1:MRR:279.1,249.0')] ).

cnf(335,plain,
    ( ~ in(skf11(u),powerset(skc14))
    | ~ equal(skf11(u),skf11(skf20(skc15,skc14))) ),
    inference(res,[status(thm),theory(equality)],[133,281]),
    [iquote('1:Res:133.0,281.0')] ).

cnf(338,plain,
    ~ equal(skf11(skf20(skc15,skc14)),skf11(skf20(skc15,skc14))),
    inference(res,[status(thm),theory(equality)],[182,335]),
    [iquote('1:Res:182.0,335.0')] ).

cnf(347,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[338]),
    [iquote('1:Obv:338.0')] ).

cnf(348,plain,
    in(skf12(u),skc15),
    inference(spt,[spt(split,[position(s2)])],[73]),
    [iquote('1:Spt:347.0,73.1')] ).

cnf(352,plain,
    ( in(skf11(skf20(skc15,skc14)),powerset(skc14))
    | in(skf11(skf20(skc15,skc14)),powerset(skc14)) ),
    inference(res,[status(thm),theory(equality)],[81,127]),
    [iquote('0:Res:81.0,127.0')] ).

cnf(362,plain,
    in(skf11(skf20(skc15,skc14)),powerset(skc14)),
    inference(obv,[status(thm),theory(equality)],[352]),
    [iquote('0:Obv:352.0')] ).

cnf(368,plain,
    ( ~ in(skf12(u),v)
    | ~ in(set_difference(skf12(u),singleton(skc14)),powerset(skc14))
    | in(skf11(u),u)
    | in(skf11(u),skf20(v,skc14)) ),
    inference(spr,[status(thm),theory(equality)],[94,207]),
    [iquote('0:SpR:94.1,207.2')] ).

cnf(382,plain,
    ( ~ in(skf12(u),v)
    | ~ in(skf11(u),powerset(skc14))
    | in(skf11(u),u)
    | in(skf11(u),skf20(v,skc14)) ),
    inference(rew,[status(thm),theory(equality)],[94,368]),
    [iquote('0:Rew:94.1,368.1')] ).

cnf(383,plain,
    ( ~ in(skf12(u),v)
    | in(skf11(u),u)
    | in(skf11(u),skf20(v,skc14)) ),
    inference(mrr,[status(thm)],[382,81]),
    [iquote('0:MRR:382.1,81.1')] ).

cnf(387,plain,
    ( ~ in(u,skf20(skc15,skc14))
    | ~ in(skf21(skc15,skc14,u),skc15)
    | ~ in(skf11(v),v)
    | ~ in(skf11(v),powerset(skc14))
    | ~ equal(skf11(v),u) ),
    inference(spl,[status(thm),theory(equality)],[129,98]),
    [iquote('0:SpL:129.1,98.3')] ).

cnf(389,plain,
    ( ~ in(skf12(u),skc15)
    | ~ in(skf11(v),v)
    | ~ in(skf11(v),powerset(skc14))
    | ~ equal(skf11(v),skf11(u))
    | in(skf11(u),u) ),
    inference(spl,[status(thm),theory(equality)],[94,98]),
    [iquote('0:SpL:94.1,98.3')] ).

cnf(390,plain,
    ( ~ in(skf11(u),u)
    | ~ in(skf11(u),powerset(skc14))
    | ~ equal(skf11(u),skf11(v))
    | in(skf11(v),v) ),
    inference(mrr,[status(thm)],[389,348]),
    [iquote('1:MRR:389.0,348.0')] ).

cnf(391,plain,
    ( ~ in(u,skf20(skc15,skc14))
    | ~ in(skf11(v),v)
    | ~ in(skf11(v),powerset(skc14))
    | ~ equal(skf11(v),u) ),
    inference(mrr,[status(thm)],[387,128]),
    [iquote('0:MRR:387.1,128.1')] ).

cnf(402,plain,
    ( in(skf11(u),u)
    | in(skf11(u),skf20(skc15,skc14)) ),
    inference(res,[status(thm),theory(equality)],[348,383]),
    [iquote('1:Res:348.0,383.0')] ).

cnf(403,plain,
    in(skf11(skf20(skc15,skc14)),skf20(skc15,skc14)),
    inference(fac,[status(thm)],[402]),
    [iquote('1:Fac:402.0,402.1')] ).

cnf(418,plain,
    ( ~ in(skf11(skf20(skc15,skc14)),skf20(skc15,skc14))
    | ~ equal(skf11(skf20(skc15,skc14)),skf11(u))
    | in(skf11(u),u) ),
    inference(res,[status(thm),theory(equality)],[362,390]),
    [iquote('1:Res:362.0,390.1')] ).

cnf(424,plain,
    ( ~ equal(skf11(skf20(skc15,skc14)),skf11(u))
    | in(skf11(u),u) ),
    inference(mrr,[status(thm)],[418,403]),
    [iquote('1:MRR:418.0,403.0')] ).

cnf(514,plain,
    ( ~ in(skf11(u),u)
    | ~ in(skf11(u),powerset(skc14))
    | ~ equal(skf11(u),skf11(skf20(skc15,skc14))) ),
    inference(res,[status(thm),theory(equality)],[403,391]),
    [iquote('1:Res:403.0,391.0')] ).

cnf(515,plain,
    ( ~ in(skf11(u),powerset(skc14))
    | ~ equal(skf11(u),skf11(skf20(skc15,skc14))) ),
    inference(mrr,[status(thm)],[514,424]),
    [iquote('1:MRR:514.0,424.1')] ).

cnf(520,plain,
    ~ equal(skf11(skf20(skc15,skc14)),skf11(skf20(skc15,skc14))),
    inference(res,[status(thm),theory(equality)],[362,515]),
    [iquote('1:Res:362.0,515.0')] ).

cnf(525,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[520]),
    [iquote('1:Obv:520.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU298+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12  % 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 : Mon Jun 20 00:40:22 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.35/0.53  
% 0.35/0.53  SPASS V 3.9 
% 0.35/0.53  SPASS beiseite: Proof found.
% 0.35/0.53  % SZS status Theorem
% 0.35/0.53  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.35/0.53  SPASS derived 358 clauses, backtracked 6 clauses, performed 1 splits and kept 331 clauses.
% 0.35/0.53  SPASS allocated 98305 KBytes.
% 0.35/0.53  SPASS spent	0:00:00.18 on the problem.
% 0.35/0.53  		0:00:00.04 for the input.
% 0.35/0.53  		0:00:00.08 for the FLOTTER CNF translation.
% 0.35/0.53  		0:00:00.01 for inferences.
% 0.35/0.53  		0:00:00.00 for the backtracking.
% 0.35/0.53  		0:00:00.03 for the reduction.
% 0.35/0.53  
% 0.35/0.53  
% 0.35/0.53  Here is a proof with depth 6, length 49 :
% 0.35/0.53  % SZS output start Refutation
% See solution above
% 0.35/0.53  Formulae used in the proof : s1_xboole_0__e4_27_3_1__finset_1 s1_tarski__e4_27_3_1__finset_1__1
% 0.35/0.53  
%------------------------------------------------------------------------------