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