%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET889+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 05:29:36 EDT 2022
% Result : Theorem 49.97s 50.15s
% Output : Refutation 49.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of clauses : 32 ( 4 unt; 15 nHn; 32 RR)
% Number of literals : 86 ( 0 equ; 31 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
equal(unordered_pair(u,v),unordered_pair(v,u)),
file('SET889+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ equal(u,empty_set)
| subset(u,singleton(v)) ),
file('SET889+1.p',unknown),
[] ).
cnf(8,axiom,
~ equal(unordered_pair(empty_set,singleton(skc3)),powerset(singleton(skc3))),
file('SET889+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ equal(u,singleton(v))
| subset(u,singleton(v)) ),
file('SET889+1.p',unknown),
[] ).
cnf(10,axiom,
( subset(skf3(u,v),u)
| in(skf3(u,v),v) ),
file('SET889+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ subset(u,singleton(v))
| equal(u,empty_set)
| equal(u,singleton(v)) ),
file('SET889+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ equal(u,v)
| ~ equal(w,unordered_pair(x,v))
| in(u,w) ),
file('SET889+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ subset(skf3(u,v),u)
| ~ in(skf3(u,v),v)
| equal(v,powerset(u)) ),
file('SET889+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ in(u,v)
| ~ equal(v,unordered_pair(w,x))
| equal(u,x)
| equal(u,w) ),
file('SET889+1.p',unknown),
[] ).
cnf(39,plain,
( in(skf3(singleton(u),v),v)
| equal(skf3(singleton(u),v),empty_set)
| equal(skf3(singleton(u),v),singleton(u)) ),
inference(res,[status(thm),theory(equality)],[10,13]),
[iquote('0:Res:10.0,13.0')] ).
cnf(50,plain,
( ~ equal(u,v)
| in(u,unordered_pair(w,v)) ),
inference(eqr,[status(thm),theory(equality)],[16]),
[iquote('0:EqR:16.1')] ).
cnf(55,plain,
( ~ equal(u,v)
| in(u,unordered_pair(v,w)) ),
inference(spr,[status(thm),theory(equality)],[5,50]),
[iquote('0:SpR:5.0,50.1')] ).
cnf(126,plain,
( ~ equal(skf3(singleton(u),v),singleton(u))
| ~ in(skf3(singleton(u),v),v)
| equal(v,powerset(singleton(u))) ),
inference(res,[status(thm),theory(equality)],[9,20]),
[iquote('0:Res:9.1,20.0')] ).
cnf(127,plain,
( ~ equal(skf3(singleton(u),v),empty_set)
| ~ in(skf3(singleton(u),v),v)
| equal(v,powerset(singleton(u))) ),
inference(res,[status(thm),theory(equality)],[7,20]),
[iquote('0:Res:7.1,20.0')] ).
cnf(146,plain,
( ~ in(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[21]),
[iquote('0:EqR:21.1')] ).
cnf(173,plain,
( ~ equal(skf3(singleton(u),unordered_pair(v,w)),v)
| ~ equal(skf3(singleton(u),unordered_pair(v,w)),empty_set)
| equal(unordered_pair(v,w),powerset(singleton(u))) ),
inference(res,[status(thm),theory(equality)],[55,127]),
[iquote('0:Res:55.1,127.1')] ).
cnf(200,plain,
( equal(skf3(singleton(u),unordered_pair(v,w)),empty_set)
| equal(skf3(singleton(u),unordered_pair(v,w)),singleton(u))
| equal(skf3(singleton(u),unordered_pair(v,w)),w)
| equal(skf3(singleton(u),unordered_pair(v,w)),v) ),
inference(res,[status(thm),theory(equality)],[39,146]),
[iquote('0:Res:39.0,146.0')] ).
cnf(220,plain,
( ~ equal(skf3(singleton(u),unordered_pair(v,w)),w)
| ~ equal(skf3(singleton(u),unordered_pair(v,w)),singleton(u))
| equal(unordered_pair(v,w),powerset(singleton(u))) ),
inference(res,[status(thm),theory(equality)],[50,126]),
[iquote('0:Res:50.1,126.1')] ).
cnf(352,plain,
( ~ equal(skf3(singleton(u),unordered_pair(v,w)),w)
| ~ equal(skf3(singleton(u),unordered_pair(w,v)),singleton(u))
| equal(unordered_pair(v,w),powerset(singleton(u))) ),
inference(spl,[status(thm),theory(equality)],[5,220]),
[iquote('0:SpL:5.0,220.1')] ).
cnf(446,plain,
( equal(skf3(singleton(u),unordered_pair(singleton(u),v)),empty_set)
| equal(skf3(singleton(u),unordered_pair(singleton(u),v)),v)
| equal(skf3(singleton(u),unordered_pair(singleton(u),v)),singleton(u)) ),
inference(fac,[status(thm)],[200]),
[iquote('0:Fac:200.1,200.3')] ).
cnf(2290,plain,
( equal(skf3(singleton(u),unordered_pair(singleton(u),v)),empty_set)
| equal(skf3(singleton(u),unordered_pair(singleton(u),v)),v)
| equal(skf3(singleton(u),unordered_pair(v,singleton(u))),singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[5,446]),
[iquote('0:SpR:5.0,446.2')] ).
cnf(2315,plain,
( ~ equal(skf3(singleton(u),unordered_pair(v,singleton(u))),singleton(u))
| ~ equal(singleton(u),singleton(u))
| equal(skf3(singleton(u),unordered_pair(singleton(u),v)),empty_set)
| equal(skf3(singleton(u),unordered_pair(singleton(u),v)),v)
| equal(unordered_pair(v,singleton(u)),powerset(singleton(u))) ),
inference(spl,[status(thm),theory(equality)],[446,352]),
[iquote('0:SpL:446.2,352.1')] ).
cnf(2343,plain,
( ~ equal(skf3(singleton(u),unordered_pair(v,singleton(u))),singleton(u))
| equal(skf3(singleton(u),unordered_pair(singleton(u),v)),empty_set)
| equal(skf3(singleton(u),unordered_pair(singleton(u),v)),v)
| equal(unordered_pair(v,singleton(u)),powerset(singleton(u))) ),
inference(obv,[status(thm),theory(equality)],[2315]),
[iquote('0:Obv:2315.1')] ).
cnf(2344,plain,
( ~ equal(singleton(u),singleton(u))
| equal(skf3(singleton(u),unordered_pair(singleton(u),v)),empty_set)
| equal(skf3(singleton(u),unordered_pair(singleton(u),v)),v)
| equal(unordered_pair(v,singleton(u)),powerset(singleton(u))) ),
inference(rew,[status(thm),theory(equality)],[2290,2343]),
[iquote('0:Rew:2290.2,2343.0')] ).
cnf(2345,plain,
( equal(skf3(singleton(u),unordered_pair(singleton(u),v)),empty_set)
| equal(skf3(singleton(u),unordered_pair(singleton(u),v)),v)
| equal(unordered_pair(v,singleton(u)),powerset(singleton(u))) ),
inference(obv,[status(thm),theory(equality)],[2344]),
[iquote('0:Obv:2344.0')] ).
cnf(23127,plain,
( equal(skf3(singleton(u),unordered_pair(singleton(u),empty_set)),empty_set)
| equal(unordered_pair(empty_set,singleton(u)),powerset(singleton(u))) ),
inference(fac,[status(thm)],[2345]),
[iquote('0:Fac:2345.0,2345.1')] ).
cnf(23228,plain,
( equal(skf3(singleton(u),unordered_pair(empty_set,singleton(u))),empty_set)
| equal(unordered_pair(empty_set,singleton(u)),powerset(singleton(u))) ),
inference(rew,[status(thm),theory(equality)],[5,23127]),
[iquote('0:Rew:5.0,23127.0')] ).
cnf(28338,plain,
( ~ equal(empty_set,empty_set)
| ~ equal(skf3(singleton(u),unordered_pair(empty_set,singleton(u))),empty_set)
| equal(unordered_pair(empty_set,singleton(u)),powerset(singleton(u)))
| equal(unordered_pair(empty_set,singleton(u)),powerset(singleton(u))) ),
inference(spl,[status(thm),theory(equality)],[23228,173]),
[iquote('0:SpL:23228.0,173.0')] ).
cnf(28344,plain,
( ~ equal(skf3(singleton(u),unordered_pair(empty_set,singleton(u))),empty_set)
| equal(unordered_pair(empty_set,singleton(u)),powerset(singleton(u))) ),
inference(obv,[status(thm),theory(equality)],[28338]),
[iquote('0:Obv:28338.2')] ).
cnf(28345,plain,
( ~ equal(empty_set,empty_set)
| equal(unordered_pair(empty_set,singleton(u)),powerset(singleton(u))) ),
inference(rew,[status(thm),theory(equality)],[23228,28344]),
[iquote('0:Rew:23228.0,28344.0')] ).
cnf(28346,plain,
equal(unordered_pair(empty_set,singleton(u)),powerset(singleton(u))),
inference(obv,[status(thm),theory(equality)],[28345]),
[iquote('0:Obv:28345.0')] ).
cnf(28347,plain,
$false,
inference(unc,[status(thm)],[28346,8]),
[iquote('0:UnC:28346.0,8.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SET889+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.00/0.07 % Command : run_spass %d %s
% 0.06/0.25 % Computer : n013.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 600
% 0.06/0.25 % DateTime : Sun Jul 10 04:09:44 EDT 2022
% 0.06/0.25 % CPUTime :
% 49.97/50.15
% 49.97/50.15 SPASS V 3.9
% 49.97/50.15 SPASS beiseite: Proof found.
% 49.97/50.15 % SZS status Theorem
% 49.97/50.15 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 49.97/50.15 SPASS derived 21046 clauses, backtracked 0 clauses, performed 0 splits and kept 4778 clauses.
% 49.97/50.15 SPASS allocated 106402 KBytes.
% 49.97/50.15 SPASS spent 0:0:47.59 on the problem.
% 49.97/50.15 0:00:00.02 for the input.
% 49.97/50.15 0:00:00.02 for the FLOTTER CNF translation.
% 49.97/50.15 0:00:00.49 for inferences.
% 49.97/50.15 0:00:00.00 for the backtracking.
% 49.97/50.15 0:0:46.98 for the reduction.
% 49.97/50.15
% 49.97/50.15
% 49.97/50.15 Here is a proof with depth 6, length 32 :
% 49.97/50.15 % SZS output start Refutation
% See solution above
% 49.97/50.15 Formulae used in the proof : commutativity_k2_tarski l4_zfmisc_1 t30_zfmisc_1 d1_zfmisc_1 reflexivity_r1_tarski d2_tarski antisymmetry_r2_hidden
% 49.97/50.15
%------------------------------------------------------------------------------