TSTP Solution File: SET986+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET986+1 : TPTP v8.1.0. Released v3.2.0.
% 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 05:30:14 EDT 2022
% Result : Theorem 0.20s 0.59s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of clauses : 34 ( 11 unt; 10 nHn; 34 RR)
% Number of literals : 69 ( 0 equ; 29 neg)
% Maximal clause size : 4 ( 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; 5 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
in(skc4,skc5),
file('SET986+1.p',unknown),
[] ).
cnf(6,axiom,
equal(set_union2(u,v),set_union2(v,u)),
file('SET986+1.p',unknown),
[] ).
cnf(12,axiom,
( subset(u,v)
| in(skf6(v,u),u) ),
file('SET986+1.p',unknown),
[] ).
cnf(14,axiom,
~ equal(set_union2(set_difference(skc5,singleton(skc4)),singleton(skc4)),skc5),
file('SET986+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ in(u,set_difference(v,singleton(w)))
| in(u,v) ),
file('SET986+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ in(u,v)
| ~ subset(v,w)
| in(u,w) ),
file('SET986+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ in(u,v)
| ~ equal(v,singleton(w))
| equal(u,w) ),
file('SET986+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ equal(u,v)
| ~ equal(w,singleton(v))
| in(u,w) ),
file('SET986+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ in(u,v)
| equal(u,w)
| in(u,set_difference(v,singleton(w))) ),
file('SET986+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ in(skf5(u,v,w),w)
| ~ in(skf5(u,v,w),v)
| equal(w,set_union2(v,u)) ),
file('SET986+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ in(skf5(u,v,w),w)
| ~ in(skf5(u,v,w),u)
| equal(w,set_union2(v,u)) ),
file('SET986+1.p',unknown),
[] ).
cnf(34,axiom,
( equal(u,set_union2(v,w))
| in(skf5(w,v,u),w)
| in(skf5(w,v,u),v)
| in(skf5(w,v,u),u) ),
file('SET986+1.p',unknown),
[] ).
cnf(36,plain,
~ equal(set_union2(singleton(skc4),set_difference(skc5,singleton(skc4))),skc5),
inference(rew,[status(thm),theory(equality)],[6,14]),
[iquote('0:Rew:6.0,14.0')] ).
cnf(55,plain,
( in(skf5(set_difference(skc5,singleton(skc4)),singleton(skc4),skc5),skc5)
| in(skf5(set_difference(skc5,singleton(skc4)),singleton(skc4),skc5),singleton(skc4))
| in(skf5(set_difference(skc5,singleton(skc4)),singleton(skc4),skc5),set_difference(skc5,singleton(skc4))) ),
inference(res,[status(thm),theory(equality)],[34,36]),
[iquote('0:Res:34.3,36.0')] ).
cnf(56,plain,
( ~ in(skf5(set_difference(skc5,singleton(skc4)),singleton(skc4),skc5),skc5)
| ~ in(skf5(set_difference(skc5,singleton(skc4)),singleton(skc4),skc5),singleton(skc4)) ),
inference(res,[status(thm),theory(equality)],[32,36]),
[iquote('0:Res:32.2,36.0')] ).
cnf(57,plain,
( ~ in(skf5(set_difference(skc5,singleton(skc4)),singleton(skc4),skc5),set_difference(skc5,singleton(skc4)))
| ~ in(skf5(set_difference(skc5,singleton(skc4)),singleton(skc4),skc5),skc5) ),
inference(res,[status(thm),theory(equality)],[33,36]),
[iquote('0:Res:33.2,36.0')] ).
cnf(58,plain,
~ in(skf5(set_difference(skc5,singleton(skc4)),singleton(skc4),skc5),set_difference(skc5,singleton(skc4))),
inference(mrr,[status(thm)],[57,15]),
[iquote('0:MRR:57.1,15.1')] ).
cnf(59,plain,
( in(skf5(set_difference(skc5,singleton(skc4)),singleton(skc4),skc5),skc5)
| in(skf5(set_difference(skc5,singleton(skc4)),singleton(skc4),skc5),singleton(skc4)) ),
inference(mrr,[status(thm)],[55,58]),
[iquote('0:MRR:55.2,58.0')] ).
cnf(126,plain,
( ~ equal(u,v)
| in(u,singleton(v)) ),
inference(eqr,[status(thm),theory(equality)],[20]),
[iquote('0:EqR:20.1')] ).
cnf(127,plain,
( ~ equal(u,v)
| ~ subset(singleton(v),w)
| in(u,w) ),
inference(res,[status(thm),theory(equality)],[126,17]),
[iquote('0:Res:126.1,17.0')] ).
cnf(141,plain,
( ~ in(u,singleton(v))
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[19]),
[iquote('0:EqR:19.1')] ).
cnf(144,plain,
( subset(singleton(u),v)
| equal(skf6(v,singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[12,141]),
[iquote('0:Res:12.1,141.0')] ).
cnf(146,plain,
( subset(singleton(u),v)
| subset(singleton(u),v)
| in(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[144,12]),
[iquote('0:SpR:144.1,12.1')] ).
cnf(151,plain,
( subset(singleton(u),v)
| in(u,singleton(u)) ),
inference(obv,[status(thm),theory(equality)],[146]),
[iquote('0:Obv:146.0')] ).
cnf(881,plain,
( ~ equal(u,v)
| in(v,singleton(v))
| in(u,w) ),
inference(res,[status(thm),theory(equality)],[151,127]),
[iquote('0:Res:151.0,127.1')] ).
cnf(884,plain,
( in(u,singleton(u))
| in(u,v) ),
inference(eqr,[status(thm),theory(equality)],[881]),
[iquote('0:EqR:881.0')] ).
cnf(885,plain,
in(u,singleton(u)),
inference(con,[status(thm)],[884]),
[iquote('0:Con:884.1')] ).
cnf(969,plain,
( ~ in(skf5(set_difference(skc5,singleton(skc4)),singleton(skc4),skc5),skc5)
| equal(skf5(set_difference(skc5,singleton(skc4)),singleton(skc4),skc5),skc4) ),
inference(res,[status(thm),theory(equality)],[24,58]),
[iquote('0:Res:24.2,58.0')] ).
cnf(973,plain,
( ~ in(skf5(set_difference(skc5,singleton(skc4)),singleton(skc4),skc5),skc5)
| ~ in(skc4,singleton(skc4)) ),
inference(rew,[status(thm),theory(equality)],[969,56]),
[iquote('0:Rew:969.1,56.1')] ).
cnf(974,plain,
~ in(skf5(set_difference(skc5,singleton(skc4)),singleton(skc4),skc5),skc5),
inference(mrr,[status(thm)],[973,885]),
[iquote('0:MRR:973.1,885.0')] ).
cnf(975,plain,
in(skf5(set_difference(skc5,singleton(skc4)),singleton(skc4),skc5),singleton(skc4)),
inference(mrr,[status(thm)],[59,974]),
[iquote('0:MRR:59.0,974.0')] ).
cnf(1049,plain,
equal(skf5(set_difference(skc5,singleton(skc4)),singleton(skc4),skc5),skc4),
inference(res,[status(thm),theory(equality)],[975,141]),
[iquote('0:Res:975.0,141.0')] ).
cnf(1051,plain,
~ in(skc4,skc5),
inference(rew,[status(thm),theory(equality)],[1049,974]),
[iquote('0:Rew:1049.0,974.0')] ).
cnf(1055,plain,
$false,
inference(mrr,[status(thm)],[1051,2]),
[iquote('0:MRR:1051.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET986+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n012.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat Jul 9 19:58:28 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.59
% 0.20/0.59 SPASS V 3.9
% 0.20/0.59 SPASS beiseite: Proof found.
% 0.20/0.59 % SZS status Theorem
% 0.20/0.59 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.59 SPASS derived 986 clauses, backtracked 1 clauses, performed 1 splits and kept 481 clauses.
% 0.20/0.59 SPASS allocated 86116 KBytes.
% 0.20/0.59 SPASS spent 0:00:00.24 on the problem.
% 0.20/0.59 0:00:00.03 for the input.
% 0.20/0.59 0:00:00.05 for the FLOTTER CNF translation.
% 0.20/0.59 0:00:00.01 for inferences.
% 0.20/0.59 0:00:00.00 for the backtracking.
% 0.20/0.59 0:00:00.11 for the reduction.
% 0.20/0.59
% 0.20/0.59
% 0.20/0.59 Here is a proof with depth 5, length 34 :
% 0.20/0.59 % SZS output start Refutation
% See solution above
% 0.20/0.59 Formulae used in the proof : t140_zfmisc_1 commutativity_k2_xboole_0 d3_tarski t64_zfmisc_1 d1_tarski d2_xboole_0
% 0.20/0.59
%------------------------------------------------------------------------------