TSTP Solution File: SET992+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET992+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 05:30:17 EDT 2022
% Result : Theorem 0.18s 0.52s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of clauses : 41 ( 16 unt; 6 nHn; 41 RR)
% Number of literals : 85 ( 0 equ; 46 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
function(skc8),
file('SET992+1.p',unknown),
[] ).
cnf(2,axiom,
relation(skc8),
file('SET992+1.p',unknown),
[] ).
cnf(21,axiom,
element(skf13(u),u),
file('SET992+1.p',unknown),
[] ).
cnf(23,axiom,
~ empty(singleton(u)),
file('SET992+1.p',unknown),
[] ).
cnf(24,axiom,
equal(relation_dom(skc8),singleton(skc9)),
file('SET992+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ empty(u)
| empty(relation_dom(u)) ),
file('SET992+1.p',unknown),
[] ).
cnf(37,axiom,
~ equal(singleton(apply(skc8,skc9)),relation_rng(skc8)),
file('SET992+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ relation(u)
| ~ empty(relation_rng(u))
| empty(u) ),
file('SET992+1.p',unknown),
[] ).
cnf(43,axiom,
( ~ element(u,v)
| empty(v)
| in(u,v) ),
file('SET992+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ equal(skf8(u,v),u)
| ~ in(skf8(u,v),v) ),
file('SET992+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ in(u,v)
| ~ equal(v,singleton(w))
| equal(u,w) ),
file('SET992+1.p',unknown),
[] ).
cnf(52,axiom,
( equal(u,singleton(v))
| equal(skf8(v,u),v)
| in(skf8(v,u),u) ),
file('SET992+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,w)
| ~ equal(w,relation_rng(u))
| in(skf9(u,x),relation_dom(u)) ),
file('SET992+1.p',unknown),
[] ).
cnf(56,axiom,
( ~ function(u)
| ~ relation(u)
| ~ in(v,w)
| ~ equal(w,relation_rng(u))
| equal(apply(u,skf9(u,v)),v) ),
file('SET992+1.p',unknown),
[] ).
cnf(61,plain,
( ~ function(skc8)
| ~ in(u,v)
| ~ equal(v,relation_rng(skc8))
| equal(apply(skc8,skf9(skc8,u)),u) ),
inference(res,[status(thm),theory(equality)],[2,56]),
[iquote('0:Res:2.0,56.0')] ).
cnf(62,plain,
( ~ function(skc8)
| ~ in(u,v)
| ~ equal(v,relation_rng(skc8))
| in(skf9(skc8,w),relation_dom(skc8)) ),
inference(res,[status(thm),theory(equality)],[2,55]),
[iquote('0:Res:2.0,55.0')] ).
cnf(65,plain,
( ~ empty(relation_rng(skc8))
| empty(skc8) ),
inference(res,[status(thm),theory(equality)],[2,42]),
[iquote('0:Res:2.0,42.0')] ).
cnf(80,plain,
( in(skf8(apply(skc8,skc9),relation_rng(skc8)),relation_rng(skc8))
| equal(skf8(apply(skc8,skc9),relation_rng(skc8)),apply(skc8,skc9)) ),
inference(res,[status(thm),theory(equality)],[52,37]),
[iquote('0:Res:52.2,37.0')] ).
cnf(87,plain,
( ~ function(skc8)
| ~ in(u,v)
| ~ equal(v,relation_rng(skc8))
| in(skf9(skc8,w),singleton(skc9)) ),
inference(rew,[status(thm),theory(equality)],[24,62]),
[iquote('0:Rew:24.0,62.3')] ).
cnf(88,plain,
( ~ in(u,v)
| ~ equal(v,relation_rng(skc8))
| in(skf9(skc8,w),singleton(skc9)) ),
inference(mrr,[status(thm)],[87,1]),
[iquote('0:MRR:87.0,1.0')] ).
cnf(93,plain,
( ~ in(u,v)
| ~ equal(v,relation_rng(skc8))
| equal(apply(skc8,skf9(skc8,u)),u) ),
inference(mrr,[status(thm)],[61,1]),
[iquote('0:MRR:61.0,1.0')] ).
cnf(120,plain,
( ~ empty(skc8)
| empty(singleton(skc9)) ),
inference(spr,[status(thm),theory(equality)],[24,29]),
[iquote('0:SpR:24.0,29.1')] ).
cnf(121,plain,
~ empty(skc8),
inference(mrr,[status(thm)],[120,23]),
[iquote('0:MRR:120.1,23.0')] ).
cnf(122,plain,
~ empty(relation_rng(skc8)),
inference(mrr,[status(thm)],[65,121]),
[iquote('0:MRR:65.1,121.0')] ).
cnf(174,plain,
( empty(u)
| in(skf13(u),u) ),
inference(res,[status(thm),theory(equality)],[21,43]),
[iquote('0:Res:21.0,43.0')] ).
cnf(208,plain,
( ~ in(u,singleton(v))
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[46]),
[iquote('0:EqR:46.1')] ).
cnf(825,plain,
( ~ in(u,relation_rng(skc8))
| in(skf9(skc8,v),singleton(skc9)) ),
inference(eqr,[status(thm),theory(equality)],[88]),
[iquote('0:EqR:88.1')] ).
cnf(873,plain,
( empty(relation_rng(skc8))
| in(skf9(skc8,u),singleton(skc9)) ),
inference(res,[status(thm),theory(equality)],[174,825]),
[iquote('0:Res:174.1,825.0')] ).
cnf(884,plain,
in(skf9(skc8,u),singleton(skc9)),
inference(mrr,[status(thm)],[873,122]),
[iquote('0:MRR:873.0,122.0')] ).
cnf(887,plain,
equal(skf9(skc8,u),skc9),
inference(res,[status(thm),theory(equality)],[884,208]),
[iquote('0:Res:884.0,208.0')] ).
cnf(889,plain,
( ~ in(u,v)
| ~ equal(v,relation_rng(skc8))
| equal(apply(skc8,skc9),u) ),
inference(rew,[status(thm),theory(equality)],[887,93]),
[iquote('0:Rew:887.0,93.2')] ).
cnf(892,plain,
( ~ in(u,relation_rng(skc8))
| equal(apply(skc8,skc9),u) ),
inference(eqr,[status(thm),theory(equality)],[889]),
[iquote('0:EqR:889.1')] ).
cnf(894,plain,
equal(skf8(apply(skc8,skc9),relation_rng(skc8)),apply(skc8,skc9)),
inference(mrr,[status(thm)],[80,892]),
[iquote('0:MRR:80.0,892.0')] ).
cnf(899,plain,
( ~ equal(skf8(apply(skc8,skc9),relation_rng(skc8)),apply(skc8,skc9))
| ~ in(apply(skc8,skc9),relation_rng(skc8)) ),
inference(spl,[status(thm),theory(equality)],[894,45]),
[iquote('0:SpL:894.0,45.1')] ).
cnf(901,plain,
( ~ equal(apply(skc8,skc9),apply(skc8,skc9))
| ~ in(apply(skc8,skc9),relation_rng(skc8)) ),
inference(rew,[status(thm),theory(equality)],[894,899]),
[iquote('0:Rew:894.0,899.0')] ).
cnf(902,plain,
~ in(apply(skc8,skc9),relation_rng(skc8)),
inference(obv,[status(thm),theory(equality)],[901]),
[iquote('0:Obv:901.0')] ).
cnf(910,plain,
( empty(relation_rng(skc8))
| equal(apply(skc8,skc9),skf13(relation_rng(skc8))) ),
inference(res,[status(thm),theory(equality)],[174,892]),
[iquote('0:Res:174.1,892.0')] ).
cnf(921,plain,
equal(apply(skc8,skc9),skf13(relation_rng(skc8))),
inference(mrr,[status(thm)],[910,122]),
[iquote('0:MRR:910.0,122.0')] ).
cnf(928,plain,
~ in(skf13(relation_rng(skc8)),relation_rng(skc8)),
inference(rew,[status(thm),theory(equality)],[921,902]),
[iquote('0:Rew:921.0,902.0')] ).
cnf(963,plain,
empty(relation_rng(skc8)),
inference(res,[status(thm),theory(equality)],[174,928]),
[iquote('0:Res:174.1,928.0')] ).
cnf(964,plain,
$false,
inference(mrr,[status(thm)],[963,122]),
[iquote('0:MRR:963.0,122.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET992+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n009.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 : Sun Jul 10 05:31:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.52
% 0.18/0.52 SPASS V 3.9
% 0.18/0.52 SPASS beiseite: Proof found.
% 0.18/0.52 % SZS status Theorem
% 0.18/0.52 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.52 SPASS derived 743 clauses, backtracked 2 clauses, performed 1 splits and kept 408 clauses.
% 0.18/0.52 SPASS allocated 98386 KBytes.
% 0.18/0.52 SPASS spent 0:00:00.18 on the problem.
% 0.18/0.52 0:00:00.03 for the input.
% 0.18/0.52 0:00:00.05 for the FLOTTER CNF translation.
% 0.18/0.52 0:00:00.01 for inferences.
% 0.18/0.52 0:00:00.00 for the backtracking.
% 0.18/0.52 0:00:00.06 for the reduction.
% 0.18/0.52
% 0.18/0.52
% 0.18/0.52 Here is a proof with depth 4, length 41 :
% 0.18/0.52 % SZS output start Refutation
% See solution above
% 0.18/0.52 Formulae used in the proof : t14_funct_1 existence_m1_subset_1 fc2_subset_1 fc7_relat_1 fc6_relat_1 t2_subset d1_tarski antisymmetry_r2_hidden d5_funct_1
% 0.18/0.52
%------------------------------------------------------------------------------