TSTP Solution File: SEU262+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU262+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 14:35:38 EDT 2022
% Result : Theorem 0.20s 0.64s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of clauses : 35 ( 7 unt; 7 nHn; 35 RR)
% Number of literals : 75 ( 0 equ; 37 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
relation_of2_as_subset(skc7,skc5,skc6),
file('SEU262+1.p',unknown),
[] ).
cnf(15,axiom,
( subset(u,v)
| in(skf10(v,u),u) ),
file('SEU262+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ element(u,powerset(cartesian_product2(v,w)))
| relation(u) ),
file('SEU262+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ in(skf10(u,v),u)
| subset(w,u) ),
file('SEU262+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ element(u,v)
| empty(v)
| in(u,v) ),
file('SEU262+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ subset(relation_rng(skc7),skc6)
| ~ subset(relation_dom(skc7),skc5) ),
file('SEU262+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ relation_of2_as_subset(u,v,w)
| element(u,powerset(cartesian_product2(v,w))) ),
file('SEU262+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ in(ordered_pair(u,v),cartesian_product2(w,x))
| in(u,w) ),
file('SEU262+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ in(ordered_pair(u,v),cartesian_product2(w,x))
| in(v,x) ),
file('SEU262+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ in(u,v)
| ~ element(v,powerset(w))
| element(u,w) ),
file('SEU262+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ empty(u)
| ~ in(v,w)
| ~ element(w,powerset(u)) ),
file('SEU262+1.p',unknown),
[] ).
cnf(35,axiom,
( ~ relation(u)
| ~ in(v,w)
| ~ equal(w,relation_dom(u))
| in(ordered_pair(v,skf11(u,v)),u) ),
file('SEU262+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ relation(u)
| ~ in(v,w)
| ~ equal(w,relation_rng(u))
| in(ordered_pair(skf15(u,v),v),u) ),
file('SEU262+1.p',unknown),
[] ).
cnf(42,plain,
element(skc7,powerset(cartesian_product2(skc5,skc6))),
inference(res,[status(thm),theory(equality)],[5,27]),
[iquote('0:Res:5.0,27.0')] ).
cnf(61,plain,
relation(skc7),
inference(res,[status(thm),theory(equality)],[42,18]),
[iquote('0:Res:42.0,18.0')] ).
cnf(152,plain,
( ~ empty(cartesian_product2(skc5,skc6))
| ~ in(u,skc7) ),
inference(res,[status(thm),theory(equality)],[42,31]),
[iquote('0:Res:42.0,31.2')] ).
cnf(166,plain,
( ~ in(u,skc7)
| element(u,cartesian_product2(skc5,skc6)) ),
inference(res,[status(thm),theory(equality)],[42,30]),
[iquote('0:Res:42.0,30.1')] ).
cnf(203,plain,
( ~ in(u,skc7)
| empty(cartesian_product2(skc5,skc6))
| in(u,cartesian_product2(skc5,skc6)) ),
inference(res,[status(thm),theory(equality)],[166,22]),
[iquote('0:Res:166.1,22.0')] ).
cnf(204,plain,
( ~ in(u,skc7)
| in(u,cartesian_product2(skc5,skc6)) ),
inference(mrr,[status(thm)],[203,152]),
[iquote('0:MRR:203.1,152.0')] ).
cnf(218,plain,
( ~ in(ordered_pair(u,v),skc7)
| in(u,skc5) ),
inference(res,[status(thm),theory(equality)],[204,28]),
[iquote('0:Res:204.1,28.0')] ).
cnf(219,plain,
( ~ in(ordered_pair(u,v),skc7)
| in(v,skc6) ),
inference(res,[status(thm),theory(equality)],[204,29]),
[iquote('0:Res:204.1,29.0')] ).
cnf(248,plain,
( ~ relation(u)
| ~ in(v,relation_rng(u))
| in(ordered_pair(skf15(u,v),v),u) ),
inference(eqr,[status(thm),theory(equality)],[36]),
[iquote('0:EqR:36.2')] ).
cnf(256,plain,
( ~ relation(u)
| ~ in(v,relation_dom(u))
| in(ordered_pair(v,skf11(u,v)),u) ),
inference(eqr,[status(thm),theory(equality)],[35]),
[iquote('0:EqR:35.2')] ).
cnf(851,plain,
( ~ relation(skc7)
| ~ in(u,relation_rng(skc7))
| in(u,skc6) ),
inference(res,[status(thm),theory(equality)],[248,219]),
[iquote('0:Res:248.2,219.0')] ).
cnf(857,plain,
( ~ in(u,relation_rng(skc7))
| in(u,skc6) ),
inference(ssi,[status(thm)],[851,61]),
[iquote('0:SSi:851.0,61.0')] ).
cnf(886,plain,
( subset(relation_rng(skc7),u)
| in(skf10(u,relation_rng(skc7)),skc6) ),
inference(res,[status(thm),theory(equality)],[15,857]),
[iquote('0:Res:15.1,857.0')] ).
cnf(918,plain,
( ~ relation(skc7)
| ~ in(u,relation_dom(skc7))
| in(u,skc5) ),
inference(res,[status(thm),theory(equality)],[256,218]),
[iquote('0:Res:256.2,218.0')] ).
cnf(923,plain,
( ~ in(u,relation_dom(skc7))
| in(u,skc5) ),
inference(ssi,[status(thm)],[918,61]),
[iquote('0:SSi:918.0,61.0')] ).
cnf(952,plain,
( subset(relation_dom(skc7),u)
| in(skf10(u,relation_dom(skc7)),skc5) ),
inference(res,[status(thm),theory(equality)],[15,923]),
[iquote('0:Res:15.1,923.0')] ).
cnf(1378,plain,
( subset(relation_dom(skc7),skc5)
| subset(u,skc5) ),
inference(res,[status(thm),theory(equality)],[952,19]),
[iquote('0:Res:952.1,19.0')] ).
cnf(1382,plain,
subset(relation_dom(skc7),skc5),
inference(con,[status(thm)],[1378]),
[iquote('0:Con:1378.1')] ).
cnf(1394,plain,
~ subset(relation_rng(skc7),skc6),
inference(mrr,[status(thm)],[24,1382]),
[iquote('0:MRR:24.1,1382.0')] ).
cnf(1617,plain,
( subset(relation_rng(skc7),skc6)
| subset(u,skc6) ),
inference(res,[status(thm),theory(equality)],[886,19]),
[iquote('0:Res:886.1,19.0')] ).
cnf(1621,plain,
subset(relation_rng(skc7),skc6),
inference(con,[status(thm)],[1617]),
[iquote('0:Con:1617.1')] ).
cnf(1622,plain,
$false,
inference(mrr,[status(thm)],[1621,1394]),
[iquote('0:MRR:1621.0,1394.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU262+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n006.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 : Mon Jun 20 13:00:55 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.64
% 0.20/0.64 SPASS V 3.9
% 0.20/0.64 SPASS beiseite: Proof found.
% 0.20/0.64 % SZS status Theorem
% 0.20/0.64 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.64 SPASS derived 1285 clauses, backtracked 63 clauses, performed 4 splits and kept 663 clauses.
% 0.20/0.64 SPASS allocated 99034 KBytes.
% 0.20/0.64 SPASS spent 0:00:00.28 on the problem.
% 0.20/0.64 0:00:00.03 for the input.
% 0.20/0.64 0:00:00.05 for the FLOTTER CNF translation.
% 0.20/0.64 0:00:00.02 for inferences.
% 0.20/0.64 0:00:00.00 for the backtracking.
% 0.20/0.64 0:00:00.15 for the reduction.
% 0.20/0.64
% 0.20/0.64
% 0.20/0.64 Here is a proof with depth 7, length 35 :
% 0.20/0.64 % SZS output start Refutation
% See solution above
% 0.20/0.64 Formulae used in the proof : t12_relset_1 d3_tarski cc1_relset_1 t2_subset dt_m2_relset_1 t106_zfmisc_1 t4_subset t5_subset d4_relat_1 d5_relat_1
% 0.20/0.64
%------------------------------------------------------------------------------