TSTP Solution File: SEU153+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU153+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 14:34:25 EDT 2022
% Result : Theorem 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of clauses : 44 ( 12 unt; 7 nHn; 44 RR)
% Number of literals : 90 ( 0 equ; 45 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
in(skc4,skc5),
file('SEU153+1.p',unknown),
[] ).
cnf(5,axiom,
disjoint(singleton(skc4),skc5),
file('SEU153+1.p',unknown),
[] ).
cnf(7,axiom,
equal(set_intersection2(u,v),set_intersection2(v,u)),
file('SEU153+1.p',unknown),
[] ).
cnf(8,axiom,
( equal(u,empty_set)
| in(skf4(u),u) ),
file('SEU153+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ in(u,v)
| ~ equal(v,empty_set) ),
file('SEU153+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ disjoint(u,v)
| equal(set_intersection2(u,v),empty_set) ),
file('SEU153+1.p',unknown),
[] ).
cnf(14,axiom,
( equal(skf3(u,v),u)
| in(skf3(u,v),v) ),
file('SEU153+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ in(u,v)
| ~ equal(v,singleton(w))
| equal(u,w) ),
file('SEU153+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ equal(u,v)
| ~ equal(w,singleton(v))
| in(u,w) ),
file('SEU153+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ in(u,v)
| ~ equal(v,set_intersection2(w,x))
| in(u,x) ),
file('SEU153+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ equal(skf3(u,v),u)
| ~ in(skf3(u,v),v)
| equal(v,singleton(u)) ),
file('SEU153+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ in(u,v)
| ~ in(u,w)
| ~ equal(x,set_intersection2(w,v))
| in(u,x) ),
file('SEU153+1.p',unknown),
[] ).
cnf(26,plain,
( ~ equal(u,set_intersection2(skc5,v))
| ~ in(skc4,v)
| in(skc4,u) ),
inference(res,[status(thm),theory(equality)],[3,20]),
[iquote('0:Res:3.0,20.0')] ).
cnf(58,plain,
( ~ disjoint(u,v)
| equal(set_intersection2(v,u),empty_set) ),
inference(spr,[status(thm),theory(equality)],[12,7]),
[iquote('0:SpR:12.1,7.0')] ).
cnf(100,plain,
( ~ equal(u,v)
| in(u,singleton(v)) ),
inference(eqr,[status(thm),theory(equality)],[16]),
[iquote('0:EqR:16.1')] ).
cnf(102,plain,
( ~ equal(u,v)
| ~ equal(singleton(v),empty_set) ),
inference(res,[status(thm),theory(equality)],[100,11]),
[iquote('0:Res:100.1,11.0')] ).
cnf(103,plain,
~ equal(singleton(u),empty_set),
inference(aed,[status(thm),theory(equality)],[102]),
[iquote('0:AED:102.0')] ).
cnf(106,plain,
( ~ in(u,singleton(v))
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[15]),
[iquote('0:EqR:15.1')] ).
cnf(107,plain,
( equal(singleton(u),empty_set)
| equal(skf4(singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[8,106]),
[iquote('0:Res:8.1,106.0')] ).
cnf(111,plain,
equal(skf4(singleton(u)),u),
inference(mrr,[status(thm)],[107,103]),
[iquote('0:MRR:107.0,103.0')] ).
cnf(112,plain,
( equal(singleton(u),empty_set)
| in(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[111,8]),
[iquote('0:SpR:111.0,8.1')] ).
cnf(115,plain,
in(u,singleton(u)),
inference(mrr,[status(thm)],[112,103]),
[iquote('0:MRR:112.0,103.0')] ).
cnf(121,plain,
( ~ in(u,set_intersection2(v,w))
| in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[18]),
[iquote('0:EqR:18.1')] ).
cnf(129,plain,
( ~ disjoint(u,v)
| ~ in(w,empty_set)
| in(w,u) ),
inference(spl,[status(thm),theory(equality)],[58,121]),
[iquote('0:SpL:58.1,121.0')] ).
cnf(144,plain,
( ~ in(u,empty_set)
| in(u,singleton(skc4)) ),
inference(res,[status(thm),theory(equality)],[5,129]),
[iquote('0:Res:5.0,129.0')] ).
cnf(161,plain,
( ~ in(u,empty_set)
| equal(u,skc4) ),
inference(res,[status(thm),theory(equality)],[144,106]),
[iquote('0:Res:144.1,106.0')] ).
cnf(169,plain,
( equal(skf3(u,empty_set),u)
| equal(skf3(u,empty_set),skc4) ),
inference(res,[status(thm),theory(equality)],[14,161]),
[iquote('0:Res:14.1,161.0')] ).
cnf(189,plain,
equal(skf3(skc4,empty_set),skc4),
inference(fac,[status(thm)],[169]),
[iquote('0:Fac:169.0,169.1')] ).
cnf(194,plain,
( equal(skf3(u,empty_set),u)
| equal(skf3(u,empty_set),u)
| in(skc4,empty_set) ),
inference(spr,[status(thm),theory(equality)],[169,14]),
[iquote('0:SpR:169.1,14.1')] ).
cnf(204,plain,
( equal(skf3(u,empty_set),u)
| in(skc4,empty_set) ),
inference(obv,[status(thm),theory(equality)],[194]),
[iquote('0:Obv:194.0')] ).
cnf(212,plain,
( ~ equal(skf3(skc4,empty_set),skc4)
| ~ in(skc4,empty_set)
| equal(singleton(skc4),empty_set) ),
inference(spl,[status(thm),theory(equality)],[189,19]),
[iquote('0:SpL:189.0,19.1')] ).
cnf(214,plain,
( ~ equal(skc4,skc4)
| ~ in(skc4,empty_set)
| equal(singleton(skc4),empty_set) ),
inference(rew,[status(thm),theory(equality)],[189,212]),
[iquote('0:Rew:189.0,212.0')] ).
cnf(215,plain,
( ~ in(skc4,empty_set)
| equal(singleton(skc4),empty_set) ),
inference(obv,[status(thm),theory(equality)],[214]),
[iquote('0:Obv:214.0')] ).
cnf(216,plain,
~ in(skc4,empty_set),
inference(mrr,[status(thm)],[215,103]),
[iquote('0:MRR:215.1,103.0')] ).
cnf(217,plain,
equal(skf3(u,empty_set),u),
inference(mrr,[status(thm)],[204,216]),
[iquote('0:MRR:204.1,216.0')] ).
cnf(243,plain,
( ~ equal(skf3(u,empty_set),u)
| ~ in(u,empty_set)
| equal(singleton(u),empty_set) ),
inference(spl,[status(thm),theory(equality)],[217,19]),
[iquote('0:SpL:217.0,19.1')] ).
cnf(245,plain,
( ~ equal(u,u)
| ~ in(u,empty_set)
| equal(singleton(u),empty_set) ),
inference(rew,[status(thm),theory(equality)],[217,243]),
[iquote('0:Rew:217.0,243.0')] ).
cnf(246,plain,
( ~ in(u,empty_set)
| equal(singleton(u),empty_set) ),
inference(obv,[status(thm),theory(equality)],[245]),
[iquote('0:Obv:245.0')] ).
cnf(247,plain,
~ in(u,empty_set),
inference(mrr,[status(thm)],[246,103]),
[iquote('0:MRR:246.1,103.0')] ).
cnf(494,plain,
( ~ in(skc4,u)
| in(skc4,set_intersection2(skc5,u)) ),
inference(eqr,[status(thm),theory(equality)],[26]),
[iquote('0:EqR:26.0')] ).
cnf(507,plain,
( ~ disjoint(u,skc5)
| ~ in(skc4,u)
| in(skc4,empty_set) ),
inference(spr,[status(thm),theory(equality)],[58,494]),
[iquote('0:SpR:58.1,494.1')] ).
cnf(519,plain,
( ~ disjoint(u,skc5)
| ~ in(skc4,u) ),
inference(mrr,[status(thm)],[507,247]),
[iquote('0:MRR:507.2,247.0')] ).
cnf(526,plain,
~ disjoint(singleton(skc4),skc5),
inference(res,[status(thm),theory(equality)],[115,519]),
[iquote('0:Res:115.0,519.1')] ).
cnf(527,plain,
$false,
inference(mrr,[status(thm)],[526,5]),
[iquote('0:MRR:526.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU153+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n023.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 : Sat Jun 18 21:37:19 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.48
% 0.18/0.48 SPASS V 3.9
% 0.18/0.48 SPASS beiseite: Proof found.
% 0.18/0.48 % SZS status Theorem
% 0.18/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.48 SPASS derived 440 clauses, backtracked 0 clauses, performed 0 splits and kept 212 clauses.
% 0.18/0.48 SPASS allocated 85453 KBytes.
% 0.18/0.48 SPASS spent 0:00:00.14 on the problem.
% 0.18/0.48 0:00:00.04 for the input.
% 0.18/0.48 0:00:00.04 for the FLOTTER CNF translation.
% 0.18/0.48 0:00:00.01 for inferences.
% 0.18/0.48 0:00:00.00 for the backtracking.
% 0.18/0.48 0:00:00.03 for the reduction.
% 0.18/0.48
% 0.18/0.48
% 0.18/0.48 Here is a proof with depth 7, length 44 :
% 0.18/0.48 % SZS output start Refutation
% See solution above
% 0.18/0.48 Formulae used in the proof : l25_zfmisc_1 commutativity_k3_xboole_0 d1_xboole_0 d7_xboole_0 d1_tarski idempotence_k3_xboole_0 d3_xboole_0
% 0.18/0.48
%------------------------------------------------------------------------------