TSTP Solution File: SEU154+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU154+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 0.47s 0.64s
% Output : Refutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of clauses : 36 ( 9 unt; 14 nHn; 36 RR)
% Number of literals : 73 ( 0 equ; 21 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
subset(empty_set,u),
file('SEU154+1.p',unknown),
[] ).
cnf(6,axiom,
~ in(skc4,skc5),
file('SEU154+1.p',unknown),
[] ).
cnf(7,axiom,
~ disjoint(singleton(skc4),skc5),
file('SEU154+1.p',unknown),
[] ).
cnf(9,axiom,
equal(set_intersection2(u,v),set_intersection2(v,u)),
file('SEU154+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ disjoint(u,v)
| disjoint(v,u) ),
file('SEU154+1.p',unknown),
[] ).
cnf(14,axiom,
( subset(u,v)
| in(skf4(v,u),u) ),
file('SEU154+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ in(skf4(u,v),u)
| subset(w,u) ),
file('SEU154+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ equal(set_intersection2(u,v),empty_set)
| disjoint(u,v) ),
file('SEU154+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal(v,u) ),
file('SEU154+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ in(u,v)
| ~ equal(v,singleton(w))
| equal(u,w) ),
file('SEU154+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ in(u,v)
| ~ equal(v,set_intersection2(w,x))
| in(u,w) ),
file('SEU154+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ in(u,v)
| ~ equal(v,set_intersection2(w,x))
| in(u,x) ),
file('SEU154+1.p',unknown),
[] ).
cnf(27,axiom,
( equal(u,set_intersection2(v,w))
| in(skf5(w,v,u),u)
| in(skf5(w,v,u),v) ),
file('SEU154+1.p',unknown),
[] ).
cnf(28,axiom,
( equal(u,set_intersection2(v,w))
| in(skf5(w,v,u),u)
| in(skf5(w,v,u),w) ),
file('SEU154+1.p',unknown),
[] ).
cnf(36,plain,
~ disjoint(skc5,singleton(skc4)),
inference(res,[status(thm),theory(equality)],[12,7]),
[iquote('0:Res:12.1,7.0')] ).
cnf(53,plain,
( ~ equal(set_intersection2(u,v),empty_set)
| disjoint(v,u) ),
inference(spl,[status(thm),theory(equality)],[9,17]),
[iquote('0:SpL:9.0,17.0')] ).
cnf(85,plain,
( ~ subset(u,empty_set)
| equal(u,empty_set) ),
inference(res,[status(thm),theory(equality)],[5,18]),
[iquote('0:Res:5.0,18.0')] ).
cnf(110,plain,
( ~ in(u,singleton(v))
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[20]),
[iquote('0:EqR:20.1')] ).
cnf(124,plain,
( ~ in(u,set_intersection2(v,w))
| in(u,w) ),
inference(eqr,[status(thm),theory(equality)],[23]),
[iquote('0:EqR:23.1')] ).
cnf(149,plain,
( ~ in(u,set_intersection2(v,w))
| in(u,v) ),
inference(eqr,[status(thm),theory(equality)],[22]),
[iquote('0:EqR:22.1')] ).
cnf(162,plain,
( subset(set_intersection2(u,v),w)
| in(skf4(w,set_intersection2(u,v)),v) ),
inference(res,[status(thm),theory(equality)],[14,124]),
[iquote('0:Res:14.1,124.0')] ).
cnf(499,plain,
( subset(set_intersection2(u,v),v)
| subset(w,v) ),
inference(res,[status(thm),theory(equality)],[162,15]),
[iquote('0:Res:162.1,15.0')] ).
cnf(501,plain,
subset(set_intersection2(u,v),v),
inference(con,[status(thm)],[499]),
[iquote('0:Con:499.1')] ).
cnf(513,plain,
equal(set_intersection2(u,empty_set),empty_set),
inference(res,[status(thm),theory(equality)],[501,85]),
[iquote('0:Res:501.0,85.0')] ).
cnf(533,plain,
( ~ in(u,empty_set)
| in(u,v) ),
inference(spl,[status(thm),theory(equality)],[513,149]),
[iquote('0:SpL:513.0,149.0')] ).
cnf(593,plain,
( equal(set_intersection2(u,v),empty_set)
| in(skf5(v,u,empty_set),u)
| in(skf5(v,u,empty_set),w) ),
inference(res,[status(thm),theory(equality)],[27,533]),
[iquote('0:Res:27.1,533.0')] ).
cnf(594,plain,
( equal(set_intersection2(u,v),empty_set)
| in(skf5(v,u,empty_set),v)
| in(skf5(v,u,empty_set),w) ),
inference(res,[status(thm),theory(equality)],[28,533]),
[iquote('0:Res:28.1,533.0')] ).
cnf(602,plain,
( equal(set_intersection2(u,v),empty_set)
| in(skf5(v,u,empty_set),u) ),
inference(con,[status(thm)],[593]),
[iquote('0:Con:593.2')] ).
cnf(603,plain,
( equal(set_intersection2(u,v),empty_set)
| in(skf5(v,u,empty_set),v) ),
inference(con,[status(thm)],[594]),
[iquote('0:Con:594.2')] ).
cnf(730,plain,
( equal(set_intersection2(singleton(u),v),empty_set)
| equal(skf5(v,singleton(u),empty_set),u) ),
inference(res,[status(thm),theory(equality)],[602,110]),
[iquote('0:Res:602.1,110.0')] ).
cnf(1547,plain,
( equal(set_intersection2(singleton(u),v),empty_set)
| equal(set_intersection2(singleton(u),v),empty_set)
| in(u,v) ),
inference(spr,[status(thm),theory(equality)],[730,603]),
[iquote('0:SpR:730.1,603.1')] ).
cnf(1565,plain,
( equal(set_intersection2(singleton(u),v),empty_set)
| in(u,v) ),
inference(obv,[status(thm),theory(equality)],[1547]),
[iquote('0:Obv:1547.0')] ).
cnf(1608,plain,
( ~ equal(empty_set,empty_set)
| in(u,v)
| disjoint(v,singleton(u)) ),
inference(spl,[status(thm),theory(equality)],[1565,53]),
[iquote('0:SpL:1565.0,53.0')] ).
cnf(1628,plain,
( in(u,v)
| disjoint(v,singleton(u)) ),
inference(obv,[status(thm),theory(equality)],[1608]),
[iquote('0:Obv:1608.0')] ).
cnf(1647,plain,
in(skc4,skc5),
inference(res,[status(thm),theory(equality)],[1628,36]),
[iquote('0:Res:1628.1,36.0')] ).
cnf(1652,plain,
$false,
inference(mrr,[status(thm)],[1647,6]),
[iquote('0:MRR:1647.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU154+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n025.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 Jun 19 12:06:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.47/0.64
% 0.47/0.64 SPASS V 3.9
% 0.47/0.64 SPASS beiseite: Proof found.
% 0.47/0.64 % SZS status Theorem
% 0.47/0.64 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.47/0.64 SPASS derived 1333 clauses, backtracked 0 clauses, performed 0 splits and kept 530 clauses.
% 0.47/0.64 SPASS allocated 86315 KBytes.
% 0.47/0.64 SPASS spent 0:00:00.30 on the problem.
% 0.47/0.64 0:00:00.04 for the input.
% 0.47/0.64 0:00:00.04 for the FLOTTER CNF translation.
% 0.47/0.64 0:00:00.02 for inferences.
% 0.47/0.64 0:00:00.00 for the backtracking.
% 0.47/0.64 0:00:00.17 for the reduction.
% 0.47/0.64
% 0.47/0.64
% 0.47/0.64 Here is a proof with depth 10, length 36 :
% 0.47/0.64 % SZS output start Refutation
% See solution above
% 0.47/0.64 Formulae used in the proof : t2_xboole_1 l28_zfmisc_1 commutativity_k3_xboole_0 symmetry_r1_xboole_0 d3_tarski d7_xboole_0 d10_xboole_0 d1_tarski d3_xboole_0
% 0.47/0.64
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