%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU162+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 14:34:33 EDT 2022
% Result : Theorem 0.50s 0.66s
% Output : Refutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of clauses : 37 ( 18 unt; 4 nHn; 37 RR)
% Number of literals : 56 ( 0 equ; 26 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
empty(skc60),
file('SEU162+2.p',unknown),
[] ).
cnf(7,axiom,
in(u,skf27(v,u)),
file('SEU162+2.p',unknown),
[] ).
cnf(21,axiom,
( ~ empty(u)
| equal(u,empty_set) ),
file('SEU162+2.p',unknown),
[] ).
cnf(32,axiom,
( in(u,v)
| disjoint(singleton(u),v) ),
file('SEU162+2.p',unknown),
[] ).
cnf(33,axiom,
( ~ disjoint(u,v)
| disjoint(v,u) ),
file('SEU162+2.p',unknown),
[] ).
cnf(36,axiom,
( ~ in(u,v)
| ~ in(v,u) ),
file('SEU162+2.p',unknown),
[] ).
cnf(48,axiom,
( disjoint(u,v)
| in(skf33(v,u),u) ),
file('SEU162+2.p',unknown),
[] ).
cnf(52,axiom,
( ~ disjoint(u,v)
| equal(set_intersection2(u,v),empty_set) ),
file('SEU162+2.p',unknown),
[] ).
cnf(54,axiom,
( ~ in(u,v)
| ~ disjoint(singleton(u),v) ),
file('SEU162+2.p',unknown),
[] ).
cnf(69,axiom,
( ~ disjoint(u,v)
| equal(set_difference(u,v),u) ),
file('SEU162+2.p',unknown),
[] ).
cnf(70,axiom,
( ~ equal(set_difference(u,v),u)
| disjoint(u,v) ),
file('SEU162+2.p',unknown),
[] ).
cnf(72,axiom,
( ~ in(skc5,skc4)
| equal(set_difference(skc4,singleton(skc5)),skc4) ),
file('SEU162+2.p',unknown),
[] ).
cnf(73,axiom,
( ~ equal(set_difference(skc4,singleton(skc5)),skc4)
| in(skc5,skc4) ),
file('SEU162+2.p',unknown),
[] ).
cnf(79,axiom,
( ~ in(u,set_intersection2(v,w))
| ~ disjoint(v,w) ),
file('SEU162+2.p',unknown),
[] ).
cnf(148,plain,
( ~ disjoint(u,v)
| ~ in(w,empty_set) ),
inference(rew,[status(thm),theory(equality)],[52,79]),
[iquote('0:Rew:52.1,79.0')] ).
cnf(163,plain,
equal(empty_set,skc60),
inference(ems,[status(thm)],[21,2]),
[iquote('0:EmS:21.0,2.0')] ).
cnf(183,plain,
( ~ disjoint(u,v)
| ~ in(w,skc60) ),
inference(rew,[status(thm),theory(equality)],[163,148]),
[iquote('0:Rew:163.0,148.1')] ).
cnf(243,plain,
( in(u,v)
| disjoint(v,singleton(u)) ),
inference(res,[status(thm),theory(equality)],[32,33]),
[iquote('0:Res:32.1,33.0')] ).
cnf(251,plain,
( ~ in(u,skc60)
| in(v,w) ),
inference(res,[status(thm),theory(equality)],[32,183]),
[iquote('0:Res:32.1,183.0')] ).
cnf(256,plain,
~ in(skf27(u,v),v),
inference(res,[status(thm),theory(equality)],[7,36]),
[iquote('0:Res:7.0,36.0')] ).
cnf(261,plain,
( disjoint(skc60,u)
| in(v,w) ),
inference(res,[status(thm),theory(equality)],[48,251]),
[iquote('0:Res:48.1,251.0')] ).
cnf(263,plain,
in(u,v),
inference(spt,[spt(split,[position(s1)])],[261]),
[iquote('1:Spt:261.1')] ).
cnf(264,plain,
$false,
inference(unc,[status(thm)],[263,256]),
[iquote('1:UnC:263.0,256.0')] ).
cnf(265,plain,
disjoint(skc60,u),
inference(spt,[spt(split,[position(s2)])],[261]),
[iquote('1:Spt:264.0,261.0')] ).
cnf(469,plain,
~ in(skc5,skc4),
inference(spt,[spt(split,[position(s2s1)])],[72]),
[iquote('2:Spt:72.0')] ).
cnf(470,plain,
~ equal(set_difference(skc4,singleton(skc5)),skc4),
inference(mrr,[status(thm)],[73,469]),
[iquote('2:MRR:73.1,469.0')] ).
cnf(471,plain,
( ~ disjoint(skc4,singleton(skc5))
| ~ equal(skc4,skc4) ),
inference(spl,[status(thm),theory(equality)],[69,470]),
[iquote('2:SpL:69.1,470.0')] ).
cnf(472,plain,
~ disjoint(skc4,singleton(skc5)),
inference(obv,[status(thm),theory(equality)],[471]),
[iquote('2:Obv:471.1')] ).
cnf(477,plain,
in(skc5,skc4),
inference(res,[status(thm),theory(equality)],[243,472]),
[iquote('2:Res:243.1,472.0')] ).
cnf(478,plain,
$false,
inference(mrr,[status(thm)],[477,469]),
[iquote('2:MRR:477.0,469.0')] ).
cnf(479,plain,
in(skc5,skc4),
inference(spt,[spt(split,[position(s2sa)])],[478,469]),
[iquote('2:Spt:478.0,72.0,469.0')] ).
cnf(480,plain,
equal(set_difference(skc4,singleton(skc5)),skc4),
inference(spt,[spt(split,[position(s2s2)])],[72]),
[iquote('2:Spt:478.0,72.1')] ).
cnf(485,plain,
( ~ equal(skc4,skc4)
| disjoint(skc4,singleton(skc5)) ),
inference(spl,[status(thm),theory(equality)],[480,70]),
[iquote('2:SpL:480.0,70.0')] ).
cnf(487,plain,
disjoint(skc4,singleton(skc5)),
inference(obv,[status(thm),theory(equality)],[485]),
[iquote('2:Obv:485.0')] ).
cnf(499,plain,
disjoint(singleton(skc5),skc4),
inference(res,[status(thm),theory(equality)],[487,33]),
[iquote('2:Res:487.0,33.0')] ).
cnf(500,plain,
~ in(skc5,skc4),
inference(res,[status(thm),theory(equality)],[499,54]),
[iquote('2:Res:499.0,54.1')] ).
cnf(502,plain,
$false,
inference(mrr,[status(thm)],[500,479]),
[iquote('2:MRR:500.0,479.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SEU162+2 : TPTP v8.1.0. Released v3.3.0.
% 0.09/0.15 % Command : run_spass %d %s
% 0.16/0.37 % Computer : n013.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 600
% 0.16/0.37 % DateTime : Mon Jun 20 01:04:29 EDT 2022
% 0.16/0.37 % CPUTime :
% 0.50/0.66
% 0.50/0.66 SPASS V 3.9
% 0.50/0.66 SPASS beiseite: Proof found.
% 0.50/0.66 % SZS status Theorem
% 0.50/0.66 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.50/0.66 SPASS derived 313 clauses, backtracked 4 clauses, performed 2 splits and kept 242 clauses.
% 0.50/0.66 SPASS allocated 100078 KBytes.
% 0.50/0.66 SPASS spent 0:00:00.27 on the problem.
% 0.50/0.66 0:00:00.03 for the input.
% 0.50/0.66 0:00:00.19 for the FLOTTER CNF translation.
% 0.50/0.66 0:00:00.00 for inferences.
% 0.50/0.66 0:00:00.00 for the backtracking.
% 0.50/0.66 0:00:00.02 for the reduction.
% 0.50/0.66
% 0.50/0.66
% 0.50/0.66 Here is a proof with depth 4, length 37 :
% 0.50/0.66 % SZS output start Refutation
% See solution above
% 0.50/0.66 Formulae used in the proof : rc1_xboole_0 d4_tarski reflexivity_r1_tarski l2_zfmisc_1 t6_boole l28_zfmisc_1 symmetry_r1_xboole_0 antisymmetry_r2_hidden t3_xboole_0 d7_xboole_0 l25_zfmisc_1 t83_xboole_1 t65_zfmisc_1 t4_xboole_0
% 0.50/0.66
%------------------------------------------------------------------------------