%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET636+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 05:27:44 EDT 2022
% Result : Theorem 0.52s 0.73s
% Output : Refutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 18
% Syntax : Number of clauses : 71 ( 18 unt; 20 nHn; 71 RR)
% Number of literals : 138 ( 0 equ; 59 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
~ member(u,empty_set),
file('SET636+3.p',unknown),
[] ).
cnf(3,axiom,
( disjoint(u,v)
| intersect(u,v) ),
file('SET636+3.p',unknown),
[] ).
cnf(4,axiom,
( empty(u)
| member(skf6(u),u) ),
file('SET636+3.p',unknown),
[] ).
cnf(6,axiom,
( ~ equal(u,v)
| subset(v,u) ),
file('SET636+3.p',unknown),
[] ).
cnf(8,axiom,
( ~ intersect(u,v)
| intersect(v,u) ),
file('SET636+3.p',unknown),
[] ).
cnf(9,axiom,
( ~ empty(u)
| ~ member(v,u) ),
file('SET636+3.p',unknown),
[] ).
cnf(10,axiom,
( disjoint(skc2,skc3)
| equal(intersection(skc2,skc3),empty_set) ),
file('SET636+3.p',unknown),
[] ).
cnf(11,axiom,
( ~ intersect(u,v)
| ~ disjoint(u,v) ),
file('SET636+3.p',unknown),
[] ).
cnf(12,axiom,
( subset(u,v)
| member(skf5(v,u),u) ),
file('SET636+3.p',unknown),
[] ).
cnf(13,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET636+3.p',unknown),
[] ).
cnf(14,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET636+3.p',unknown),
[] ).
cnf(15,axiom,
( ~ intersect(u,v)
| member(skf4(v,u),u) ),
file('SET636+3.p',unknown),
[] ).
cnf(16,axiom,
( ~ intersect(u,v)
| member(skf4(v,w),v) ),
file('SET636+3.p',unknown),
[] ).
cnf(18,axiom,
( ~ disjoint(skc2,skc3)
| ~ equal(intersection(skc2,skc3),empty_set) ),
file('SET636+3.p',unknown),
[] ).
cnf(19,axiom,
( ~ member(u,v)
| ~ member(u,w)
| intersect(w,v) ),
file('SET636+3.p',unknown),
[] ).
cnf(20,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal(v,u) ),
file('SET636+3.p',unknown),
[] ).
cnf(21,axiom,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
file('SET636+3.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(v,w)) ),
file('SET636+3.p',unknown),
[] ).
cnf(33,plain,
( disjoint(u,v)
| intersect(v,u) ),
inference(res,[status(thm),theory(equality)],[3,8]),
[iquote('0:Res:3.1,8.0')] ).
cnf(34,plain,
disjoint(skc2,skc3),
inference(spt,[spt(split,[position(s1)])],[10]),
[iquote('1:Spt:10.0')] ).
cnf(35,plain,
~ equal(intersection(skc2,skc3),empty_set),
inference(mrr,[status(thm)],[18,34]),
[iquote('1:MRR:18.0,34.0')] ).
cnf(40,plain,
subset(empty_set,u),
inference(res,[status(thm),theory(equality)],[12,2]),
[iquote('0:Res:12.1,2.0')] ).
cnf(41,plain,
( ~ empty(u)
| subset(u,v) ),
inference(res,[status(thm),theory(equality)],[12,9]),
[iquote('0:Res:12.1,9.1')] ).
cnf(44,plain,
( ~ empty(u)
| ~ intersect(u,v) ),
inference(res,[status(thm),theory(equality)],[15,9]),
[iquote('0:Res:15.1,9.1')] ).
cnf(52,plain,
( ~ empty(u)
| disjoint(v,u) ),
inference(res,[status(thm),theory(equality)],[33,44]),
[iquote('0:Res:33.1,44.1')] ).
cnf(65,plain,
( empty(intersection(u,v))
| member(skf6(intersection(u,v)),v) ),
inference(res,[status(thm),theory(equality)],[4,14]),
[iquote('0:Res:4.1,14.0')] ).
cnf(74,plain,
( ~ intersect(intersection(u,v),w)
| member(skf4(w,intersection(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[15,13]),
[iquote('0:Res:15.1,13.0')] ).
cnf(82,plain,
( ~ empty(u)
| empty(intersection(v,u)) ),
inference(res,[status(thm),theory(equality)],[65,9]),
[iquote('0:Res:65.1,9.1')] ).
cnf(89,plain,
( ~ subset(u,empty_set)
| equal(u,empty_set) ),
inference(res,[status(thm),theory(equality)],[40,20]),
[iquote('0:Res:40.0,20.0')] ).
cnf(90,plain,
( ~ empty(u)
| ~ subset(v,u)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[41,20]),
[iquote('0:Res:41.1,20.0')] ).
cnf(94,plain,
( ~ empty(u)
| equal(u,empty_set) ),
inference(res,[status(thm),theory(equality)],[41,89]),
[iquote('0:Res:41.1,89.0')] ).
cnf(115,plain,
( ~ member(skf6(u),v)
| empty(u)
| intersect(v,u) ),
inference(res,[status(thm),theory(equality)],[4,19]),
[iquote('0:Res:4.1,19.0')] ).
cnf(116,plain,
( ~ member(skf5(u,v),w)
| subset(v,u)
| intersect(w,v) ),
inference(res,[status(thm),theory(equality)],[12,19]),
[iquote('0:Res:12.1,19.0')] ).
cnf(122,plain,
( ~ empty(u)
| equal(intersection(v,u),empty_set) ),
inference(ems,[status(thm)],[94,82]),
[iquote('0:EmS:94.0,82.1')] ).
cnf(144,plain,
( ~ empty(skc3)
| ~ equal(empty_set,empty_set) ),
inference(spl,[status(thm),theory(equality)],[122,35]),
[iquote('1:SpL:122.1,35.0')] ).
cnf(145,plain,
~ empty(skc3),
inference(obv,[status(thm),theory(equality)],[144]),
[iquote('1:Obv:144.1')] ).
cnf(147,plain,
( ~ subset(u,v)
| empty(u)
| member(skf6(u),v) ),
inference(res,[status(thm),theory(equality)],[4,21]),
[iquote('0:Res:4.1,21.0')] ).
cnf(207,plain,
( empty(u)
| empty(u)
| intersect(u,u) ),
inference(res,[status(thm),theory(equality)],[4,115]),
[iquote('0:Res:4.1,115.0')] ).
cnf(209,plain,
( empty(intersection(u,v))
| empty(intersection(u,v))
| intersect(v,intersection(u,v)) ),
inference(res,[status(thm),theory(equality)],[65,115]),
[iquote('0:Res:65.1,115.0')] ).
cnf(211,plain,
( empty(u)
| intersect(u,u) ),
inference(obv,[status(thm),theory(equality)],[207]),
[iquote('0:Obv:207.0')] ).
cnf(213,plain,
( empty(intersection(u,v))
| intersect(v,intersection(u,v)) ),
inference(obv,[status(thm),theory(equality)],[209]),
[iquote('0:Obv:209.0')] ).
cnf(230,plain,
( empty(u)
| member(skf4(u,v),u) ),
inference(res,[status(thm),theory(equality)],[211,16]),
[iquote('0:Res:211.1,16.0')] ).
cnf(295,plain,
( empty(intersection(u,v))
| intersect(intersection(u,v),v) ),
inference(res,[status(thm),theory(equality)],[213,8]),
[iquote('0:Res:213.1,8.0')] ).
cnf(384,plain,
( ~ subset(u,empty_set)
| empty(u) ),
inference(res,[status(thm),theory(equality)],[147,2]),
[iquote('0:Res:147.2,2.0')] ).
cnf(393,plain,
( ~ equal(empty_set,u)
| empty(u) ),
inference(res,[status(thm),theory(equality)],[6,384]),
[iquote('0:Res:6.1,384.0')] ).
cnf(399,plain,
~ equal(skc3,empty_set),
inference(sor,[status(thm)],[145,393]),
[iquote('1:SoR:145.0,393.1')] ).
cnf(591,plain,
( subset(u,v)
| subset(u,v)
| intersect(u,u) ),
inference(res,[status(thm),theory(equality)],[12,116]),
[iquote('0:Res:12.1,116.0')] ).
cnf(594,plain,
( subset(u,v)
| intersect(u,u) ),
inference(obv,[status(thm),theory(equality)],[591]),
[iquote('0:Obv:591.0')] ).
cnf(598,plain,
( ~ empty(u)
| intersect(v,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[594,90]),
[iquote('0:Res:594.0,90.1')] ).
cnf(789,plain,
( ~ empty(u)
| ~ equal(u,empty_set)
| intersect(skc3,skc3) ),
inference(spl,[status(thm),theory(equality)],[598,399]),
[iquote('1:SpL:598.2,399.0')] ).
cnf(809,plain,
( ~ equal(u,empty_set)
| intersect(skc3,skc3) ),
inference(mrr,[status(thm)],[789,393]),
[iquote('1:MRR:789.0,393.1')] ).
cnf(819,plain,
intersect(skc3,skc3),
inference(eqr,[status(thm),theory(equality)],[809]),
[iquote('1:EqR:809.0')] ).
cnf(825,plain,
member(skf4(skc3,u),skc3),
inference(res,[status(thm),theory(equality)],[819,16]),
[iquote('1:Res:819.0,16.0')] ).
cnf(859,plain,
( ~ member(skf4(skc3,u),v)
| intersect(v,skc3) ),
inference(res,[status(thm),theory(equality)],[825,19]),
[iquote('1:Res:825.0,19.0')] ).
cnf(1501,plain,
( ~ intersect(intersection(u,v),skc3)
| intersect(u,skc3) ),
inference(res,[status(thm),theory(equality)],[74,859]),
[iquote('1:Res:74.1,859.0')] ).
cnf(2149,plain,
( empty(intersection(u,skc3))
| intersect(u,skc3) ),
inference(res,[status(thm),theory(equality)],[295,1501]),
[iquote('1:Res:295.1,1501.0')] ).
cnf(2160,plain,
( equal(intersection(u,skc3),empty_set)
| intersect(u,skc3) ),
inference(ems,[status(thm)],[94,2149]),
[iquote('1:EmS:94.0,2149.0')] ).
cnf(2277,plain,
( ~ equal(empty_set,empty_set)
| intersect(skc2,skc3) ),
inference(spl,[status(thm),theory(equality)],[2160,35]),
[iquote('1:SpL:2160.0,35.0')] ).
cnf(2278,plain,
intersect(skc2,skc3),
inference(obv,[status(thm),theory(equality)],[2277]),
[iquote('1:Obv:2277.0')] ).
cnf(2312,plain,
~ disjoint(skc2,skc3),
inference(res,[status(thm),theory(equality)],[2278,11]),
[iquote('1:Res:2278.0,11.0')] ).
cnf(2314,plain,
$false,
inference(mrr,[status(thm)],[2312,34]),
[iquote('1:MRR:2312.0,34.0')] ).
cnf(2315,plain,
~ disjoint(skc2,skc3),
inference(spt,[spt(split,[position(sa)])],[2314,34]),
[iquote('1:Spt:2314.0,10.0,34.0')] ).
cnf(2316,plain,
equal(intersection(skc2,skc3),empty_set),
inference(spt,[spt(split,[position(s2)])],[10]),
[iquote('1:Spt:2314.0,10.1')] ).
cnf(2324,plain,
( ~ member(u,skc2)
| ~ member(u,skc3)
| member(u,empty_set) ),
inference(spr,[status(thm),theory(equality)],[2316,24]),
[iquote('1:SpR:2316.0,24.2')] ).
cnf(2369,plain,
( ~ member(u,skc2)
| ~ member(u,skc3) ),
inference(mrr,[status(thm)],[2324,2]),
[iquote('1:MRR:2324.2,2.0')] ).
cnf(2386,plain,
~ empty(skc3),
inference(res,[status(thm),theory(equality)],[52,2315]),
[iquote('1:Res:52.1,2315.0')] ).
cnf(2428,plain,
( ~ member(skf4(skc3,u),skc2)
| empty(skc3) ),
inference(res,[status(thm),theory(equality)],[230,2369]),
[iquote('1:Res:230.1,2369.1')] ).
cnf(2453,plain,
~ member(skf4(skc3,u),skc2),
inference(mrr,[status(thm)],[2428,2386]),
[iquote('1:MRR:2428.1,2386.0')] ).
cnf(2677,plain,
~ intersect(skc2,skc3),
inference(res,[status(thm),theory(equality)],[15,2453]),
[iquote('1:Res:15.1,2453.0')] ).
cnf(2684,plain,
disjoint(skc2,skc3),
inference(res,[status(thm),theory(equality)],[3,2677]),
[iquote('1:Res:3.1,2677.0')] ).
cnf(2687,plain,
$false,
inference(mrr,[status(thm)],[2684,2315]),
[iquote('1:MRR:2684.0,2315.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET636+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n018.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 Jul 11 04:15:58 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.52/0.73
% 0.52/0.73 SPASS V 3.9
% 0.52/0.73 SPASS beiseite: Proof found.
% 0.52/0.73 % SZS status Theorem
% 0.52/0.73 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.52/0.73 SPASS derived 2063 clauses, backtracked 3 clauses, performed 1 splits and kept 686 clauses.
% 0.52/0.73 SPASS allocated 99103 KBytes.
% 0.52/0.73 SPASS spent 0:00:00.37 on the problem.
% 0.52/0.73 0:00:00.04 for the input.
% 0.52/0.73 0:00:00.04 for the FLOTTER CNF translation.
% 0.52/0.73 0:00:00.03 for inferences.
% 0.52/0.73 0:00:00.00 for the backtracking.
% 0.52/0.73 0:00:00.24 for the reduction.
% 0.52/0.73
% 0.52/0.73
% 0.52/0.73 Here is a proof with depth 15, length 71 :
% 0.52/0.73 % SZS output start Refutation
% See solution above
% 0.52/0.73 Formulae used in the proof : empty_set_defn disjoint_defn empty_defn equal_defn symmetry_of_intersect prove_th118 subset_defn intersection_defn intersect_defn
% 0.52/0.73
%------------------------------------------------------------------------------