TSTP Solution File: SET637+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET637+3 : TPTP v8.1.0. Released v2.2.0.
% 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 05:27:45 EDT 2022
% Result : Theorem 0.34s 0.53s
% Output : Refutation 0.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of clauses : 58 ( 17 unt; 17 nHn; 58 RR)
% Number of literals : 109 ( 0 equ; 43 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 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(1,axiom,
~ member(u,empty_set),
file('SET637+3.p',unknown),
[] ).
cnf(2,axiom,
( not_equal(u,v)
| equal(u,v) ),
file('SET637+3.p',unknown),
[] ).
cnf(3,axiom,
( empty(u)
| member(skf5(u),u) ),
file('SET637+3.p',unknown),
[] ).
cnf(4,axiom,
equal(intersection(u,v),intersection(v,u)),
file('SET637+3.p',unknown),
[] ).
cnf(5,axiom,
( ~ intersect(u,v)
| intersect(v,u) ),
file('SET637+3.p',unknown),
[] ).
cnf(6,axiom,
( ~ empty(u)
| ~ member(v,u) ),
file('SET637+3.p',unknown),
[] ).
cnf(7,axiom,
( intersect(skc2,skc3)
| not_equal(intersection(skc2,skc3),empty_set) ),
file('SET637+3.p',unknown),
[] ).
cnf(8,axiom,
( ~ equal(u,v)
| ~ not_equal(u,v) ),
file('SET637+3.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET637+3.p',unknown),
[] ).
cnf(11,axiom,
( ~ intersect(u,v)
| member(skf3(v,u),u) ),
file('SET637+3.p',unknown),
[] ).
cnf(12,axiom,
( ~ intersect(u,v)
| member(skf3(v,w),v) ),
file('SET637+3.p',unknown),
[] ).
cnf(13,axiom,
( ~ intersect(skc2,skc3)
| ~ not_equal(intersection(skc2,skc3),empty_set) ),
file('SET637+3.p',unknown),
[] ).
cnf(14,axiom,
( ~ member(u,v)
| ~ member(u,w)
| intersect(w,v) ),
file('SET637+3.p',unknown),
[] ).
cnf(17,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(v,w)) ),
file('SET637+3.p',unknown),
[] ).
cnf(18,axiom,
( equal(u,v)
| member(skf4(v,u),v)
| member(skf4(v,u),u) ),
file('SET637+3.p',unknown),
[] ).
cnf(26,plain,
intersect(skc2,skc3),
inference(spt,[spt(split,[position(s1)])],[7]),
[iquote('1:Spt:7.0')] ).
cnf(27,plain,
~ not_equal(intersection(skc2,skc3),empty_set),
inference(mrr,[status(thm)],[13,26]),
[iquote('1:MRR:13.0,26.0')] ).
cnf(30,plain,
equal(intersection(skc2,skc3),empty_set),
inference(res,[status(thm),theory(equality)],[2,27]),
[iquote('1:Res:2.0,27.0')] ).
cnf(37,plain,
member(skf3(skc3,u),skc3),
inference(res,[status(thm),theory(equality)],[26,12]),
[iquote('1:Res:26.0,12.0')] ).
cnf(51,plain,
( empty(intersection(u,v))
| member(skf5(intersection(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[3,9]),
[iquote('0:Res:3.1,9.0')] ).
cnf(52,plain,
( ~ intersect(intersection(u,v),w)
| member(skf3(w,intersection(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[11,9]),
[iquote('0:Res:11.1,9.0')] ).
cnf(61,plain,
( ~ member(skf5(u),v)
| empty(u)
| intersect(v,u) ),
inference(res,[status(thm),theory(equality)],[3,14]),
[iquote('0:Res:3.1,14.0')] ).
cnf(62,plain,
( ~ intersect(u,v)
| ~ member(skf3(v,u),w)
| intersect(w,u) ),
inference(res,[status(thm),theory(equality)],[11,14]),
[iquote('0:Res:11.1,14.0')] ).
cnf(89,plain,
( ~ member(u,skc2)
| ~ member(u,skc3)
| member(u,empty_set) ),
inference(spr,[status(thm),theory(equality)],[30,17]),
[iquote('1:SpR:30.0,17.2')] ).
cnf(93,plain,
( ~ empty(intersection(u,v))
| ~ member(w,u)
| ~ member(w,v) ),
inference(res,[status(thm),theory(equality)],[17,6]),
[iquote('0:Res:17.2,6.1')] ).
cnf(96,plain,
( ~ member(u,skc2)
| ~ member(u,skc3) ),
inference(mrr,[status(thm)],[89,1]),
[iquote('1:MRR:89.2,1.0')] ).
cnf(99,plain,
~ member(skf3(skc3,u),skc2),
inference(res,[status(thm),theory(equality)],[37,96]),
[iquote('1:Res:37.0,96.1')] ).
cnf(102,plain,
~ intersect(skc2,skc3),
inference(res,[status(thm),theory(equality)],[11,99]),
[iquote('1:Res:11.1,99.0')] ).
cnf(103,plain,
$false,
inference(mrr,[status(thm)],[102,26]),
[iquote('1:MRR:102.0,26.0')] ).
cnf(104,plain,
~ intersect(skc2,skc3),
inference(spt,[spt(split,[position(sa)])],[103,26]),
[iquote('1:Spt:103.0,7.0,26.0')] ).
cnf(105,plain,
not_equal(intersection(skc2,skc3),empty_set),
inference(spt,[spt(split,[position(s2)])],[7]),
[iquote('1:Spt:103.0,7.1')] ).
cnf(106,plain,
~ equal(intersection(skc2,skc3),empty_set),
inference(res,[status(thm),theory(equality)],[105,8]),
[iquote('1:Res:105.0,8.1')] ).
cnf(108,plain,
( equal(u,empty_set)
| member(skf4(empty_set,u),u) ),
inference(res,[status(thm),theory(equality)],[18,1]),
[iquote('0:Res:18.1,1.0')] ).
cnf(122,plain,
( ~ empty(u)
| equal(u,empty_set) ),
inference(res,[status(thm),theory(equality)],[108,6]),
[iquote('0:Res:108.1,6.1')] ).
cnf(224,plain,
( empty(intersection(u,v))
| empty(intersection(u,v))
| intersect(u,intersection(u,v)) ),
inference(res,[status(thm),theory(equality)],[51,61]),
[iquote('0:Res:51.1,61.0')] ).
cnf(228,plain,
( empty(intersection(u,v))
| intersect(u,intersection(u,v)) ),
inference(obv,[status(thm),theory(equality)],[224]),
[iquote('0:Obv:224.0')] ).
cnf(247,plain,
( empty(intersection(u,v))
| intersect(u,intersection(v,u)) ),
inference(spr,[status(thm),theory(equality)],[4,228]),
[iquote('0:SpR:4.0,228.1')] ).
cnf(254,plain,
( empty(intersection(u,v))
| intersect(intersection(u,v),u) ),
inference(res,[status(thm),theory(equality)],[228,5]),
[iquote('0:Res:228.1,5.0')] ).
cnf(293,plain,
( empty(intersection(u,v))
| intersect(intersection(v,u),u) ),
inference(res,[status(thm),theory(equality)],[247,5]),
[iquote('0:Res:247.1,5.0')] ).
cnf(308,plain,
( empty(intersection(u,v))
| member(skf3(u,w),u) ),
inference(res,[status(thm),theory(equality)],[254,12]),
[iquote('0:Res:254.1,12.0')] ).
cnf(360,plain,
( ~ member(u,v)
| ~ member(u,w)
| member(skf3(v,x),v) ),
inference(sor,[status(thm)],[93,308]),
[iquote('0:SoR:93.0,308.0')] ).
cnf(376,plain,
( ~ member(u,v)
| member(skf3(v,w),v) ),
inference(con,[status(thm)],[360]),
[iquote('0:Con:360.1')] ).
cnf(434,plain,
( ~ intersect(u,v)
| member(skf3(u,w),u) ),
inference(res,[status(thm),theory(equality)],[11,376]),
[iquote('0:Res:11.1,376.0')] ).
cnf(613,plain,
( ~ intersect(u,v)
| ~ intersect(u,v)
| intersect(u,u) ),
inference(res,[status(thm),theory(equality)],[11,62]),
[iquote('0:Res:11.1,62.1')] ).
cnf(620,plain,
( ~ intersect(u,v)
| intersect(u,u) ),
inference(obv,[status(thm),theory(equality)],[613]),
[iquote('0:Obv:613.0')] ).
cnf(628,plain,
( empty(intersection(u,v))
| intersect(u,u) ),
inference(res,[status(thm),theory(equality)],[228,620]),
[iquote('0:Res:228.1,620.0')] ).
cnf(633,plain,
( equal(intersection(u,v),empty_set)
| intersect(u,u) ),
inference(ems,[status(thm)],[122,628]),
[iquote('0:EmS:122.0,628.0')] ).
cnf(762,plain,
( ~ equal(empty_set,empty_set)
| intersect(skc2,skc2) ),
inference(spl,[status(thm),theory(equality)],[633,106]),
[iquote('1:SpL:633.0,106.0')] ).
cnf(768,plain,
intersect(skc2,skc2),
inference(obv,[status(thm),theory(equality)],[762]),
[iquote('1:Obv:762.0')] ).
cnf(785,plain,
member(skf3(skc2,u),skc2),
inference(res,[status(thm),theory(equality)],[768,434]),
[iquote('1:Res:768.0,434.0')] ).
cnf(792,plain,
( ~ member(skf3(skc2,u),v)
| intersect(v,skc2) ),
inference(res,[status(thm),theory(equality)],[785,14]),
[iquote('1:Res:785.0,14.0')] ).
cnf(874,plain,
( ~ intersect(intersection(u,v),skc2)
| intersect(u,skc2) ),
inference(res,[status(thm),theory(equality)],[52,792]),
[iquote('1:Res:52.1,792.0')] ).
cnf(913,plain,
( empty(intersection(skc2,u))
| intersect(u,skc2) ),
inference(res,[status(thm),theory(equality)],[293,874]),
[iquote('1:Res:293.1,874.0')] ).
cnf(932,plain,
( equal(intersection(skc2,u),empty_set)
| intersect(u,skc2) ),
inference(ems,[status(thm)],[122,913]),
[iquote('1:EmS:122.0,913.0')] ).
cnf(1104,plain,
( ~ equal(empty_set,empty_set)
| intersect(skc3,skc2) ),
inference(spl,[status(thm),theory(equality)],[932,106]),
[iquote('1:SpL:932.0,106.0')] ).
cnf(1105,plain,
intersect(skc3,skc2),
inference(obv,[status(thm),theory(equality)],[1104]),
[iquote('1:Obv:1104.0')] ).
cnf(1129,plain,
intersect(skc2,skc3),
inference(res,[status(thm),theory(equality)],[1105,5]),
[iquote('1:Res:1105.0,5.0')] ).
cnf(1130,plain,
$false,
inference(mrr,[status(thm)],[1129,104]),
[iquote('1:MRR:1129.0,104.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET637+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 23:35:45 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.34/0.53
% 0.34/0.53 SPASS V 3.9
% 0.34/0.53 SPASS beiseite: Proof found.
% 0.34/0.53 % SZS status Theorem
% 0.34/0.53 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.34/0.53 SPASS derived 812 clauses, backtracked 3 clauses, performed 1 splits and kept 223 clauses.
% 0.34/0.53 SPASS allocated 98175 KBytes.
% 0.34/0.53 SPASS spent 0:00:00.17 on the problem.
% 0.34/0.53 0:00:00.04 for the input.
% 0.34/0.53 0:00:00.03 for the FLOTTER CNF translation.
% 0.34/0.53 0:00:00.01 for inferences.
% 0.34/0.53 0:00:00.00 for the backtracking.
% 0.34/0.53 0:00:00.06 for the reduction.
% 0.34/0.53
% 0.34/0.53
% 0.34/0.53 Here is a proof with depth 13, length 58 :
% 0.34/0.53 % SZS output start Refutation
% See solution above
% 0.34/0.53 Formulae used in the proof : empty_set_defn not_equal_defn empty_defn commutativity_of_intersection symmetry_of_intersect prove_th119 intersection_defn intersect_defn equal_member_defn
% 0.34/0.53
%------------------------------------------------------------------------------