TSTP Solution File: SET587+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET587+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 05:27:09 EDT 2022
% Result : Theorem 0.47s 0.66s
% Output : Refutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of clauses : 35 ( 10 unt; 9 nHn; 35 RR)
% Number of literals : 66 ( 0 equ; 30 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
~ member(u,empty_set),
file('SET587+3.p',unknown),
[] ).
cnf(3,axiom,
( empty(u)
| member(skf7(u),u) ),
file('SET587+3.p',unknown),
[] ).
cnf(6,axiom,
( ~ empty(u)
| ~ member(v,u) ),
file('SET587+3.p',unknown),
[] ).
cnf(7,axiom,
( subset(skc2,skc3)
| equal(difference(skc2,skc3),empty_set) ),
file('SET587+3.p',unknown),
[] ).
cnf(8,axiom,
( subset(u,v)
| member(skf5(v,u),u) ),
file('SET587+3.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(u,difference(v,w))
| member(u,v) ),
file('SET587+3.p',unknown),
[] ).
cnf(10,axiom,
( ~ member(skf5(u,v),u)
| subset(w,u) ),
file('SET587+3.p',unknown),
[] ).
cnf(11,axiom,
( ~ subset(skc2,skc3)
| ~ equal(difference(skc2,skc3),empty_set) ),
file('SET587+3.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,v)
| ~ member(u,difference(w,v)) ),
file('SET587+3.p',unknown),
[] ).
cnf(13,axiom,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
file('SET587+3.p',unknown),
[] ).
cnf(14,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal(v,u) ),
file('SET587+3.p',unknown),
[] ).
cnf(17,axiom,
( ~ member(u,v)
| member(u,w)
| member(u,difference(v,w)) ),
file('SET587+3.p',unknown),
[] ).
cnf(24,plain,
subset(skc2,skc3),
inference(spt,[spt(split,[position(s1)])],[7]),
[iquote('1:Spt:7.0')] ).
cnf(25,plain,
~ equal(difference(skc2,skc3),empty_set),
inference(mrr,[status(thm)],[11,24]),
[iquote('1:MRR:11.0,24.0')] ).
cnf(26,plain,
subset(empty_set,u),
inference(res,[status(thm),theory(equality)],[8,2]),
[iquote('0:Res:8.1,2.0')] ).
cnf(27,plain,
( ~ empty(u)
| subset(u,v) ),
inference(res,[status(thm),theory(equality)],[8,6]),
[iquote('0:Res:8.1,6.1')] ).
cnf(30,plain,
( empty(difference(u,v))
| member(skf7(difference(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[3,9]),
[iquote('0:Res:3.1,9.0')] ).
cnf(32,plain,
( ~ member(skf7(difference(u,v)),v)
| empty(difference(u,v)) ),
inference(res,[status(thm),theory(equality)],[3,12]),
[iquote('0:Res:3.1,12.1')] ).
cnf(36,plain,
( ~ subset(u,empty_set)
| equal(u,empty_set) ),
inference(res,[status(thm),theory(equality)],[26,14]),
[iquote('0:Res:26.0,14.0')] ).
cnf(44,plain,
( ~ empty(u)
| equal(u,empty_set) ),
inference(res,[status(thm),theory(equality)],[27,36]),
[iquote('0:Res:27.1,36.0')] ).
cnf(53,plain,
( ~ subset(u,v)
| empty(difference(u,w))
| member(skf7(difference(u,w)),v) ),
inference(res,[status(thm),theory(equality)],[30,13]),
[iquote('0:Res:30.1,13.0')] ).
cnf(2518,plain,
( ~ subset(u,v)
| empty(difference(u,v))
| empty(difference(u,v)) ),
inference(res,[status(thm),theory(equality)],[53,32]),
[iquote('0:Res:53.2,32.0')] ).
cnf(2522,plain,
( ~ subset(u,v)
| empty(difference(u,v)) ),
inference(obv,[status(thm),theory(equality)],[2518]),
[iquote('0:Obv:2518.1')] ).
cnf(2587,plain,
( ~ subset(u,v)
| equal(difference(u,v),empty_set) ),
inference(ems,[status(thm)],[44,2522]),
[iquote('0:EmS:44.0,2522.1')] ).
cnf(2855,plain,
( ~ subset(skc2,skc3)
| ~ equal(empty_set,empty_set) ),
inference(spl,[status(thm),theory(equality)],[2587,25]),
[iquote('1:SpL:2587.1,25.0')] ).
cnf(2856,plain,
~ subset(skc2,skc3),
inference(obv,[status(thm),theory(equality)],[2855]),
[iquote('1:Obv:2855.1')] ).
cnf(2857,plain,
$false,
inference(mrr,[status(thm)],[2856,24]),
[iquote('1:MRR:2856.0,24.0')] ).
cnf(2890,plain,
~ subset(skc2,skc3),
inference(spt,[spt(split,[position(sa)])],[2857,24]),
[iquote('1:Spt:2857.0,7.0,24.0')] ).
cnf(2891,plain,
equal(difference(skc2,skc3),empty_set),
inference(spt,[spt(split,[position(s2)])],[7]),
[iquote('1:Spt:2857.0,7.1')] ).
cnf(2892,plain,
( ~ member(u,skc2)
| member(u,skc3)
| member(u,empty_set) ),
inference(spr,[status(thm),theory(equality)],[2891,17]),
[iquote('1:SpR:2891.0,17.2')] ).
cnf(2953,plain,
( ~ member(u,skc2)
| member(u,skc3) ),
inference(mrr,[status(thm)],[2892,2]),
[iquote('1:MRR:2892.2,2.0')] ).
cnf(2998,plain,
( ~ member(skf5(skc3,u),skc2)
| subset(v,skc3) ),
inference(res,[status(thm),theory(equality)],[2953,10]),
[iquote('1:Res:2953.1,10.0')] ).
cnf(3116,plain,
( subset(skc2,skc3)
| subset(u,skc3) ),
inference(res,[status(thm),theory(equality)],[8,2998]),
[iquote('1:Res:8.1,2998.0')] ).
cnf(3119,plain,
subset(skc2,skc3),
inference(con,[status(thm)],[3116]),
[iquote('1:Con:3116.1')] ).
cnf(3120,plain,
$false,
inference(mrr,[status(thm)],[3119,2890]),
[iquote('1:MRR:3119.0,2890.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET587+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 9 18:27:13 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.47/0.66
% 0.47/0.66 SPASS V 3.9
% 0.47/0.66 SPASS beiseite: Proof found.
% 0.47/0.66 % SZS status Theorem
% 0.47/0.66 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.47/0.66 SPASS derived 2263 clauses, backtracked 24 clauses, performed 2 splits and kept 515 clauses.
% 0.47/0.66 SPASS allocated 99424 KBytes.
% 0.47/0.66 SPASS spent 0:00:00.30 on the problem.
% 0.47/0.66 0:00:00.03 for the input.
% 0.47/0.66 0:00:00.03 for the FLOTTER CNF translation.
% 0.47/0.66 0:00:00.03 for inferences.
% 0.47/0.66 0:00:00.00 for the backtracking.
% 0.47/0.66 0:00:00.17 for the reduction.
% 0.47/0.66
% 0.47/0.66
% 0.47/0.66 Here is a proof with depth 5, length 35 :
% 0.47/0.66 % SZS output start Refutation
% See solution above
% 0.47/0.66 Formulae used in the proof : empty_set_defn empty_defn prove_difference_empty_set subset_defn difference_defn equal_defn
% 0.47/0.66
%------------------------------------------------------------------------------