TSTP Solution File: SET638+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET638+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 0.21s 0.46s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of clauses : 20 ( 10 unt; 3 nHn; 20 RR)
% Number of literals : 35 ( 0 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
~ subset(skc3,skc5),
file('SET638+3.p',unknown),
[] ).
cnf(3,axiom,
~ member(u,empty_set),
file('SET638+3.p',unknown),
[] ).
cnf(4,axiom,
subset(skc3,union(skc5,skc4)),
file('SET638+3.p',unknown),
[] ).
cnf(5,axiom,
equal(intersection(skc3,skc4),empty_set),
file('SET638+3.p',unknown),
[] ).
cnf(11,axiom,
equal(union(u,v),union(v,u)),
file('SET638+3.p',unknown),
[] ).
cnf(14,axiom,
( subset(u,v)
| member(skf3(v,u),u) ),
file('SET638+3.p',unknown),
[] ).
cnf(20,axiom,
( ~ member(skf3(u,v),u)
| subset(w,u) ),
file('SET638+3.p',unknown),
[] ).
cnf(21,axiom,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
file('SET638+3.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,union(v,w))
| member(u,v)
| member(u,w) ),
file('SET638+3.p',unknown),
[] ).
cnf(27,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(v,w)) ),
file('SET638+3.p',unknown),
[] ).
cnf(30,plain,
subset(skc3,union(skc4,skc5)),
inference(rew,[status(thm),theory(equality)],[11,4]),
[iquote('0:Rew:11.0,4.0')] ).
cnf(31,plain,
member(skf3(skc5,skc3),skc3),
inference(res,[status(thm),theory(equality)],[14,2]),
[iquote('0:Res:14.1,2.0')] ).
cnf(33,plain,
~ member(skf3(skc5,u),skc5),
inference(res,[status(thm),theory(equality)],[20,2]),
[iquote('0:Res:20.1,2.0')] ).
cnf(39,plain,
( ~ member(u,skc3)
| member(u,union(skc4,skc5)) ),
inference(res,[status(thm),theory(equality)],[30,21]),
[iquote('0:Res:30.0,21.0')] ).
cnf(185,plain,
( ~ member(u,skc3)
| member(u,skc4)
| member(u,skc5) ),
inference(res,[status(thm),theory(equality)],[39,25]),
[iquote('0:Res:39.1,25.0')] ).
cnf(193,plain,
( ~ member(skf3(skc5,u),skc3)
| member(skf3(skc5,u),skc4) ),
inference(res,[status(thm),theory(equality)],[185,33]),
[iquote('0:Res:185.2,33.0')] ).
cnf(329,plain,
( ~ member(u,skc3)
| ~ member(u,skc4)
| member(u,empty_set) ),
inference(spr,[status(thm),theory(equality)],[5,27]),
[iquote('0:SpR:5.0,27.2')] ).
cnf(342,plain,
( ~ member(u,skc3)
| ~ member(u,skc4) ),
inference(mrr,[status(thm)],[329,3]),
[iquote('0:MRR:329.2,3.0')] ).
cnf(346,plain,
~ member(skf3(skc5,u),skc3),
inference(mrr,[status(thm)],[193,342]),
[iquote('0:MRR:193.1,342.1')] ).
cnf(347,plain,
$false,
inference(unc,[status(thm)],[346,31]),
[iquote('0:UnC:346.0,31.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET638+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n009.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 23:47:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.21/0.46
% 0.21/0.46 SPASS V 3.9
% 0.21/0.46 SPASS beiseite: Proof found.
% 0.21/0.46 % SZS status Theorem
% 0.21/0.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.46 SPASS derived 271 clauses, backtracked 0 clauses, performed 0 splits and kept 124 clauses.
% 0.21/0.46 SPASS allocated 97884 KBytes.
% 0.21/0.46 SPASS spent 0:00:00.11 on the problem.
% 0.21/0.46 0:00:00.04 for the input.
% 0.21/0.46 0:00:00.03 for the FLOTTER CNF translation.
% 0.21/0.46 0:00:00.00 for inferences.
% 0.21/0.46 0:00:00.00 for the backtracking.
% 0.21/0.46 0:00:00.01 for the reduction.
% 0.21/0.46
% 0.21/0.46
% 0.21/0.46 Here is a proof with depth 3, length 20 :
% 0.21/0.46 % SZS output start Refutation
% See solution above
% 0.21/0.46 Formulae used in the proof : prove_th120 empty_set_defn commutativity_of_union subset_defn union_defn intersection_defn
% 0.21/0.46
%------------------------------------------------------------------------------