TSTP Solution File: SET183+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET183+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 05:24:49 EDT 2022
% Result : Theorem 0.18s 0.53s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 18 ( 6 unt; 4 nHn; 18 RR)
% Number of literals : 37 ( 0 equ; 19 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
subset(skc2,skc3),
file('SET183+3.p',unknown),
[] ).
cnf(3,axiom,
subset(intersection(u,v),u),
file('SET183+3.p',unknown),
[] ).
cnf(4,axiom,
~ equal(intersection(skc2,skc3),skc2),
file('SET183+3.p',unknown),
[] ).
cnf(8,axiom,
( subset(u,v)
| member(skf2(v,u),u) ),
file('SET183+3.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(skf2(u,v),u)
| subset(w,u) ),
file('SET183+3.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
file('SET183+3.p',unknown),
[] ).
cnf(13,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal(v,u) ),
file('SET183+3.p',unknown),
[] ).
cnf(16,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(v,w)) ),
file('SET183+3.p',unknown),
[] ).
cnf(22,plain,
( ~ subset(intersection(skc2,skc3),skc2)
| ~ subset(skc2,intersection(skc2,skc3)) ),
inference(res,[status(thm),theory(equality)],[13,4]),
[iquote('0:Res:13.2,4.0')] ).
cnf(28,plain,
~ subset(skc2,intersection(skc2,skc3)),
inference(mrr,[status(thm)],[22,3]),
[iquote('0:MRR:22.0,3.0')] ).
cnf(56,plain,
( ~ subset(u,v)
| subset(u,w)
| member(skf2(w,u),v) ),
inference(res,[status(thm),theory(equality)],[8,12]),
[iquote('0:Res:8.1,12.0')] ).
cnf(64,plain,
( ~ member(skf2(intersection(u,v),w),u)
| ~ member(skf2(intersection(u,v),w),v)
| subset(x,intersection(u,v)) ),
inference(res,[status(thm),theory(equality)],[16,11]),
[iquote('0:Res:16.2,11.0')] ).
cnf(498,plain,
( ~ member(skf2(intersection(u,v),u),v)
| subset(u,intersection(u,v))
| subset(w,intersection(u,v)) ),
inference(res,[status(thm),theory(equality)],[8,64]),
[iquote('0:Res:8.1,64.0')] ).
cnf(505,plain,
( ~ member(skf2(intersection(u,v),u),v)
| subset(u,intersection(u,v)) ),
inference(con,[status(thm)],[498]),
[iquote('0:Con:498.2')] ).
cnf(520,plain,
( ~ subset(u,v)
| subset(u,intersection(u,v))
| subset(u,intersection(u,v)) ),
inference(res,[status(thm),theory(equality)],[56,505]),
[iquote('0:Res:56.2,505.0')] ).
cnf(524,plain,
( ~ subset(u,v)
| subset(u,intersection(u,v)) ),
inference(obv,[status(thm),theory(equality)],[520]),
[iquote('0:Obv:520.1')] ).
cnf(898,plain,
~ subset(skc2,skc3),
inference(res,[status(thm),theory(equality)],[524,28]),
[iquote('0:Res:524.1,28.0')] ).
cnf(903,plain,
$false,
inference(mrr,[status(thm)],[898,1]),
[iquote('0:MRR:898.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET183+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.11/0.33 % Computer : n003.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun Jul 10 21:58:14 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.18/0.53
% 0.18/0.53 SPASS V 3.9
% 0.18/0.53 SPASS beiseite: Proof found.
% 0.18/0.53 % SZS status Theorem
% 0.18/0.53 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.53 SPASS derived 763 clauses, backtracked 53 clauses, performed 1 splits and kept 365 clauses.
% 0.18/0.53 SPASS allocated 85828 KBytes.
% 0.18/0.53 SPASS spent 0:00:00.19 on the problem.
% 0.18/0.53 0:00:00.04 for the input.
% 0.18/0.53 0:00:00.04 for the FLOTTER CNF translation.
% 0.18/0.53 0:00:00.01 for inferences.
% 0.18/0.53 0:00:00.00 for the backtracking.
% 0.18/0.53 0:00:00.08 for the reduction.
% 0.18/0.53
% 0.18/0.53
% 0.18/0.53 Here is a proof with depth 4, length 18 :
% 0.18/0.53 % SZS output start Refutation
% See solution above
% 0.18/0.53 Formulae used in the proof : prove_subset_intersection intersection_is_subset subset_defn equal_defn intersection_defn
% 0.18/0.53
%------------------------------------------------------------------------------