TSTP Solution File: SET635+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET635+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 05:27:43 EDT 2022
% Result : Theorem 0.20s 0.47s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of clauses : 31 ( 19 unt; 4 nHn; 31 RR)
% Number of literals : 44 ( 0 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
~ member(u,empty_set),
file('SET635+3.p',unknown),
[] ).
cnf(4,axiom,
equal(union(u,empty_set),u),
file('SET635+3.p',unknown),
[] ).
cnf(5,axiom,
( empty(u)
| member(skf5(u),u) ),
file('SET635+3.p',unknown),
[] ).
cnf(8,axiom,
equal(union(u,v),union(v,u)),
file('SET635+3.p',unknown),
[] ).
cnf(9,axiom,
equal(intersection(u,v),intersection(v,u)),
file('SET635+3.p',unknown),
[] ).
cnf(10,axiom,
( ~ empty(u)
| ~ member(v,u) ),
file('SET635+3.p',unknown),
[] ).
cnf(11,axiom,
( subset(u,v)
| member(skf3(v,u),u) ),
file('SET635+3.p',unknown),
[] ).
cnf(16,axiom,
( ~ member(u,difference(v,w))
| member(u,v) ),
file('SET635+3.p',unknown),
[] ).
cnf(18,axiom,
( ~ member(u,v)
| ~ member(u,difference(w,v)) ),
file('SET635+3.p',unknown),
[] ).
cnf(19,axiom,
equal(difference(intersection(u,v),w),intersection(u,difference(v,w))),
file('SET635+3.p',unknown),
[] ).
cnf(20,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal(v,u) ),
file('SET635+3.p',unknown),
[] ).
cnf(25,axiom,
equal(union(difference(u,v),difference(u,w)),difference(u,intersection(v,w))),
file('SET635+3.p',unknown),
[] ).
cnf(28,axiom,
~ equal(difference(intersection(skc5,skc4),intersection(skc5,skc3)),intersection(skc5,difference(skc4,skc3))),
file('SET635+3.p',unknown),
[] ).
cnf(30,plain,
~ equal(intersection(skc4,difference(skc5,intersection(skc3,skc5))),intersection(skc5,difference(skc4,skc3))),
inference(rew,[status(thm),theory(equality)],[19,28,9]),
[iquote('0:Rew:19.0,28.0,9.0,28.0,9.0,28.0')] ).
cnf(48,plain,
equal(union(empty_set,u),u),
inference(spr,[status(thm),theory(equality)],[8,4]),
[iquote('0:SpR:8.0,4.0')] ).
cnf(58,plain,
subset(empty_set,u),
inference(res,[status(thm),theory(equality)],[11,2]),
[iquote('0:Res:11.1,2.0')] ).
cnf(59,plain,
( ~ empty(u)
| subset(u,v) ),
inference(res,[status(thm),theory(equality)],[11,10]),
[iquote('0:Res:11.1,10.1')] ).
cnf(65,plain,
( empty(difference(u,v))
| member(skf5(difference(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[5,16]),
[iquote('0:Res:5.1,16.0')] ).
cnf(76,plain,
( ~ member(skf5(difference(u,v)),v)
| empty(difference(u,v)) ),
inference(res,[status(thm),theory(equality)],[5,18]),
[iquote('0:Res:5.1,18.1')] ).
cnf(92,plain,
( ~ subset(u,empty_set)
| equal(u,empty_set) ),
inference(res,[status(thm),theory(equality)],[58,20]),
[iquote('0:Res:58.0,20.0')] ).
cnf(100,plain,
( ~ empty(u)
| equal(u,empty_set) ),
inference(res,[status(thm),theory(equality)],[59,92]),
[iquote('0:Res:59.1,92.0')] ).
cnf(122,plain,
equal(difference(intersection(u,v),w),intersection(v,difference(u,w))),
inference(spr,[status(thm),theory(equality)],[9,19]),
[iquote('0:SpR:9.0,19.0')] ).
cnf(131,plain,
equal(intersection(u,difference(v,w)),intersection(v,difference(u,w))),
inference(rew,[status(thm),theory(equality)],[19,122]),
[iquote('0:Rew:19.0,122.0')] ).
cnf(132,plain,
~ equal(intersection(skc4,difference(skc5,intersection(skc3,skc5))),intersection(skc4,difference(skc5,skc3))),
inference(rew,[status(thm),theory(equality)],[131,30]),
[iquote('0:Rew:131.0,30.0')] ).
cnf(409,plain,
( empty(difference(u,u))
| empty(difference(u,u)) ),
inference(res,[status(thm),theory(equality)],[65,76]),
[iquote('0:Res:65.1,76.0')] ).
cnf(411,plain,
empty(difference(u,u)),
inference(obv,[status(thm),theory(equality)],[409]),
[iquote('0:Obv:409.0')] ).
cnf(421,plain,
equal(difference(u,u),empty_set),
inference(ems,[status(thm)],[100,411]),
[iquote('0:EmS:100.0,411.0')] ).
cnf(460,plain,
equal(difference(u,intersection(v,u)),union(difference(u,v),empty_set)),
inference(spr,[status(thm),theory(equality)],[421,25]),
[iquote('0:SpR:421.0,25.0')] ).
cnf(473,plain,
equal(difference(u,intersection(v,u)),difference(u,v)),
inference(rew,[status(thm),theory(equality)],[48,460,8]),
[iquote('0:Rew:48.0,460.0,8.0,460.0')] ).
cnf(474,plain,
~ equal(intersection(skc4,difference(skc5,skc3)),intersection(skc4,difference(skc5,skc3))),
inference(rew,[status(thm),theory(equality)],[473,132]),
[iquote('0:Rew:473.0,132.0')] ).
cnf(477,plain,
$false,
inference(obv,[status(thm),theory(equality)],[474]),
[iquote('0:Obv:474.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET635+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n024.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 13:37:13 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.47
% 0.20/0.47 SPASS V 3.9
% 0.20/0.47 SPASS beiseite: Proof found.
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.47 SPASS derived 357 clauses, backtracked 0 clauses, performed 0 splits and kept 172 clauses.
% 0.20/0.47 SPASS allocated 97931 KBytes.
% 0.20/0.47 SPASS spent 0:00:00.12 on the problem.
% 0.20/0.47 0:00:00.04 for the input.
% 0.20/0.47 0:00:00.04 for the FLOTTER CNF translation.
% 0.20/0.47 0:00:00.00 for inferences.
% 0.20/0.47 0:00:00.00 for the backtracking.
% 0.20/0.47 0:00:00.02 for the reduction.
% 0.20/0.47
% 0.20/0.47
% 0.20/0.47 Here is a proof with depth 5, length 31 :
% 0.20/0.47 % SZS output start Refutation
% See solution above
% 0.20/0.47 Formulae used in the proof : empty_set_defn union_empty_set empty_defn commutativity_of_union commutativity_of_intersection subset_defn difference_defn difference_and_intersection equal_defn difference_and_intersection_and_union prove_th117
% 0.20/0.47
%------------------------------------------------------------------------------