TSTP Solution File: SEU144+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU144+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 14:34:18 EDT 2022
% Result : Theorem 0.18s 0.43s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of clauses : 22 ( 8 unt; 4 nHn; 22 RR)
% Number of literals : 41 ( 0 equ; 20 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( in(skc2,skc3)
| subset(singleton(skc2),skc3) ),
file('SEU144+1.p',unknown),
[] ).
cnf(4,axiom,
( subset(u,v)
| in(skf3(v,u),u) ),
file('SEU144+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ in(skc2,skc3)
| ~ subset(singleton(skc2),skc3) ),
file('SEU144+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ in(skf3(u,v),u)
| subset(w,u) ),
file('SEU144+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ in(u,v)
| ~ subset(v,w)
| in(u,w) ),
file('SEU144+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ in(u,v)
| ~ equal(v,singleton(w))
| equal(u,w) ),
file('SEU144+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ equal(u,v)
| ~ equal(w,singleton(v))
| in(u,w) ),
file('SEU144+1.p',unknown),
[] ).
cnf(12,plain,
in(skc2,skc3),
inference(spt,[spt(split,[position(s1)])],[2]),
[iquote('1:Spt:2.0')] ).
cnf(13,plain,
~ subset(singleton(skc2),skc3),
inference(mrr,[status(thm)],[5,12]),
[iquote('1:MRR:5.0,12.0')] ).
cnf(20,plain,
( ~ equal(u,v)
| in(u,singleton(v)) ),
inference(eqr,[status(thm),theory(equality)],[9]),
[iquote('0:EqR:9.1')] ).
cnf(22,plain,
( ~ equal(u,v)
| ~ subset(singleton(v),w)
| in(u,w) ),
inference(res,[status(thm),theory(equality)],[20,7]),
[iquote('0:Res:20.1,7.0')] ).
cnf(27,plain,
( ~ in(u,singleton(v))
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[8]),
[iquote('0:EqR:8.1')] ).
cnf(29,plain,
( subset(singleton(u),v)
| equal(skf3(v,singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[4,27]),
[iquote('0:Res:4.1,27.0')] ).
cnf(33,plain,
( ~ in(u,v)
| subset(singleton(u),v)
| subset(w,v) ),
inference(spl,[status(thm),theory(equality)],[29,6]),
[iquote('0:SpL:29.1,6.0')] ).
cnf(34,plain,
( ~ in(u,v)
| subset(singleton(u),v) ),
inference(con,[status(thm)],[33]),
[iquote('0:Con:33.2')] ).
cnf(37,plain,
~ in(skc2,skc3),
inference(res,[status(thm),theory(equality)],[34,13]),
[iquote('1:Res:34.1,13.0')] ).
cnf(38,plain,
$false,
inference(mrr,[status(thm)],[37,12]),
[iquote('1:MRR:37.0,12.0')] ).
cnf(39,plain,
~ in(skc2,skc3),
inference(spt,[spt(split,[position(sa)])],[38,12]),
[iquote('1:Spt:38.0,2.0,12.0')] ).
cnf(40,plain,
subset(singleton(skc2),skc3),
inference(spt,[spt(split,[position(s2)])],[2]),
[iquote('1:Spt:38.0,2.1')] ).
cnf(55,plain,
( ~ equal(u,skc2)
| in(u,skc3) ),
inference(res,[status(thm),theory(equality)],[40,22]),
[iquote('1:Res:40.0,22.1')] ).
cnf(61,plain,
~ equal(skc2,skc2),
inference(res,[status(thm),theory(equality)],[55,39]),
[iquote('1:Res:55.1,39.0')] ).
cnf(62,plain,
$false,
inference(obv,[status(thm),theory(equality)],[61]),
[iquote('1:Obv:61.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU144+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 06:30:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.43
% 0.18/0.43 SPASS V 3.9
% 0.18/0.43 SPASS beiseite: Proof found.
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 SPASS derived 42 clauses, backtracked 3 clauses, performed 1 splits and kept 46 clauses.
% 0.18/0.43 SPASS allocated 85251 KBytes.
% 0.18/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.18/0.43 0:00:00.04 for the input.
% 0.18/0.43 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.43 0:00:00.00 for inferences.
% 0.18/0.43 0:00:00.00 for the backtracking.
% 0.18/0.43 0:00:00.00 for the reduction.
% 0.18/0.43
% 0.18/0.43
% 0.18/0.43 Here is a proof with depth 4, length 22 :
% 0.18/0.43 % SZS output start Refutation
% See solution above
% 0.18/0.43 Formulae used in the proof : l2_zfmisc_1 d3_tarski d1_tarski
% 0.18/0.43
%------------------------------------------------------------------------------