TSTP Solution File: SET873+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET873+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 05:29:30 EDT 2022
% Result : Theorem 0.21s 0.45s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 12 ( 6 unt; 0 nHn; 12 RR)
% Number of literals : 19 ( 0 equ; 9 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(3,axiom,
subset(u,u),
file('SET873+1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(skc5,skc4),
file('SET873+1.p',unknown),
[] ).
cnf(6,axiom,
equal(set_union2(u,v),set_union2(v,u)),
file('SET873+1.p',unknown),
[] ).
cnf(9,axiom,
equal(set_union2(singleton(skc4),singleton(skc5)),singleton(skc4)),
file('SET873+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ subset(set_union2(singleton(u),v),v)
| in(u,v) ),
file('SET873+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ in(u,v)
| ~ equal(v,singleton(w))
| equal(u,w) ),
file('SET873+1.p',unknown),
[] ).
cnf(20,plain,
( ~ in(u,set_union2(singleton(skc4),singleton(skc5)))
| equal(u,skc4) ),
inference(res,[status(thm),theory(equality)],[9,13]),
[iquote('0:Res:9.0,13.1')] ).
cnf(23,plain,
( ~ in(u,singleton(skc4))
| equal(u,skc4) ),
inference(rew,[status(thm),theory(equality)],[9,20]),
[iquote('0:Rew:9.0,20.0')] ).
cnf(25,plain,
~ in(skc5,singleton(skc4)),
inference(res,[status(thm),theory(equality)],[23,4]),
[iquote('0:Res:23.1,4.0')] ).
cnf(48,plain,
( ~ subset(set_union2(u,singleton(v)),u)
| in(v,u) ),
inference(spl,[status(thm),theory(equality)],[6,12]),
[iquote('0:SpL:6.0,12.0')] ).
cnf(93,plain,
( ~ subset(singleton(skc4),singleton(skc4))
| in(skc5,singleton(skc4)) ),
inference(spl,[status(thm),theory(equality)],[9,48]),
[iquote('0:SpL:9.0,48.0')] ).
cnf(94,plain,
$false,
inference(mrr,[status(thm)],[93,3,25]),
[iquote('0:MRR:93.0,93.1,3.0,25.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET873+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jul 9 20:10:53 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.45
% 0.21/0.45 SPASS V 3.9
% 0.21/0.45 SPASS beiseite: Proof found.
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.45 SPASS derived 69 clauses, backtracked 0 clauses, performed 0 splits and kept 46 clauses.
% 0.21/0.45 SPASS allocated 85150 KBytes.
% 0.21/0.45 SPASS spent 0:00:00.09 on the problem.
% 0.21/0.45 0:00:00.03 for the input.
% 0.21/0.45 0:00:00.03 for the FLOTTER CNF translation.
% 0.21/0.45 0:00:00.00 for inferences.
% 0.21/0.45 0:00:00.00 for the backtracking.
% 0.21/0.45 0:00:00.00 for the reduction.
% 0.21/0.45
% 0.21/0.45
% 0.21/0.45 Here is a proof with depth 2, length 12 :
% 0.21/0.45 % SZS output start Refutation
% See solution above
% 0.21/0.45 Formulae used in the proof : reflexivity_r1_tarski t13_zfmisc_1 commutativity_k2_xboole_0 l21_zfmisc_1 d1_tarski idempotence_k2_xboole_0
% 0.21/0.45
%------------------------------------------------------------------------------