TSTP Solution File: NUM385+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM385+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 : Mon Jul 18 14:25:48 EDT 2022
% Result : Theorem 4.47s 4.67s
% Output : Refutation 4.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 22 ( 8 unt; 8 nHn; 22 RR)
% Number of literals : 48 ( 0 equ; 22 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(29,axiom,
~ equal(skc13,skc12),
file('NUM385+1.p',unknown),
[] ).
cnf(32,axiom,
in(u,succ(u)),
file('NUM385+1.p',unknown),
[] ).
cnf(33,axiom,
equal(succ(skc13),succ(skc12)),
file('NUM385+1.p',unknown),
[] ).
cnf(40,axiom,
equal(set_union2(u,singleton(u)),succ(u)),
file('NUM385+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ in(u,v)
| ~ in(v,u) ),
file('NUM385+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ in(u,v)
| ~ equal(v,singleton(w))
| equal(u,w) ),
file('NUM385+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ in(u,v)
| ~ equal(v,set_union2(w,x))
| in(u,x)
| in(u,w) ),
file('NUM385+1.p',unknown),
[] ).
cnf(64,plain,
( ~ equal(u,singleton(skc13))
| ~ in(skc12,u) ),
inference(res,[status(thm),theory(equality)],[51,29]),
[iquote('0:Res:51.2,29.0')] ).
cnf(67,plain,
in(skc13,succ(skc12)),
inference(spr,[status(thm),theory(equality)],[33,32]),
[iquote('0:SpR:33.0,32.0')] ).
cnf(143,plain,
( ~ in(u,singleton(v))
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[51]),
[iquote('0:EqR:51.1')] ).
cnf(258,plain,
( ~ in(u,set_union2(v,w))
| in(u,w)
| in(u,v) ),
inference(eqr,[status(thm),theory(equality)],[58]),
[iquote('0:EqR:58.1')] ).
cnf(261,plain,
( ~ in(u,v)
| ~ equal(v,succ(w))
| in(u,singleton(w))
| in(u,w) ),
inference(spl,[status(thm),theory(equality)],[40,58]),
[iquote('0:SpL:40.0,58.1')] ).
cnf(380,plain,
( ~ in(u,succ(v))
| in(u,singleton(v))
| in(u,v) ),
inference(spl,[status(thm),theory(equality)],[40,258]),
[iquote('0:SpL:40.0,258.0')] ).
cnf(498,plain,
( ~ in(u,v)
| ~ equal(v,succ(skc12))
| in(u,singleton(skc13))
| in(u,skc13) ),
inference(spl,[status(thm),theory(equality)],[33,261]),
[iquote('0:SpL:33.0,261.1')] ).
cnf(2199,plain,
( ~ in(u,succ(v))
| in(u,v)
| equal(u,v) ),
inference(res,[status(thm),theory(equality)],[380,143]),
[iquote('0:Res:380.1,143.0')] ).
cnf(3055,plain,
( ~ in(u,succ(skc12))
| in(u,singleton(skc13))
| in(u,skc13) ),
inference(eqr,[status(thm),theory(equality)],[498]),
[iquote('0:EqR:498.1')] ).
cnf(14401,plain,
( in(skc13,skc12)
| equal(skc13,skc12) ),
inference(res,[status(thm),theory(equality)],[67,2199]),
[iquote('0:Res:67.0,2199.0')] ).
cnf(14508,plain,
in(skc13,skc12),
inference(mrr,[status(thm)],[14401,29]),
[iquote('0:MRR:14401.1,29.0')] ).
cnf(14539,plain,
~ in(skc12,skc13),
inference(res,[status(thm),theory(equality)],[14508,45]),
[iquote('0:Res:14508.0,45.0')] ).
cnf(14606,plain,
( ~ in(skc12,succ(skc12))
| ~ equal(singleton(skc13),singleton(skc13))
| in(skc12,skc13) ),
inference(res,[status(thm),theory(equality)],[3055,64]),
[iquote('0:Res:3055.1,64.1')] ).
cnf(14760,plain,
( ~ in(skc12,succ(skc12))
| in(skc12,skc13) ),
inference(obv,[status(thm),theory(equality)],[14606]),
[iquote('0:Obv:14606.1')] ).
cnf(14761,plain,
$false,
inference(mrr,[status(thm)],[14760,32,14539]),
[iquote('0:MRR:14760.0,14760.1,32.0,14539.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUM385+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n029.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jul 5 03:30:42 EDT 2022
% 0.14/0.36 % CPUTime :
% 4.47/4.67
% 4.47/4.67 SPASS V 3.9
% 4.47/4.67 SPASS beiseite: Proof found.
% 4.47/4.67 % SZS status Theorem
% 4.47/4.67 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.47/4.67 SPASS derived 12935 clauses, backtracked 0 clauses, performed 0 splits and kept 3703 clauses.
% 4.47/4.67 SPASS allocated 108724 KBytes.
% 4.47/4.67 SPASS spent 0:00:04.18 on the problem.
% 4.47/4.67 0:00:00.03 for the input.
% 4.47/4.67 0:00:00.03 for the FLOTTER CNF translation.
% 4.47/4.67 0:00:00.20 for inferences.
% 4.47/4.67 0:00:00.00 for the backtracking.
% 4.47/4.67 0:00:03.85 for the reduction.
% 4.47/4.67
% 4.47/4.67
% 4.47/4.67 Here is a proof with depth 5, length 22 :
% 4.47/4.67 % SZS output start Refutation
% See solution above
% 4.47/4.67 Formulae used in the proof : t12_ordinal1 t10_ordinal1 d1_ordinal1 antisymmetry_r2_hidden d1_tarski t1_boole d2_xboole_0
% 4.47/4.67
%------------------------------------------------------------------------------