TSTP Solution File: SEU230+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU230+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 14:35:18 EDT 2022
% Result : Theorem 0.19s 0.50s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 24 ( 9 unt; 4 nHn; 24 RR)
% Number of literals : 44 ( 0 equ; 23 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(29,axiom,
element(skf5(u),u),
file('SEU230+3.p',unknown),
[] ).
cnf(31,axiom,
~ in(skc11,succ(skc11)),
file('SEU230+3.p',unknown),
[] ).
cnf(34,axiom,
equal(set_union2(u,u),u),
file('SEU230+3.p',unknown),
[] ).
cnf(38,axiom,
equal(set_union2(u,singleton(u)),succ(u)),
file('SEU230+3.p',unknown),
[] ).
cnf(42,axiom,
( ~ empty(u)
| ~ in(v,u) ),
file('SEU230+3.p',unknown),
[] ).
cnf(44,axiom,
( ~ element(u,v)
| empty(v)
| in(u,v) ),
file('SEU230+3.p',unknown),
[] ).
cnf(49,axiom,
( ~ in(u,v)
| ~ equal(v,singleton(w))
| equal(u,w) ),
file('SEU230+3.p',unknown),
[] ).
cnf(50,axiom,
( ~ equal(u,v)
| ~ equal(w,singleton(v))
| in(u,w) ),
file('SEU230+3.p',unknown),
[] ).
cnf(52,axiom,
( ~ in(u,v)
| ~ equal(w,set_union2(x,v))
| in(u,w) ),
file('SEU230+3.p',unknown),
[] ).
cnf(62,plain,
( ~ in(skc11,u)
| ~ equal(set_union2(v,u),succ(skc11)) ),
inference(res,[status(thm),theory(equality)],[52,31]),
[iquote('0:Res:52.2,31.0')] ).
cnf(113,plain,
( empty(u)
| in(skf5(u),u) ),
inference(res,[status(thm),theory(equality)],[29,44]),
[iquote('0:Res:29.0,44.0')] ).
cnf(129,plain,
( ~ equal(u,v)
| in(u,singleton(v)) ),
inference(eqr,[status(thm),theory(equality)],[50]),
[iquote('0:EqR:50.1')] ).
cnf(132,plain,
( ~ empty(singleton(u))
| ~ equal(v,u) ),
inference(res,[status(thm),theory(equality)],[129,42]),
[iquote('0:Res:129.1,42.1')] ).
cnf(134,plain,
~ empty(singleton(u)),
inference(aed,[status(thm),theory(equality)],[132]),
[iquote('0:AED:132.1')] ).
cnf(138,plain,
( ~ in(u,singleton(v))
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[49]),
[iquote('0:EqR:49.1')] ).
cnf(141,plain,
( empty(singleton(u))
| equal(skf5(singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[113,138]),
[iquote('0:Res:113.1,138.0')] ).
cnf(144,plain,
equal(skf5(singleton(u)),u),
inference(mrr,[status(thm)],[141,134]),
[iquote('0:MRR:141.0,134.0')] ).
cnf(146,plain,
( empty(singleton(u))
| in(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[144,113]),
[iquote('0:SpR:144.0,113.1')] ).
cnf(150,plain,
in(u,singleton(u)),
inference(mrr,[status(thm)],[146,134]),
[iquote('0:MRR:146.0,134.0')] ).
cnf(159,plain,
( ~ in(u,singleton(v))
| ~ equal(w,succ(v))
| in(u,w) ),
inference(spl,[status(thm),theory(equality)],[38,52]),
[iquote('0:SpL:38.0,52.1')] ).
cnf(347,plain,
( ~ in(skc11,u)
| ~ equal(u,succ(skc11)) ),
inference(spl,[status(thm),theory(equality)],[34,62]),
[iquote('0:SpL:34.0,62.1')] ).
cnf(520,plain,
( ~ equal(u,succ(v))
| in(v,u) ),
inference(res,[status(thm),theory(equality)],[150,159]),
[iquote('0:Res:150.0,159.0')] ).
cnf(524,plain,
~ equal(u,succ(skc11)),
inference(mrr,[status(thm)],[347,520]),
[iquote('0:MRR:347.0,520.1')] ).
cnf(525,plain,
$false,
inference(obv,[status(thm),theory(equality)],[524]),
[iquote('0:Obv:524.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU230+3 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n019.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 07:35:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.50
% 0.19/0.50 SPASS V 3.9
% 0.19/0.50 SPASS beiseite: Proof found.
% 0.19/0.50 % SZS status Theorem
% 0.19/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.50 SPASS derived 435 clauses, backtracked 3 clauses, performed 1 splits and kept 273 clauses.
% 0.19/0.50 SPASS allocated 98022 KBytes.
% 0.19/0.50 SPASS spent 0:00:00.15 on the problem.
% 0.19/0.50 0:00:00.04 for the input.
% 0.19/0.50 0:00:00.04 for the FLOTTER CNF translation.
% 0.19/0.50 0:00:00.01 for inferences.
% 0.19/0.50 0:00:00.00 for the backtracking.
% 0.19/0.50 0:00:00.04 for the reduction.
% 0.19/0.50
% 0.19/0.50
% 0.19/0.50 Here is a proof with depth 4, length 24 :
% 0.19/0.50 % SZS output start Refutation
% See solution above
% 0.19/0.50 Formulae used in the proof : existence_m1_subset_1 t10_ordinal1 idempotence_k2_xboole_0 d1_ordinal1 t7_boole t2_subset d1_tarski t1_boole d2_xboole_0
% 0.19/0.50
%------------------------------------------------------------------------------