TSTP Solution File: SET072+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET072+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 05:23:33 EDT 2022
% Result : Theorem 0.83s 1.08s
% Output : Refutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of clauses : 21 ( 11 unt; 2 nHn; 21 RR)
% Number of literals : 35 ( 0 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
member(skc6,universal_class),
file('SET072+1.p',unknown),
[] ).
cnf(4,axiom,
member(skc5,universal_class),
file('SET072+1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(skc6,skc5),
file('SET072+1.p',unknown),
[] ).
cnf(14,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET072+1.p',unknown),
[] ).
cnf(18,axiom,
equal(unordered_pair(skc6,skc7),unordered_pair(skc5,skc7)),
file('SET072+1.p',unknown),
[] ).
cnf(65,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET072+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ equal(u,v)
| ~ member(u,universal_class)
| member(u,unordered_pair(v,w)) ),
file('SET072+1.p',unknown),
[] ).
cnf(129,plain,
( ~ equal(skc6,u)
| member(skc6,unordered_pair(u,v)) ),
inference(res,[status(thm),theory(equality)],[3,73]),
[iquote('0:Res:3.0,73.1')] ).
cnf(159,plain,
( ~ member(skc5,unordered_pair(skc6,u))
| equal(skc5,u) ),
inference(res,[status(thm),theory(equality)],[65,7]),
[iquote('0:Res:65.1,7.0')] ).
cnf(1204,plain,
( ~ member(u,singleton(v))
| equal(u,v)
| equal(u,v) ),
inference(spl,[status(thm),theory(equality)],[14,65]),
[iquote('0:SpL:14.0,65.0')] ).
cnf(1216,plain,
( ~ member(u,singleton(v))
| equal(u,v) ),
inference(obv,[status(thm),theory(equality)],[1204]),
[iquote('0:Obv:1204.1')] ).
cnf(3842,plain,
( ~ member(skc5,unordered_pair(skc5,skc7))
| equal(skc7,skc5) ),
inference(spl,[status(thm),theory(equality)],[18,159]),
[iquote('0:SpL:18.0,159.0')] ).
cnf(3849,plain,
( ~ equal(skc5,skc5)
| ~ member(skc5,universal_class)
| equal(skc7,skc5) ),
inference(res,[status(thm),theory(equality)],[73,3842]),
[iquote('0:Res:73.2,3842.0')] ).
cnf(3855,plain,
( ~ member(skc5,universal_class)
| equal(skc7,skc5) ),
inference(obv,[status(thm),theory(equality)],[3849]),
[iquote('0:Obv:3849.0')] ).
cnf(3856,plain,
equal(skc7,skc5),
inference(mrr,[status(thm)],[3855,4]),
[iquote('0:MRR:3855.0,4.0')] ).
cnf(3858,plain,
equal(unordered_pair(skc6,skc5),unordered_pair(skc5,skc5)),
inference(rew,[status(thm),theory(equality)],[3856,18]),
[iquote('0:Rew:3856.0,18.0')] ).
cnf(3866,plain,
equal(unordered_pair(skc6,skc5),singleton(skc5)),
inference(rew,[status(thm),theory(equality)],[14,3858]),
[iquote('0:Rew:14.0,3858.0')] ).
cnf(4183,plain,
( ~ equal(skc6,skc6)
| member(skc6,singleton(skc5)) ),
inference(spr,[status(thm),theory(equality)],[3866,129]),
[iquote('0:SpR:3866.0,129.1')] ).
cnf(4195,plain,
member(skc6,singleton(skc5)),
inference(obv,[status(thm),theory(equality)],[4183]),
[iquote('0:Obv:4183.0')] ).
cnf(4200,plain,
equal(skc6,skc5),
inference(res,[status(thm),theory(equality)],[4195,1216]),
[iquote('0:Res:4195.0,1216.0')] ).
cnf(4203,plain,
$false,
inference(mrr,[status(thm)],[4200,7]),
[iquote('0:MRR:4200.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET072+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n005.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 Jul 10 01:11:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.83/1.08
% 0.83/1.08 SPASS V 3.9
% 0.83/1.08 SPASS beiseite: Proof found.
% 0.83/1.08 % SZS status Theorem
% 0.83/1.08 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.83/1.08 SPASS derived 3766 clauses, backtracked 621 clauses, performed 7 splits and kept 2487 clauses.
% 0.83/1.08 SPASS allocated 100322 KBytes.
% 0.83/1.08 SPASS spent 0:00:00.72 on the problem.
% 0.83/1.08 0:00:00.04 for the input.
% 0.83/1.08 0:00:00.06 for the FLOTTER CNF translation.
% 0.83/1.08 0:00:00.04 for inferences.
% 0.83/1.08 0:00:00.01 for the backtracking.
% 0.83/1.08 0:00:00.52 for the reduction.
% 0.83/1.08
% 0.83/1.08
% 0.83/1.08 Here is a proof with depth 3, length 21 :
% 0.83/1.08 % SZS output start Refutation
% See solution above
% 0.83/1.08 Formulae used in the proof : right_cancellation singleton_set_defn unordered_pair_defn
% 0.83/1.08
%------------------------------------------------------------------------------