TSTP Solution File: SET017+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET017+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 05:22:36 EDT 2022
% Result : Theorem 0.76s 1.00s
% Output : Refutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of clauses : 21 ( 11 unt; 2 nHn; 21 RR)
% Number of literals : 34 ( 0 equ; 12 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('SET017+1.p',unknown),
[] ).
cnf(4,axiom,
member(skc5,universal_class),
file('SET017+1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(skc6,skc5),
file('SET017+1.p',unknown),
[] ).
cnf(14,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET017+1.p',unknown),
[] ).
cnf(18,axiom,
equal(unordered_pair(skc7,skc6),unordered_pair(skc7,skc5)),
file('SET017+1.p',unknown),
[] ).
cnf(65,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET017+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ equal(u,v)
| ~ member(u,universal_class)
| member(u,unordered_pair(w,v)) ),
file('SET017+1.p',unknown),
[] ).
cnf(99,plain,
( ~ equal(skc5,u)
| member(skc5,unordered_pair(v,u)) ),
inference(res,[status(thm),theory(equality)],[4,74]),
[iquote('0:Res:4.0,74.1')] ).
cnf(130,plain,
( ~ equal(skc6,u)
| member(skc6,unordered_pair(v,u)) ),
inference(res,[status(thm),theory(equality)],[3,74]),
[iquote('0:Res:3.0,74.1')] ).
cnf(161,plain,
( ~ member(skc5,unordered_pair(u,skc6))
| equal(skc5,u) ),
inference(res,[status(thm),theory(equality)],[65,7]),
[iquote('0:Res:65.2,7.0')] ).
cnf(1203,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(1215,plain,
( ~ member(u,singleton(v))
| equal(u,v) ),
inference(obv,[status(thm),theory(equality)],[1203]),
[iquote('0:Obv:1203.1')] ).
cnf(2638,plain,
( ~ member(skc5,unordered_pair(skc7,skc5))
| equal(skc7,skc5) ),
inference(spl,[status(thm),theory(equality)],[18,161]),
[iquote('0:SpL:18.0,161.0')] ).
cnf(2652,plain,
( ~ equal(skc5,skc5)
| equal(skc7,skc5) ),
inference(res,[status(thm),theory(equality)],[99,2638]),
[iquote('0:Res:99.1,2638.0')] ).
cnf(2653,plain,
equal(skc7,skc5),
inference(obv,[status(thm),theory(equality)],[2652]),
[iquote('0:Obv:2652.0')] ).
cnf(2654,plain,
equal(unordered_pair(skc5,skc6),unordered_pair(skc5,skc5)),
inference(rew,[status(thm),theory(equality)],[2653,18]),
[iquote('0:Rew:2653.0,18.0')] ).
cnf(2657,plain,
equal(unordered_pair(skc5,skc6),singleton(skc5)),
inference(rew,[status(thm),theory(equality)],[14,2654]),
[iquote('0:Rew:14.0,2654.0')] ).
cnf(2990,plain,
( ~ equal(skc6,skc6)
| member(skc6,singleton(skc5)) ),
inference(spr,[status(thm),theory(equality)],[2657,130]),
[iquote('0:SpR:2657.0,130.1')] ).
cnf(3002,plain,
member(skc6,singleton(skc5)),
inference(obv,[status(thm),theory(equality)],[2990]),
[iquote('0:Obv:2990.0')] ).
cnf(3006,plain,
equal(skc6,skc5),
inference(res,[status(thm),theory(equality)],[3002,1215]),
[iquote('0:Res:3002.0,1215.0')] ).
cnf(3010,plain,
$false,
inference(mrr,[status(thm)],[3006,7]),
[iquote('0:MRR:3006.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET017+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 16:52:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.76/1.00
% 0.76/1.00 SPASS V 3.9
% 0.76/1.00 SPASS beiseite: Proof found.
% 0.76/1.00 % SZS status Theorem
% 0.76/1.00 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.76/1.00 SPASS derived 2682 clauses, backtracked 239 clauses, performed 6 splits and kept 1862 clauses.
% 0.76/1.00 SPASS allocated 99639 KBytes.
% 0.76/1.00 SPASS spent 0:00:00.63 on the problem.
% 0.76/1.00 0:00:00.04 for the input.
% 0.76/1.00 0:00:00.06 for the FLOTTER CNF translation.
% 0.76/1.00 0:00:00.03 for inferences.
% 0.76/1.00 0:00:00.01 for the backtracking.
% 0.76/1.00 0:00:00.44 for the reduction.
% 0.76/1.00
% 0.76/1.00
% 0.76/1.00 Here is a proof with depth 3, length 21 :
% 0.76/1.00 % SZS output start Refutation
% See solution above
% 0.76/1.00 Formulae used in the proof : left_cancellation singleton_set_defn unordered_pair_defn
% 0.76/1.00
%------------------------------------------------------------------------------