TSTP Solution File: SET930+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET930+1 : TPTP v8.1.0. Released v3.2.0.
% 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 05:29:54 EDT 2022
% Result : Theorem 0.19s 0.43s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 17 ( 8 unt; 4 nHn; 17 RR)
% Number of literals : 31 ( 0 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
equal(unordered_pair(u,v),unordered_pair(v,u)),
file('SET930+1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(set_difference(unordered_pair(skc5,skc6),skc7),empty_set),
file('SET930+1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(set_difference(unordered_pair(skc5,skc6),skc7),singleton(skc5)),
file('SET930+1.p',unknown),
[] ).
cnf(8,axiom,
~ equal(set_difference(unordered_pair(skc5,skc6),skc7),singleton(skc6)),
file('SET930+1.p',unknown),
[] ).
cnf(9,axiom,
~ equal(set_difference(unordered_pair(skc5,skc6),skc7),unordered_pair(skc5,skc6)),
file('SET930+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ in(u,v)
| in(w,v)
| equal(set_difference(unordered_pair(w,u),v),singleton(w)) ),
file('SET930+1.p',unknown),
[] ).
cnf(18,axiom,
( in(u,v)
| in(w,v)
| equal(set_difference(unordered_pair(u,w),v),unordered_pair(u,w)) ),
file('SET930+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ in(u,v)
| ~ in(w,v)
| equal(set_difference(unordered_pair(u,w),v),empty_set) ),
file('SET930+1.p',unknown),
[] ).
cnf(20,plain,
( ~ in(skc6,skc7)
| ~ in(skc5,skc7) ),
inference(res,[status(thm),theory(equality)],[19,5]),
[iquote('0:Res:19.2,5.0')] ).
cnf(26,plain,
( ~ in(skc6,skc7)
| in(skc5,skc7) ),
inference(res,[status(thm),theory(equality)],[16,7]),
[iquote('0:Res:16.1,7.0')] ).
cnf(29,plain,
( in(skc6,skc7)
| in(skc5,skc7) ),
inference(res,[status(thm),theory(equality)],[18,9]),
[iquote('0:Res:18.1,9.0')] ).
cnf(32,plain,
in(skc5,skc7),
inference(mrr,[status(thm)],[26,29]),
[iquote('0:MRR:26.0,29.0')] ).
cnf(33,plain,
~ in(skc6,skc7),
inference(mrr,[status(thm)],[20,32]),
[iquote('0:MRR:20.1,32.0')] ).
cnf(94,plain,
( ~ in(u,v)
| in(w,v)
| equal(set_difference(unordered_pair(u,w),v),singleton(w)) ),
inference(spr,[status(thm),theory(equality)],[4,16]),
[iquote('0:SpR:4.0,16.2')] ).
cnf(184,plain,
( ~ in(skc5,skc7)
| ~ equal(singleton(skc6),singleton(skc6))
| in(skc6,skc7) ),
inference(spl,[status(thm),theory(equality)],[94,8]),
[iquote('0:SpL:94.2,8.0')] ).
cnf(194,plain,
( ~ in(skc5,skc7)
| in(skc6,skc7) ),
inference(obv,[status(thm),theory(equality)],[184]),
[iquote('0:Obv:184.1')] ).
cnf(195,plain,
$false,
inference(mrr,[status(thm)],[194,32,33]),
[iquote('0:MRR:194.0,194.1,32.0,33.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET930+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n021.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 : Sat Jul 9 21:19:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.43
% 0.19/0.43 SPASS V 3.9
% 0.19/0.43 SPASS beiseite: Proof found.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.43 SPASS derived 135 clauses, backtracked 0 clauses, performed 0 splits and kept 44 clauses.
% 0.19/0.43 SPASS allocated 85197 KBytes.
% 0.19/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.19/0.43 0:00:00.03 for the input.
% 0.19/0.43 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.43 0:00:00.00 for inferences.
% 0.19/0.43 0:00:00.00 for the backtracking.
% 0.19/0.43 0:00:00.00 for the reduction.
% 0.19/0.43
% 0.19/0.43
% 0.19/0.43 Here is a proof with depth 2, length 17 :
% 0.19/0.43 % SZS output start Refutation
% See solution above
% 0.19/0.43 Formulae used in the proof : commutativity_k2_tarski t74_zfmisc_1 l39_zfmisc_1 t72_zfmisc_1 t73_zfmisc_1
% 0.19/0.43
%------------------------------------------------------------------------------