TSTP Solution File: SET874+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET874+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 05:29:30 EDT 2022
% Result : Theorem 0.19s 0.44s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 9 ( 6 unt; 0 nHn; 9 RR)
% Number of literals : 13 ( 0 equ; 8 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
equal(unordered_pair(u,v),unordered_pair(v,u)),
file('SET874+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ in(u,v)
| equal(set_union2(singleton(u),v),v) ),
file('SET874+1.p',unknown),
[] ).
cnf(10,axiom,
~ equal(set_union2(singleton(skc5),unordered_pair(skc5,skc4)),unordered_pair(skc5,skc4)),
file('SET874+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ equal(u,v)
| ~ equal(w,unordered_pair(x,v))
| in(u,w) ),
file('SET874+1.p',unknown),
[] ).
cnf(17,plain,
~ equal(set_union2(singleton(skc5),unordered_pair(skc4,skc5)),unordered_pair(skc4,skc5)),
inference(rew,[status(thm),theory(equality)],[4,10]),
[iquote('0:Rew:4.0,10.0')] ).
cnf(18,plain,
~ in(skc5,unordered_pair(skc4,skc5)),
inference(res,[status(thm),theory(equality)],[9,17]),
[iquote('0:Res:9.1,17.0')] ).
cnf(57,plain,
( ~ equal(u,v)
| in(u,unordered_pair(w,v)) ),
inference(eqr,[status(thm),theory(equality)],[12]),
[iquote('0:EqR:12.1')] ).
cnf(65,plain,
~ equal(skc5,skc5),
inference(res,[status(thm),theory(equality)],[57,18]),
[iquote('0:Res:57.1,18.0')] ).
cnf(68,plain,
$false,
inference(obv,[status(thm),theory(equality)],[65]),
[iquote('0:Obv:65.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET874+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n024.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 : Mon Jul 11 06:52:13 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.44
% 0.19/0.44 SPASS V 3.9
% 0.19/0.44 SPASS beiseite: Proof found.
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 SPASS derived 45 clauses, backtracked 0 clauses, performed 0 splits and kept 27 clauses.
% 0.19/0.44 SPASS allocated 85221 KBytes.
% 0.19/0.44 SPASS spent 0:00:00.09 on the problem.
% 0.19/0.44 0:00:00.03 for the input.
% 0.19/0.44 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.44 0:00:00.00 for inferences.
% 0.19/0.44 0:00:00.00 for the backtracking.
% 0.19/0.44 0:00:00.00 for the reduction.
% 0.19/0.44
% 0.19/0.44
% 0.19/0.44 Here is a proof with depth 2, length 9 :
% 0.19/0.44 % SZS output start Refutation
% See solution above
% 0.19/0.44 Formulae used in the proof : commutativity_k2_tarski l23_zfmisc_1 t14_zfmisc_1 d2_tarski idempotence_k2_xboole_0
% 0.19/0.44
%------------------------------------------------------------------------------