TSTP Solution File: SET977+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET977+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 05:30:10 EDT 2022
% Result : Theorem 0.20s 0.44s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 15 ( 4 unt; 2 nHn; 15 RR)
% Number of literals : 31 ( 0 equ; 21 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
~ equal(skc5,empty_set),
file('SET977+1.p',unknown),
[] ).
cnf(7,axiom,
( equal(u,empty_set)
| in(skf1(u),u) ),
file('SET977+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ in(u,v)
| ~ equal(v,empty_set) ),
file('SET977+1.p',unknown),
[] ).
cnf(11,axiom,
( equal(cartesian_product2(skc5,singleton(skc7)),empty_set)
| equal(cartesian_product2(singleton(skc6),skc5),empty_set) ),
file('SET977+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ equal(u,v)
| ~ in(w,x)
| in(ordered_pair(u,w),cartesian_product2(singleton(v),x)) ),
file('SET977+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ in(u,v)
| ~ equal(w,x)
| in(ordered_pair(u,w),cartesian_product2(v,singleton(x))) ),
file('SET977+1.p',unknown),
[] ).
cnf(19,plain,
in(skf1(skc5),skc5),
inference(res,[status(thm),theory(equality)],[7,4]),
[iquote('0:Res:7.1,4.0')] ).
cnf(71,plain,
( ~ equal(u,v)
| ~ in(w,x)
| ~ equal(cartesian_product2(singleton(v),x),empty_set) ),
inference(res,[status(thm),theory(equality)],[16,9]),
[iquote('0:Res:16.2,9.0')] ).
cnf(83,plain,
( ~ in(u,v)
| ~ equal(cartesian_product2(singleton(w),v),empty_set) ),
inference(aed,[status(thm),theory(equality)],[4,71]),
[iquote('0:AED:4.0,71.0')] ).
cnf(93,plain,
( ~ in(u,v)
| ~ equal(w,x)
| ~ equal(cartesian_product2(v,singleton(x)),empty_set) ),
inference(res,[status(thm),theory(equality)],[17,9]),
[iquote('0:Res:17.2,9.0')] ).
cnf(105,plain,
( ~ in(u,v)
| ~ equal(cartesian_product2(v,singleton(w)),empty_set) ),
inference(aed,[status(thm),theory(equality)],[4,93]),
[iquote('0:AED:4.0,93.1')] ).
cnf(109,plain,
( ~ in(u,skc5)
| ~ equal(empty_set,empty_set)
| equal(cartesian_product2(skc5,singleton(skc7)),empty_set) ),
inference(spl,[status(thm),theory(equality)],[11,83]),
[iquote('0:SpL:11.1,83.1')] ).
cnf(110,plain,
( ~ in(u,skc5)
| equal(cartesian_product2(skc5,singleton(skc7)),empty_set) ),
inference(obv,[status(thm),theory(equality)],[109]),
[iquote('0:Obv:109.1')] ).
cnf(111,plain,
~ in(u,skc5),
inference(mrr,[status(thm)],[110,105]),
[iquote('0:MRR:110.1,105.1')] ).
cnf(112,plain,
$false,
inference(unc,[status(thm)],[111,19]),
[iquote('0:UnC:111.0,19.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET977+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jul 9 22:45:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.44
% 0.20/0.44 SPASS V 3.9
% 0.20/0.44 SPASS beiseite: Proof found.
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.44 SPASS derived 78 clauses, backtracked 0 clauses, performed 0 splits and kept 52 clauses.
% 0.20/0.44 SPASS allocated 85175 KBytes.
% 0.20/0.44 SPASS spent 0:00:00.09 on the problem.
% 0.20/0.44 0:00:00.03 for the input.
% 0.20/0.44 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.44 0:00:00.00 for inferences.
% 0.20/0.44 0:00:00.00 for the backtracking.
% 0.20/0.44 0:00:00.00 for the reduction.
% 0.20/0.44
% 0.20/0.44
% 0.20/0.44 Here is a proof with depth 2, length 15 :
% 0.20/0.44 % SZS output start Refutation
% See solution above
% 0.20/0.44 Formulae used in the proof : t130_zfmisc_1 d1_xboole_0 t128_zfmisc_1 t129_zfmisc_1
% 0.20/0.44
%------------------------------------------------------------------------------