%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU112+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 14:34:01 EDT 2022
% Result : Theorem 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 12 ( 8 unt; 0 nHn; 12 RR)
% Number of literals : 17 ( 0 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(45,axiom,
subset(u,set_union2(u,v)),
file('SEU112+1.p',unknown),
[] ).
cnf(51,axiom,
equal(set_union2(u,v),set_union2(v,u)),
file('SEU112+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ subset(u,v)
| subset(finite_subsets(u),finite_subsets(v)) ),
file('SEU112+1.p',unknown),
[] ).
cnf(65,axiom,
~ subset(set_union2(finite_subsets(skc7),finite_subsets(skc6)),finite_subsets(set_union2(skc7,skc6))),
file('SEU112+1.p',unknown),
[] ).
cnf(68,axiom,
( ~ subset(u,v)
| ~ subset(w,v)
| subset(set_union2(w,u),v) ),
file('SEU112+1.p',unknown),
[] ).
cnf(69,plain,
~ subset(set_union2(finite_subsets(skc6),finite_subsets(skc7)),finite_subsets(set_union2(skc6,skc7))),
inference(rew,[status(thm),theory(equality)],[51,65]),
[iquote('0:Rew:51.0,65.0,51.0,65.0')] ).
cnf(71,plain,
( ~ subset(finite_subsets(skc7),finite_subsets(set_union2(skc6,skc7)))
| ~ subset(finite_subsets(skc6),finite_subsets(set_union2(skc6,skc7))) ),
inference(res,[status(thm),theory(equality)],[68,69]),
[iquote('0:Res:68.2,69.0')] ).
cnf(104,plain,
subset(u,set_union2(v,u)),
inference(spr,[status(thm),theory(equality)],[51,45]),
[iquote('0:SpR:51.0,45.0')] ).
cnf(542,plain,
( ~ subset(skc7,set_union2(skc6,skc7))
| ~ subset(finite_subsets(skc6),finite_subsets(set_union2(skc6,skc7))) ),
inference(res,[status(thm),theory(equality)],[60,71]),
[iquote('0:Res:60.1,71.0')] ).
cnf(543,plain,
~ subset(finite_subsets(skc6),finite_subsets(set_union2(skc6,skc7))),
inference(mrr,[status(thm)],[542,104]),
[iquote('0:MRR:542.0,104.0')] ).
cnf(549,plain,
~ subset(skc6,set_union2(skc6,skc7)),
inference(res,[status(thm),theory(equality)],[60,543]),
[iquote('0:Res:60.1,543.0')] ).
cnf(550,plain,
$false,
inference(mrr,[status(thm)],[549,45]),
[iquote('0:MRR:549.0,45.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU112+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n028.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 : Mon Jun 20 11:36:16 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.47
% 0.19/0.47 SPASS V 3.9
% 0.19/0.47 SPASS beiseite: Proof found.
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47 SPASS derived 419 clauses, backtracked 0 clauses, performed 0 splits and kept 259 clauses.
% 0.19/0.47 SPASS allocated 97976 KBytes.
% 0.19/0.47 SPASS spent 0:00:00.12 on the problem.
% 0.19/0.47 0:00:00.03 for the input.
% 0.19/0.47 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.47 0:00:00.01 for inferences.
% 0.19/0.47 0:00:00.00 for the backtracking.
% 0.19/0.47 0:00:00.02 for the reduction.
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 Here is a proof with depth 3, length 12 :
% 0.19/0.47 % SZS output start Refutation
% See solution above
% 0.19/0.47 Formulae used in the proof : t7_xboole_1 commutativity_k2_xboole_0 t23_finsub_1 t25_finsub_1 t8_xboole_1
% 0.19/0.47
%------------------------------------------------------------------------------