%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU153+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 14:34:25 EDT 2022
% Result : Theorem 0.18s 0.55s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 25 ( 21 unt; 0 nHn; 25 RR)
% Number of literals : 29 ( 0 equ; 6 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 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(2,axiom,
empty(skc40),
file('SEU153+2.p',unknown),
[] ).
cnf(3,axiom,
in(skc4,skc5),
file('SEU153+2.p',unknown),
[] ).
cnf(7,axiom,
disjoint(singleton(skc4),skc5),
file('SEU153+2.p',unknown),
[] ).
cnf(11,axiom,
~ equal(singleton(u),empty_set),
file('SEU153+2.p',unknown),
[] ).
cnf(13,axiom,
equal(set_union2(u,empty_set),u),
file('SEU153+2.p',unknown),
[] ).
cnf(18,axiom,
equal(set_difference(empty_set,u),empty_set),
file('SEU153+2.p',unknown),
[] ).
cnf(21,axiom,
( ~ empty(u)
| equal(u,empty_set) ),
file('SEU153+2.p',unknown),
[] ).
cnf(23,axiom,
equal(set_union2(u,v),set_union2(v,u)),
file('SEU153+2.p',unknown),
[] ).
cnf(56,axiom,
equal(set_difference(set_union2(u,v),v),set_difference(u,v)),
file('SEU153+2.p',unknown),
[] ).
cnf(59,axiom,
( ~ disjoint(u,v)
| equal(set_difference(u,v),u) ),
file('SEU153+2.p',unknown),
[] ).
cnf(63,axiom,
( ~ in(u,v)
| equal(set_union2(singleton(u),v),v) ),
file('SEU153+2.p',unknown),
[] ).
cnf(135,plain,
equal(set_union2(singleton(skc4),skc5),skc5),
inference(res,[status(thm),theory(equality)],[3,63]),
[iquote('0:Res:3.0,63.0')] ).
cnf(146,plain,
equal(set_union2(skc5,singleton(skc4)),skc5),
inference(rew,[status(thm),theory(equality)],[23,135]),
[iquote('0:Rew:23.0,135.0')] ).
cnf(171,plain,
equal(empty_set,skc40),
inference(ems,[status(thm)],[21,2]),
[iquote('0:EmS:21.0,2.0')] ).
cnf(176,plain,
equal(set_difference(skc40,u),skc40),
inference(rew,[status(thm),theory(equality)],[171,18]),
[iquote('0:Rew:171.0,18.0')] ).
cnf(178,plain,
~ equal(singleton(u),skc40),
inference(rew,[status(thm),theory(equality)],[171,11]),
[iquote('0:Rew:171.0,11.0')] ).
cnf(181,plain,
equal(set_union2(u,skc40),u),
inference(rew,[status(thm),theory(equality)],[171,13]),
[iquote('0:Rew:171.0,13.0')] ).
cnf(237,plain,
equal(set_union2(skc40,u),u),
inference(spr,[status(thm),theory(equality)],[23,181]),
[iquote('0:SpR:23.0,181.0')] ).
cnf(355,plain,
equal(set_difference(set_union2(u,v),u),set_difference(v,u)),
inference(spr,[status(thm),theory(equality)],[23,56]),
[iquote('0:SpR:23.0,56.0')] ).
cnf(358,plain,
equal(set_difference(u,u),set_difference(skc40,u)),
inference(spr,[status(thm),theory(equality)],[237,56]),
[iquote('0:SpR:237.0,56.0')] ).
cnf(361,plain,
equal(set_difference(u,u),skc40),
inference(rew,[status(thm),theory(equality)],[176,358]),
[iquote('0:Rew:176.0,358.0')] ).
cnf(543,plain,
equal(set_difference(singleton(skc4),skc5),set_difference(skc5,skc5)),
inference(spr,[status(thm),theory(equality)],[146,355]),
[iquote('0:SpR:146.0,355.0')] ).
cnf(551,plain,
equal(set_difference(singleton(skc4),skc5),skc40),
inference(rew,[status(thm),theory(equality)],[361,543]),
[iquote('0:Rew:361.0,543.0')] ).
cnf(558,plain,
( ~ disjoint(singleton(skc4),skc5)
| equal(singleton(skc4),skc40) ),
inference(spr,[status(thm),theory(equality)],[551,59]),
[iquote('0:SpR:551.0,59.1')] ).
cnf(567,plain,
$false,
inference(mrr,[status(thm)],[558,7,178]),
[iquote('0:MRR:558.0,558.1,7.0,178.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU153+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 19 15:42:54 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.18/0.55
% 0.18/0.55 SPASS V 3.9
% 0.18/0.55 SPASS beiseite: Proof found.
% 0.18/0.55 % SZS status Theorem
% 0.18/0.55 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.55 SPASS derived 404 clauses, backtracked 0 clauses, performed 0 splits and kept 232 clauses.
% 0.18/0.55 SPASS allocated 99256 KBytes.
% 0.18/0.55 SPASS spent 0:00:00.21 on the problem.
% 0.18/0.55 0:00:00.03 for the input.
% 0.18/0.55 0:00:00.13 for the FLOTTER CNF translation.
% 0.18/0.55 0:00:00.00 for inferences.
% 0.18/0.55 0:00:00.00 for the backtracking.
% 0.18/0.55 0:00:00.01 for the reduction.
% 0.18/0.55
% 0.18/0.55
% 0.18/0.55 Here is a proof with depth 3, length 25 :
% 0.18/0.55 % SZS output start Refutation
% See solution above
% 0.18/0.55 Formulae used in the proof : rc1_xboole_0 l25_zfmisc_1 l1_zfmisc_1 t1_boole t4_boole t6_boole commutativity_k2_xboole_0 t40_xboole_1 t83_xboole_1 l23_zfmisc_1
% 0.18/0.55
%------------------------------------------------------------------------------