%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU174+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 14:34:42 EDT 2022
% Result : Theorem 0.19s 0.53s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 22 ( 14 unt; 3 nHn; 22 RR)
% Number of literals : 37 ( 0 equ; 14 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
empty(empty_set),
file('SEU174+1.p',unknown),
[] ).
cnf(3,axiom,
empty(skf9(u)),
file('SEU174+1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(skc4,empty_set),
file('SEU174+1.p',unknown),
[] ).
cnf(9,axiom,
element(skc4,powerset(powerset(skc5))),
file('SEU174+1.p',unknown),
[] ).
cnf(10,axiom,
equal(complements_of_subsets(skc5,skc4),empty_set),
file('SEU174+1.p',unknown),
[] ).
cnf(12,axiom,
element(skf9(u),powerset(u)),
file('SEU174+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ empty(u)
| equal(u,empty_set) ),
file('SEU174+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ empty(u)
| ~ in(v,w)
| ~ element(w,powerset(u)) ),
file('SEU174+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ element(u,powerset(powerset(v)))
| equal(complements_of_subsets(v,complements_of_subsets(v,u)),u) ),
file('SEU174+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ element(u,powerset(powerset(v)))
| ~ element(w,powerset(powerset(v)))
| equal(u,complements_of_subsets(v,w))
| in(subset_complement(v,skf6(w,u,v)),w)
| in(skf6(w,u,v),u) ),
file('SEU174+1.p',unknown),
[] ).
cnf(57,plain,
equal(complements_of_subsets(skc5,complements_of_subsets(skc5,skc4)),skc4),
inference(res,[status(thm),theory(equality)],[9,31]),
[iquote('0:Res:9.0,31.0')] ).
cnf(60,plain,
equal(complements_of_subsets(skc5,empty_set),skc4),
inference(rew,[status(thm),theory(equality)],[10,57]),
[iquote('0:Rew:10.0,57.0')] ).
cnf(88,plain,
equal(skf9(u),empty_set),
inference(ems,[status(thm)],[14,3]),
[iquote('0:EmS:14.0,3.0')] ).
cnf(93,plain,
element(empty_set,powerset(u)),
inference(rew,[status(thm),theory(equality)],[88,12]),
[iquote('0:Rew:88.0,12.0')] ).
cnf(177,plain,
( ~ empty(u)
| ~ in(v,empty_set) ),
inference(res,[status(thm),theory(equality)],[93,29]),
[iquote('0:Res:93.0,29.2')] ).
cnf(183,plain,
~ in(u,empty_set),
inference(ems,[status(thm)],[177,1]),
[iquote('0:EmS:177.0,1.0')] ).
cnf(320,plain,
( ~ element(u,powerset(powerset(v)))
| equal(complements_of_subsets(v,u),empty_set)
| in(subset_complement(v,skf6(u,empty_set,v)),u)
| in(skf6(u,empty_set,v),empty_set) ),
inference(res,[status(thm),theory(equality)],[93,32]),
[iquote('0:Res:93.0,32.0')] ).
cnf(325,plain,
( ~ element(u,powerset(powerset(v)))
| equal(complements_of_subsets(v,u),empty_set)
| in(subset_complement(v,skf6(u,empty_set,v)),u) ),
inference(mrr,[status(thm)],[320,183]),
[iquote('0:MRR:320.3,183.0')] ).
cnf(1207,plain,
( ~ element(empty_set,powerset(powerset(u)))
| equal(complements_of_subsets(u,empty_set),empty_set) ),
inference(res,[status(thm),theory(equality)],[325,183]),
[iquote('0:Res:325.2,183.0')] ).
cnf(1214,plain,
equal(complements_of_subsets(u,empty_set),empty_set),
inference(mrr,[status(thm)],[1207,93]),
[iquote('0:MRR:1207.0,93.0')] ).
cnf(1215,plain,
equal(skc4,empty_set),
inference(rew,[status(thm),theory(equality)],[1214,60]),
[iquote('0:Rew:1214.0,60.0')] ).
cnf(1217,plain,
$false,
inference(mrr,[status(thm)],[1215,6]),
[iquote('0:MRR:1215.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU174+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n029.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
% 0.19/0.33 % DateTime : Sun Jun 19 03:59:29 EDT 2022
% 0.19/0.33 % CPUTime :
% 0.19/0.53
% 0.19/0.53 SPASS V 3.9
% 0.19/0.53 SPASS beiseite: Proof found.
% 0.19/0.53 % SZS status Theorem
% 0.19/0.53 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.53 SPASS derived 1010 clauses, backtracked 24 clauses, performed 1 splits and kept 466 clauses.
% 0.19/0.53 SPASS allocated 98487 KBytes.
% 0.19/0.53 SPASS spent 0:00:00.19 on the problem.
% 0.19/0.53 0:00:00.03 for the input.
% 0.19/0.53 0:00:00.04 for the FLOTTER CNF translation.
% 0.19/0.53 0:00:00.01 for inferences.
% 0.19/0.53 0:00:00.00 for the backtracking.
% 0.19/0.53 0:00:00.07 for the reduction.
% 0.19/0.53
% 0.19/0.53
% 0.19/0.53 Here is a proof with depth 3, length 22 :
% 0.19/0.53 % SZS output start Refutation
% See solution above
% 0.19/0.53 Formulae used in the proof : fc1_xboole_0 rc2_subset_1 t46_setfam_1 t6_boole t5_subset involutiveness_k7_setfam_1 d8_setfam_1 existence_m1_subset_1
% 0.19/0.53
%------------------------------------------------------------------------------