%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET579+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 05:27:05 EDT 2022
% Result : Theorem 0.61s 0.82s
% Output : Refutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 25 ( 4 unt; 12 nHn; 25 RR)
% Number of literals : 54 ( 0 equ; 20 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
~ equal(difference(skc4,skc5),skc3),
file('SET579+3.p',unknown),
[] ).
cnf(3,axiom,
( ~ member(u,skc3)
| member(u,skc4) ),
file('SET579+3.p',unknown),
[] ).
cnf(6,axiom,
( ~ member(u,skc3)
| ~ member(u,skc5) ),
file('SET579+3.p',unknown),
[] ).
cnf(7,axiom,
( subset(u,v)
| member(skf1(v,u),u) ),
file('SET579+3.p',unknown),
[] ).
cnf(8,axiom,
( ~ member(u,difference(v,w))
| member(u,v) ),
file('SET579+3.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(skf1(u,v),u)
| subset(w,u) ),
file('SET579+3.p',unknown),
[] ).
cnf(10,axiom,
( ~ member(u,skc4)
| member(u,skc3)
| member(u,skc5) ),
file('SET579+3.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(u,v)
| ~ member(u,difference(w,v)) ),
file('SET579+3.p',unknown),
[] ).
cnf(12,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal(v,u) ),
file('SET579+3.p',unknown),
[] ).
cnf(14,axiom,
( ~ member(u,v)
| member(u,w)
| member(u,difference(v,w)) ),
file('SET579+3.p',unknown),
[] ).
cnf(15,plain,
( ~ subset(skc3,difference(skc4,skc5))
| ~ subset(difference(skc4,skc5),skc3) ),
inference(res,[status(thm),theory(equality)],[12,2]),
[iquote('0:Res:12.2,2.0')] ).
cnf(23,plain,
( subset(difference(u,v),w)
| member(skf1(w,difference(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[7,8]),
[iquote('0:Res:7.1,8.0')] ).
cnf(26,plain,
( ~ member(skf1(u,difference(v,w)),w)
| subset(difference(v,w),u) ),
inference(res,[status(thm),theory(equality)],[7,11]),
[iquote('0:Res:7.1,11.1')] ).
cnf(49,plain,
( ~ member(skf1(difference(u,v),w),u)
| member(skf1(difference(u,v),w),v)
| subset(x,difference(u,v)) ),
inference(res,[status(thm),theory(equality)],[14,9]),
[iquote('0:Res:14.2,9.0')] ).
cnf(103,plain,
( ~ member(skf1(u,difference(v,skc5)),skc4)
| member(skf1(u,difference(v,skc5)),skc3)
| subset(difference(v,skc5),u) ),
inference(res,[status(thm),theory(equality)],[10,26]),
[iquote('0:Res:10.2,26.0')] ).
cnf(441,plain,
( ~ member(skf1(difference(skc4,u),v),skc3)
| member(skf1(difference(skc4,u),v),u)
| subset(w,difference(skc4,u)) ),
inference(res,[status(thm),theory(equality)],[3,49]),
[iquote('0:Res:3.1,49.0')] ).
cnf(2750,plain,
( subset(difference(skc4,skc5),u)
| member(skf1(u,difference(skc4,skc5)),skc3)
| subset(difference(skc4,skc5),u) ),
inference(res,[status(thm),theory(equality)],[23,103]),
[iquote('0:Res:23.1,103.0')] ).
cnf(2755,plain,
( member(skf1(u,difference(skc4,skc5)),skc3)
| subset(difference(skc4,skc5),u) ),
inference(obv,[status(thm),theory(equality)],[2750]),
[iquote('0:Obv:2750.0')] ).
cnf(2879,plain,
( subset(skc3,difference(skc4,u))
| member(skf1(difference(skc4,u),skc3),u)
| subset(v,difference(skc4,u)) ),
inference(res,[status(thm),theory(equality)],[7,441]),
[iquote('0:Res:7.1,441.0')] ).
cnf(2890,plain,
( subset(skc3,difference(skc4,u))
| member(skf1(difference(skc4,u),skc3),u) ),
inference(con,[status(thm)],[2879]),
[iquote('0:Con:2879.2')] ).
cnf(5203,plain,
( subset(difference(skc4,skc5),skc3)
| subset(u,skc3) ),
inference(res,[status(thm),theory(equality)],[2755,9]),
[iquote('0:Res:2755.0,9.0')] ).
cnf(5208,plain,
subset(difference(skc4,skc5),skc3),
inference(con,[status(thm)],[5203]),
[iquote('0:Con:5203.1')] ).
cnf(5209,plain,
~ subset(skc3,difference(skc4,skc5)),
inference(mrr,[status(thm)],[15,5208]),
[iquote('0:MRR:15.1,5208.0')] ).
cnf(5315,plain,
( ~ member(skf1(difference(skc4,skc5),skc3),skc3)
| subset(skc3,difference(skc4,skc5)) ),
inference(res,[status(thm),theory(equality)],[2890,6]),
[iquote('0:Res:2890.1,6.1')] ).
cnf(5324,plain,
$false,
inference(mrr,[status(thm)],[5315,7,5209]),
[iquote('0:MRR:5315.0,5315.1,7.1,5209.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : SET579+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 11 04:39:58 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.61/0.82
% 0.61/0.82 SPASS V 3.9
% 0.61/0.82 SPASS beiseite: Proof found.
% 0.61/0.82 % SZS status Theorem
% 0.61/0.82 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.61/0.82 SPASS derived 4274 clauses, backtracked 47 clauses, performed 1 splits and kept 699 clauses.
% 0.61/0.82 SPASS allocated 88365 KBytes.
% 0.61/0.82 SPASS spent 0:00:00.46 on the problem.
% 0.61/0.82 0:00:00.04 for the input.
% 0.61/0.82 0:00:00.02 for the FLOTTER CNF translation.
% 0.61/0.82 0:00:00.05 for inferences.
% 0.61/0.82 0:00:00.00 for the backtracking.
% 0.61/0.82 0:00:00.32 for the reduction.
% 0.61/0.82
% 0.61/0.82
% 0.61/0.82 Here is a proof with depth 4, length 25 :
% 0.61/0.82 % SZS output start Refutation
% See solution above
% 0.61/0.82 Formulae used in the proof : prove_th20 subset_defn difference_defn equal_defn
% 0.61/0.82
%------------------------------------------------------------------------------