TSTP Solution File: SET603+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET603+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 05:27:20 EDT 2022
% Result : Theorem 0.20s 0.52s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 17 ( 6 unt; 7 nHn; 17 RR)
% Number of literals : 32 ( 0 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
~ member(u,empty_set),
file('SET603+3.p',unknown),
[] ).
cnf(3,axiom,
~ equal(difference(skc1,empty_set),skc1),
file('SET603+3.p',unknown),
[] ).
cnf(8,axiom,
( subset(u,v)
| member(skf6(v,u),u) ),
file('SET603+3.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(u,difference(v,w))
| member(u,v) ),
file('SET603+3.p',unknown),
[] ).
cnf(10,axiom,
( ~ member(skf6(u,v),u)
| subset(w,u) ),
file('SET603+3.p',unknown),
[] ).
cnf(12,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal(v,u) ),
file('SET603+3.p',unknown),
[] ).
cnf(16,axiom,
( ~ member(u,v)
| member(u,w)
| member(u,difference(v,w)) ),
file('SET603+3.p',unknown),
[] ).
cnf(21,plain,
( ~ subset(skc1,difference(skc1,empty_set))
| ~ subset(difference(skc1,empty_set),skc1) ),
inference(res,[status(thm),theory(equality)],[12,3]),
[iquote('0:Res:12.2,3.0')] ).
cnf(38,plain,
( subset(difference(u,v),w)
| member(skf6(w,difference(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[8,9]),
[iquote('0:Res:8.1,9.0')] ).
cnf(99,plain,
( ~ member(skf6(difference(u,v),w),u)
| member(skf6(difference(u,v),w),v)
| subset(x,difference(u,v)) ),
inference(res,[status(thm),theory(equality)],[16,10]),
[iquote('0:Res:16.2,10.0')] ).
cnf(285,plain,
( subset(difference(u,v),u)
| subset(w,u) ),
inference(res,[status(thm),theory(equality)],[38,10]),
[iquote('0:Res:38.1,10.0')] ).
cnf(288,plain,
subset(difference(u,v),u),
inference(con,[status(thm)],[285]),
[iquote('0:Con:285.1')] ).
cnf(289,plain,
~ subset(skc1,difference(skc1,empty_set)),
inference(mrr,[status(thm)],[21,288]),
[iquote('0:MRR:21.1,288.0')] ).
cnf(1022,plain,
( subset(u,difference(u,v))
| member(skf6(difference(u,v),u),v)
| subset(w,difference(u,v)) ),
inference(res,[status(thm),theory(equality)],[8,99]),
[iquote('0:Res:8.1,99.0')] ).
cnf(1025,plain,
( subset(u,difference(u,v))
| member(skf6(difference(u,v),u),v) ),
inference(con,[status(thm)],[1022]),
[iquote('0:Con:1022.2')] ).
cnf(1033,plain,
subset(u,difference(u,empty_set)),
inference(res,[status(thm),theory(equality)],[1025,2]),
[iquote('0:Res:1025.1,2.0')] ).
cnf(1041,plain,
$false,
inference(unc,[status(thm)],[1033,289]),
[iquote('0:UnC:1033.0,289.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET603+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 14:39:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.52
% 0.20/0.52 SPASS V 3.9
% 0.20/0.52 SPASS beiseite: Proof found.
% 0.20/0.52 % SZS status Theorem
% 0.20/0.52 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.52 SPASS derived 786 clauses, backtracked 0 clauses, performed 0 splits and kept 266 clauses.
% 0.20/0.52 SPASS allocated 98262 KBytes.
% 0.20/0.52 SPASS spent 0:00:00.17 on the problem.
% 0.20/0.52 0:00:00.03 for the input.
% 0.20/0.52 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.52 0:00:00.01 for inferences.
% 0.20/0.52 0:00:00.00 for the backtracking.
% 0.20/0.52 0:00:00.06 for the reduction.
% 0.20/0.52
% 0.20/0.52
% 0.20/0.52 Here is a proof with depth 3, length 17 :
% 0.20/0.52 % SZS output start Refutation
% See solution above
% 0.20/0.52 Formulae used in the proof : empty_set_defn prove_th74 subset_defn difference_defn equal_defn
% 0.20/0.52
%------------------------------------------------------------------------------