%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET019-4 : TPTP v8.1.0. Released v1.0.0.
% 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 05:22:40 EDT 2022
% Result : Unsatisfiable 0.61s 0.84s
% Output : Refutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of clauses : 18 ( 11 unt; 2 nHn; 18 RR)
% Number of literals : 28 ( 0 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
subset(b,a),
file('SET019-4.p',unknown),
[] ).
cnf(2,axiom,
subset(a,b),
file('SET019-4.p',unknown),
[] ).
cnf(3,axiom,
~ equal(a,b),
file('SET019-4.p',unknown),
[] ).
cnf(6,axiom,
( equal(u,v)
| member(f1(u,v),v)
| member(f1(u,v),u) ),
file('SET019-4.p',unknown),
[] ).
cnf(7,axiom,
( ~ member(f1(u,v),v)
| ~ member(f1(u,v),u)
| equal(u,v) ),
file('SET019-4.p',unknown),
[] ).
cnf(70,axiom,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
file('SET019-4.p',unknown),
[] ).
cnf(152,plain,
( ~ member(f1(b,a),a)
| ~ member(f1(b,a),b) ),
inference(res,[status(thm),theory(equality)],[7,3]),
[iquote('0:Res:7.2,3.0')] ).
cnf(153,plain,
( member(f1(b,a),a)
| member(f1(b,a),b) ),
inference(res,[status(thm),theory(equality)],[6,3]),
[iquote('0:Res:6.2,3.0')] ).
cnf(315,plain,
member(f1(b,a),a),
inference(spt,[spt(split,[position(s1)])],[153]),
[iquote('1:Spt:153.0')] ).
cnf(316,plain,
~ member(f1(b,a),b),
inference(mrr,[status(thm)],[152,315]),
[iquote('1:MRR:152.0,315.0')] ).
cnf(946,plain,
( ~ subset(a,u)
| member(f1(b,a),u) ),
inference(res,[status(thm),theory(equality)],[315,70]),
[iquote('1:Res:315.0,70.0')] ).
cnf(1031,plain,
~ subset(a,b),
inference(res,[status(thm),theory(equality)],[946,316]),
[iquote('1:Res:946.1,316.0')] ).
cnf(1032,plain,
$false,
inference(mrr,[status(thm)],[1031,2]),
[iquote('1:MRR:1031.0,2.0')] ).
cnf(1033,plain,
~ member(f1(b,a),a),
inference(spt,[spt(split,[position(sa)])],[1032,315]),
[iquote('1:Spt:1032.0,153.0,315.0')] ).
cnf(1034,plain,
member(f1(b,a),b),
inference(spt,[spt(split,[position(s2)])],[153]),
[iquote('1:Spt:1032.0,153.1')] ).
cnf(1035,plain,
( ~ subset(b,u)
| member(f1(b,a),u) ),
inference(res,[status(thm),theory(equality)],[1034,70]),
[iquote('1:Res:1034.0,70.0')] ).
cnf(2359,plain,
~ subset(b,a),
inference(res,[status(thm),theory(equality)],[1035,1033]),
[iquote('1:Res:1035.1,1033.0')] ).
cnf(2360,plain,
$false,
inference(mrr,[status(thm)],[2359,1]),
[iquote('1:MRR:2359.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET019-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.32 % Computer : n005.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 600
% 0.13/0.32 % DateTime : Mon Jul 11 07:47:07 EDT 2022
% 0.13/0.32 % CPUTime :
% 0.61/0.84
% 0.61/0.84 SPASS V 3.9
% 0.61/0.84 SPASS beiseite: Proof found.
% 0.61/0.84 % SZS status Theorem
% 0.61/0.84 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.61/0.84 SPASS derived 1786 clauses, backtracked 676 clauses, performed 9 splits and kept 1786 clauses.
% 0.61/0.84 SPASS allocated 77583 KBytes.
% 0.61/0.84 SPASS spent 0:00:00.50 on the problem.
% 0.61/0.84 0:00:00.04 for the input.
% 0.61/0.84 0:00:00.00 for the FLOTTER CNF translation.
% 0.61/0.84 0:00:00.02 for inferences.
% 0.61/0.84 0:00:00.01 for the backtracking.
% 0.61/0.84 0:00:00.38 for the reduction.
% 0.61/0.84
% 0.61/0.84
% 0.61/0.84 Here is a proof with depth 4, length 18 :
% 0.61/0.84 % SZS output start Refutation
% See solution above
% 0.61/0.84 Formulae used in the proof : a_contains_b b_contains_a prove__a_equals_b extensionality2 extensionality3 subset1
% 0.61/0.84
%------------------------------------------------------------------------------