TSTP Solution File: SET645+3 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET645+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n014.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 : 300s
% DateTime : Wed May 31 12:34:55 EDT 2023
% Result : Theorem 0.21s 0.41s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 69 ( 12 unt; 0 def)
% Number of atoms : 267 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 328 ( 130 ~; 128 |; 31 &)
% ( 10 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 147 (; 141 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ( member(ordered_pair(B,C),cross_product(D,E))
<=> ( member(B,D)
& member(C,E) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ! [F] :
( ilf_type(F,relation_type(B,C))
=> ( member(ordered_pair(D,E),F)
=> ( member(D,B)
& member(E,C) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ! [F] :
( ilf_type(F,relation_type(B,C))
=> ( member(ordered_pair(D,E),F)
=> ( member(D,B)
& member(E,C) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f24,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,set_type)
| ! [E] :
( ~ ilf_type(E,set_type)
| ( member(ordered_pair(B,C),cross_product(D,E))
<=> ( member(B,D)
& member(C,E) ) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f25,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,set_type)
| ! [E] :
( ~ ilf_type(E,set_type)
| ( ( ~ member(ordered_pair(B,C),cross_product(D,E))
| ( member(B,D)
& member(C,E) ) )
& ( member(ordered_pair(B,C),cross_product(D,E))
| ~ member(B,D)
| ~ member(C,E) ) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f36,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f50,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f51,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) )
& ( ilf_type(C,subset_type(B))
| ~ ilf_type(C,member_type(power_set(B))) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f50]) ).
fof(f52,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,subset_type(X0))
| ilf_type(X1,member_type(power_set(X0))) ),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f65,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( member(B,power_set(C))
<=> ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f66,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ member(B,power_set(C))
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) )
& ( member(B,power_set(C))
| ? [D] :
( ilf_type(D,set_type)
& member(D,B)
& ~ member(D,C) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f65]) ).
fof(f67,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ member(B,power_set(C))
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) )
& ( member(B,power_set(C))
| ( ilf_type(sk0_3(C,B),set_type)
& member(sk0_3(C,B),B)
& ~ member(sk0_3(C,B),C) ) ) ) ) ),
inference(skolemization,[status(esa)],[f66]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f67]) ).
fof(f72,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f73,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(power_set(X0)) ),
inference(cnf_transformation,[status(esa)],[f72]) ).
fof(f75,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( empty(C)
| ~ ilf_type(C,set_type)
| ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f76,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( empty(C)
| ~ ilf_type(C,set_type)
| ( ( ~ ilf_type(B,member_type(C))
| member(B,C) )
& ( ilf_type(B,member_type(C))
| ~ member(B,C) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f75]) ).
fof(f77,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| empty(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,member_type(X1))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f76]) ).
fof(f101,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f102,plain,
? [B] :
( ilf_type(B,set_type)
& ? [C] :
( ilf_type(C,set_type)
& ? [D] :
( ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,set_type)
& ? [F] :
( ilf_type(F,relation_type(B,C))
& member(ordered_pair(D,E),F)
& ( ~ member(D,B)
| ~ member(E,C) ) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f23]) ).
fof(f103,plain,
( ilf_type(sk0_9,set_type)
& ilf_type(sk0_10,set_type)
& ilf_type(sk0_11,set_type)
& ilf_type(sk0_12,set_type)
& ilf_type(sk0_13,relation_type(sk0_9,sk0_10))
& member(ordered_pair(sk0_11,sk0_12),sk0_13)
& ( ~ member(sk0_11,sk0_9)
| ~ member(sk0_12,sk0_10) ) ),
inference(skolemization,[status(esa)],[f102]) ).
fof(f108,plain,
ilf_type(sk0_13,relation_type(sk0_9,sk0_10)),
inference(cnf_transformation,[status(esa)],[f103]) ).
fof(f109,plain,
member(ordered_pair(sk0_11,sk0_12),sk0_13),
inference(cnf_transformation,[status(esa)],[f103]) ).
fof(f110,plain,
( ~ member(sk0_11,sk0_9)
| ~ member(sk0_12,sk0_10) ),
inference(cnf_transformation,[status(esa)],[f103]) ).
fof(f122,plain,
( spl0_3
<=> member(sk0_11,sk0_9) ),
introduced(split_symbol_definition) ).
fof(f124,plain,
( ~ member(sk0_11,sk0_9)
| spl0_3 ),
inference(component_clause,[status(thm)],[f122]) ).
fof(f125,plain,
( spl0_4
<=> member(sk0_12,sk0_10) ),
introduced(split_symbol_definition) ).
fof(f127,plain,
( ~ member(sk0_12,sk0_10)
| spl0_4 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f110,f122,f125]) ).
fof(f130,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,relation_type(X2,X0))
| ilf_type(X1,subset_type(cross_product(X2,X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[f38,f101]) ).
fof(f131,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[f130,f101]) ).
fof(f132,plain,
ilf_type(sk0_13,subset_type(cross_product(sk0_9,sk0_10))),
inference(resolution,[status(thm)],[f131,f108]) ).
fof(f143,plain,
! [X0] : ~ empty(power_set(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f73,f101]) ).
fof(f145,plain,
! [X0,X1,X2,X3] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X3,X0),cross_product(X1,X2))
| member(X3,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f26,f101]) ).
fof(f146,plain,
! [X0,X1,X2,X3] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X3,X0),cross_product(X1,X2))
| member(X0,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f27,f101]) ).
fof(f172,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,subset_type(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[f52,f101]) ).
fof(f757,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ member(X1,power_set(X0))
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| member(X2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f68,f101]) ).
fof(f758,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ member(X1,power_set(X0))
| ~ member(X2,X1)
| member(X2,X0) ),
inference(resolution,[status(thm)],[f757,f101]) ).
fof(f759,plain,
! [X0,X1,X2] :
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f758,f101]) ).
fof(f786,plain,
! [X0,X1,X2,X3] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1))
| member(X3,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f146,f101]) ).
fof(f787,plain,
! [X0,X1,X2,X3] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1))
| member(X2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f145,f101]) ).
fof(f1490,plain,
! [X0,X1,X2,X3] :
( ~ ilf_type(X0,set_type)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X0))
| member(X2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f786,f101]) ).
fof(f1491,plain,
! [X0,X1,X2,X3] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,X3) ),
inference(resolution,[status(thm)],[f1490,f101]) ).
fof(f1547,plain,
! [X0,X1] :
( empty(X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,member_type(X0))
| member(X1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f77,f101]) ).
fof(f1548,plain,
! [X0,X1] :
( empty(X0)
| ~ ilf_type(X1,member_type(X0))
| member(X1,X0) ),
inference(resolution,[status(thm)],[f1547,f101]) ).
fof(f1551,plain,
! [X0,X1] :
( empty(power_set(X0))
| member(X1,power_set(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,subset_type(X0)) ),
inference(resolution,[status(thm)],[f1548,f172]) ).
fof(f1552,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,subset_type(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1551,f143]) ).
fof(f1561,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1552,f101]) ).
fof(f1564,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,subset_type(X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(resolution,[status(thm)],[f1561,f759]) ).
fof(f1568,plain,
! [X0] :
( ~ member(X0,sk0_13)
| member(X0,cross_product(sk0_9,sk0_10)) ),
inference(resolution,[status(thm)],[f1564,f132]) ).
fof(f2195,plain,
member(ordered_pair(sk0_11,sk0_12),cross_product(sk0_9,sk0_10)),
inference(resolution,[status(thm)],[f1568,f109]) ).
fof(f2250,plain,
! [X0,X1,X2,X3] :
( ~ ilf_type(X0,set_type)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X0))
| member(X1,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f787,f101]) ).
fof(f2251,plain,
! [X0,X1,X2,X3] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,X2) ),
inference(resolution,[status(thm)],[f2250,f101]) ).
fof(f2288,plain,
member(sk0_12,sk0_10),
inference(resolution,[status(thm)],[f1491,f2195]) ).
fof(f2304,plain,
member(sk0_11,sk0_9),
inference(resolution,[status(thm)],[f2251,f2195]) ).
fof(f2305,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f2304,f124]) ).
fof(f2306,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f2305]) ).
fof(f2318,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f127,f2288]) ).
fof(f2319,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f2318]) ).
fof(f2320,plain,
$false,
inference(sat_refutation,[status(thm)],[f128,f2306,f2319]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET645+3 : TPTP v8.1.2. Released v2.2.0.
% 0.04/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.15/0.35 % Computer : n014.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue May 30 10:08:49 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % Drodi V3.5.1
% 0.21/0.41 % Refutation found
% 0.21/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.43 % Elapsed time: 0.073282 seconds
% 0.21/0.43 % CPU time: 0.426069 seconds
% 0.21/0.43 % Memory used: 29.499 MB
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