TSTP Solution File: SET641+3 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET641+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n020.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 : Tue Apr 30 20:40:04 EDT 2024
% Result : Theorem 0.16s 0.37s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 7 unt; 0 def)
% Number of atoms : 247 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 308 ( 122 ~; 120 |; 29 &)
% ( 11 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 119 ( 113 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( subset(B,C)
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( subset(B,cross_product(C,D))
=> ilf_type(B,relation_type(C,D)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( subset(B,cross_product(C,D))
=> ilf_type(B,relation_type(C,D)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,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)],[f1]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ilf_type(X2,relation_type(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f38,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( subset(B,C)
<=> ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f39,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ subset(B,C)
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) )
& ( subset(B,C)
| ? [D] :
( ilf_type(D,set_type)
& member(D,B)
& ~ member(D,C) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f38]) ).
fof(f40,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ subset(B,C)
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) )
& ( subset(B,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)],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f47,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)],[f7]) ).
fof(f48,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)],[f47]) ).
fof(f50,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)],[f48]) ).
fof(f56,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)],[f10]) ).
fof(f57,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)],[f56]) ).
fof(f58,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_5(C,B),set_type)
& member(sk0_5(C,B),B)
& ~ member(sk0_5(C,B),C) ) ) ) ) ),
inference(skolemization,[status(esa)],[f57]) ).
fof(f61,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(X0,power_set(X1))
| member(sk0_5(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f58]) ).
fof(f62,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(X0,power_set(X1))
| ~ member(sk0_5(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f58]) ).
fof(f66,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)],[f12]) ).
fof(f67,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)],[f66]) ).
fof(f69,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)],[f67]) ).
fof(f73,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( empty(B)
<=> ! [C] :
( ~ ilf_type(C,set_type)
| ~ member(C,B) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f74,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ( ~ empty(B)
| ! [C] :
( ~ ilf_type(C,set_type)
| ~ member(C,B) ) )
& ( empty(B)
| ? [C] :
( ilf_type(C,set_type)
& member(C,B) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f73]) ).
fof(f75,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ( ~ empty(B)
| ! [C] :
( ~ ilf_type(C,set_type)
| ~ member(C,B) ) )
& ( empty(B)
| ( ilf_type(sk0_7(B),set_type)
& member(sk0_7(B),B) ) ) ) ),
inference(skolemization,[status(esa)],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ empty(X0)
| ~ ilf_type(X1,set_type)
| ~ member(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f75]) ).
fof(f92,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f93,plain,
? [B] :
( ilf_type(B,set_type)
& ? [C] :
( ilf_type(C,set_type)
& ? [D] :
( ilf_type(D,set_type)
& subset(B,cross_product(C,D))
& ~ ilf_type(B,relation_type(C,D)) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f94,plain,
( ilf_type(sk0_11,set_type)
& ilf_type(sk0_12,set_type)
& ilf_type(sk0_13,set_type)
& subset(sk0_11,cross_product(sk0_12,sk0_13))
& ~ ilf_type(sk0_11,relation_type(sk0_12,sk0_13)) ),
inference(skolemization,[status(esa)],[f93]) ).
fof(f98,plain,
subset(sk0_11,cross_product(sk0_12,sk0_13)),
inference(cnf_transformation,[status(esa)],[f94]) ).
fof(f99,plain,
~ ilf_type(sk0_11,relation_type(sk0_12,sk0_13)),
inference(cnf_transformation,[status(esa)],[f94]) ).
fof(f100,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f69,f76]) ).
fof(f101,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ilf_type(X1,member_type(X0))
| ~ member(X1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f100,f92]) ).
fof(f117,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| member(X1,power_set(X0))
| ~ member(sk0_5(X0,X1),X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f62,f92]) ).
fof(f118,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sk0_5(X1,X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f117,f92]) ).
fof(f119,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| member(X1,power_set(X0))
| member(sk0_5(X0,X1),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f61,f92]) ).
fof(f120,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sk0_5(X1,X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f119,f92]) ).
fof(f125,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[f50,f92]) ).
fof(f126,plain,
! [X0,X1] :
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[f125,f92]) ).
fof(f133,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ subset(X1,X0)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| member(X2,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f41,f92]) ).
fof(f134,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f133,f92]) ).
fof(f147,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,subset_type(cross_product(X2,X0)))
| ilf_type(X1,relation_type(X2,X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f22,f92]) ).
fof(f148,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f147,f92]) ).
fof(f162,plain,
! [X0,X1] :
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(power_set(X1),set_type)
| ~ member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f126,f101]) ).
fof(f163,plain,
! [X0,X1] :
( ilf_type(X0,subset_type(X1))
| ~ member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f162,f92]) ).
fof(f180,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(resolution,[status(thm)],[f134,f92]) ).
fof(f190,plain,
! [X0] :
( ~ member(X0,sk0_11)
| member(X0,cross_product(sk0_12,sk0_13)) ),
inference(resolution,[status(thm)],[f180,f98]) ).
fof(f191,plain,
! [X0] :
( ~ member(sk0_5(cross_product(sk0_12,sk0_13),X0),sk0_11)
| member(X0,power_set(cross_product(sk0_12,sk0_13))) ),
inference(resolution,[status(thm)],[f190,f118]) ).
fof(f198,plain,
( spl0_1
<=> member(sk0_11,power_set(cross_product(sk0_12,sk0_13))) ),
introduced(split_symbol_definition) ).
fof(f199,plain,
( member(sk0_11,power_set(cross_product(sk0_12,sk0_13)))
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f201,plain,
( member(sk0_11,power_set(cross_product(sk0_12,sk0_13)))
| member(sk0_11,power_set(cross_product(sk0_12,sk0_13))) ),
inference(resolution,[status(thm)],[f191,f120]) ).
fof(f202,plain,
spl0_1,
inference(split_clause,[status(thm)],[f201,f198]) ).
fof(f203,plain,
( ilf_type(sk0_11,subset_type(cross_product(sk0_12,sk0_13)))
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f199,f163]) ).
fof(f458,plain,
( ilf_type(sk0_11,relation_type(sk0_12,sk0_13))
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f203,f148]) ).
fof(f459,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f458,f99]) ).
fof(f460,plain,
~ spl0_1,
inference(contradiction_clause,[status(thm)],[f459]) ).
fof(f461,plain,
$false,
inference(sat_refutation,[status(thm)],[f202,f460]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET641+3 : TPTP v8.1.2. Released v2.2.0.
% 0.10/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33 % Computer : n020.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Apr 29 21:32:17 EDT 2024
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % Drodi V3.6.0
% 0.16/0.37 % Refutation found
% 0.16/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.39 % Elapsed time: 0.053356 seconds
% 0.16/0.39 % CPU time: 0.282683 seconds
% 0.16/0.39 % Total memory used: 53.573 MB
% 0.16/0.39 % Net memory used: 53.416 MB
%------------------------------------------------------------------------------