TSTP Solution File: SET984+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET984+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n003.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 20:40:50 EDT 2024
% Result : Theorem 0.20s 0.40s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 67 ( 17 unt; 0 def)
% Number of atoms : 158 ( 80 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 140 ( 49 ~; 67 |; 12 &)
% ( 8 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 88 ( 84 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( cartesian_product2(A,B) = empty_set
<=> ( A = empty_set
| B = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C,D] :
( cartesian_product2(A,B) = cartesian_product2(C,D)
=> ( A = empty_set
| B = empty_set
| ( A = C
& B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,conjecture,
! [A,B,C,D] :
( subset(cartesian_product2(A,B),cartesian_product2(C,D))
=> ( cartesian_product2(A,B) = empty_set
| ( subset(A,C)
& subset(B,D) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
~ ! [A,B,C,D] :
( subset(cartesian_product2(A,B),cartesian_product2(C,D))
=> ( cartesian_product2(A,B) = empty_set
| ( subset(A,C)
& subset(B,D) ) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,axiom,
! [A,B] : subset(set_intersection2(A,B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f22,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(esa)],[f6]) ).
fof(f23,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f24,plain,
! [A,B] :
( ( cartesian_product2(A,B) != empty_set
| A = empty_set
| B = empty_set )
& ( cartesian_product2(A,B) = empty_set
| ( A != empty_set
& B != empty_set ) ) ),
inference(NNF_transformation,[status(esa)],[f7]) ).
fof(f25,plain,
( ! [A,B] :
( cartesian_product2(A,B) != empty_set
| A = empty_set
| B = empty_set )
& ! [A,B] :
( cartesian_product2(A,B) = empty_set
| ( A != empty_set
& B != empty_set ) ) ),
inference(miniscoping,[status(esa)],[f24]) ).
fof(f27,plain,
! [X0,X1] :
( cartesian_product2(X0,X1) = empty_set
| X0 != empty_set ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f28,plain,
! [X0,X1] :
( cartesian_product2(X0,X1) = empty_set
| X1 != empty_set ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f29,plain,
! [X0,X1,X2,X3] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f30,plain,
! [A,B,C,D] :
( cartesian_product2(A,B) != cartesian_product2(C,D)
| A = empty_set
| B = empty_set
| ( A = C
& B = D ) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
| X0 = empty_set
| X1 = empty_set
| X0 = X2 ),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
| X0 = empty_set
| X1 = empty_set
| X1 = X3 ),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f33,plain,
? [A,B,C,D] :
( subset(cartesian_product2(A,B),cartesian_product2(C,D))
& cartesian_product2(A,B) != empty_set
& ( ~ subset(A,C)
| ~ subset(B,D) ) ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f34,plain,
( subset(cartesian_product2(sk0_2,sk0_3),cartesian_product2(sk0_4,sk0_5))
& cartesian_product2(sk0_2,sk0_3) != empty_set
& ( ~ subset(sk0_2,sk0_4)
| ~ subset(sk0_3,sk0_5) ) ),
inference(skolemization,[status(esa)],[f33]) ).
fof(f35,plain,
subset(cartesian_product2(sk0_2,sk0_3),cartesian_product2(sk0_4,sk0_5)),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f36,plain,
cartesian_product2(sk0_2,sk0_3) != empty_set,
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f37,plain,
( ~ subset(sk0_2,sk0_4)
| ~ subset(sk0_3,sk0_5) ),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f38,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f39,plain,
! [A,B] :
( ~ subset(A,B)
| set_intersection2(A,B) = A ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f40,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f41,plain,
( spl0_0
<=> subset(sk0_2,sk0_4) ),
introduced(split_symbol_definition) ).
fof(f43,plain,
( ~ subset(sk0_2,sk0_4)
| spl0_0 ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,plain,
( spl0_1
<=> subset(sk0_3,sk0_5) ),
introduced(split_symbol_definition) ).
fof(f46,plain,
( ~ subset(sk0_3,sk0_5)
| spl0_1 ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f47,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f37,f41,f44]) ).
fof(f48,plain,
sk0_2 != empty_set,
inference(resolution,[status(thm)],[f27,f36]) ).
fof(f49,plain,
sk0_3 != empty_set,
inference(resolution,[status(thm)],[f28,f36]) ).
fof(f75,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X1,X0) = X0 ),
inference(paramodulation,[status(thm)],[f14,f40]) ).
fof(f91,plain,
! [X0,X1,X2,X3,X4,X5] :
( cartesian_product2(X0,X1) != set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5))
| X0 = empty_set
| X1 = empty_set
| X1 = set_intersection2(X3,X5) ),
inference(paramodulation,[status(thm)],[f29,f32]) ).
fof(f93,plain,
! [X0,X1,X2,X3,X4,X5] :
( cartesian_product2(X0,X1) != set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5))
| X0 = empty_set
| X1 = empty_set
| X0 = set_intersection2(X2,X4) ),
inference(paramodulation,[status(thm)],[f29,f31]) ).
fof(f124,plain,
! [X0,X1,X2,X3] :
( X0 = empty_set
| X1 = empty_set
| X1 = set_intersection2(X2,X1)
| ~ subset(cartesian_product2(X0,X1),cartesian_product2(X3,X2)) ),
inference(resolution,[status(thm)],[f91,f75]) ).
fof(f154,plain,
! [X0,X1,X2,X3] :
( X0 = empty_set
| X1 = empty_set
| X0 = set_intersection2(X2,X0)
| ~ subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
inference(resolution,[status(thm)],[f93,f75]) ).
fof(f175,plain,
( spl0_11
<=> sk0_2 = empty_set ),
introduced(split_symbol_definition) ).
fof(f176,plain,
( sk0_2 = empty_set
| ~ spl0_11 ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,plain,
( spl0_12
<=> sk0_3 = empty_set ),
introduced(split_symbol_definition) ).
fof(f179,plain,
( sk0_3 = empty_set
| ~ spl0_12 ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,plain,
( spl0_13
<=> sk0_3 = set_intersection2(sk0_5,sk0_3) ),
introduced(split_symbol_definition) ).
fof(f182,plain,
( sk0_3 = set_intersection2(sk0_5,sk0_3)
| ~ spl0_13 ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,plain,
( sk0_2 = empty_set
| sk0_3 = empty_set
| sk0_3 = set_intersection2(sk0_5,sk0_3) ),
inference(resolution,[status(thm)],[f124,f35]) ).
fof(f185,plain,
( spl0_11
| spl0_12
| spl0_13 ),
inference(split_clause,[status(thm)],[f184,f175,f178,f181]) ).
fof(f199,plain,
( $false
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f179,f49]) ).
fof(f200,plain,
~ spl0_12,
inference(contradiction_clause,[status(thm)],[f199]) ).
fof(f201,plain,
( $false
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f176,f48]) ).
fof(f202,plain,
~ spl0_11,
inference(contradiction_clause,[status(thm)],[f201]) ).
fof(f207,plain,
( spl0_15
<=> subset(empty_set,empty_set) ),
introduced(split_symbol_definition) ).
fof(f209,plain,
( ~ subset(empty_set,empty_set)
| spl0_15 ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f232,plain,
( $false
| spl0_15 ),
inference(forward_subsumption_resolution,[status(thm)],[f209,f23]) ).
fof(f233,plain,
spl0_15,
inference(contradiction_clause,[status(thm)],[f232]) ).
fof(f235,plain,
( subset(sk0_3,sk0_5)
| ~ spl0_13 ),
inference(paramodulation,[status(thm)],[f182,f38]) ).
fof(f236,plain,
( $false
| spl0_1
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f235,f46]) ).
fof(f237,plain,
( spl0_1
| ~ spl0_13 ),
inference(contradiction_clause,[status(thm)],[f236]) ).
fof(f241,plain,
( spl0_20
<=> sk0_2 = set_intersection2(sk0_4,sk0_2) ),
introduced(split_symbol_definition) ).
fof(f242,plain,
( sk0_2 = set_intersection2(sk0_4,sk0_2)
| ~ spl0_20 ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f244,plain,
( sk0_2 = empty_set
| sk0_3 = empty_set
| sk0_2 = set_intersection2(sk0_4,sk0_2) ),
inference(resolution,[status(thm)],[f154,f35]) ).
fof(f245,plain,
( spl0_11
| spl0_12
| spl0_20 ),
inference(split_clause,[status(thm)],[f244,f175,f178,f241]) ).
fof(f263,plain,
( subset(sk0_2,sk0_4)
| ~ spl0_20 ),
inference(paramodulation,[status(thm)],[f242,f38]) ).
fof(f264,plain,
( $false
| spl0_0
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[status(thm)],[f263,f43]) ).
fof(f265,plain,
( spl0_0
| ~ spl0_20 ),
inference(contradiction_clause,[status(thm)],[f264]) ).
fof(f266,plain,
$false,
inference(sat_refutation,[status(thm)],[f47,f185,f200,f202,f233,f237,f245,f265]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET984+1 : TPTP v8.1.2. Released v3.2.0.
% 0.04/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 21:40:03 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.36 % Drodi V3.6.0
% 0.20/0.40 % Refutation found
% 0.20/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.42 % Elapsed time: 0.052489 seconds
% 0.20/0.42 % CPU time: 0.301238 seconds
% 0.20/0.42 % Total memory used: 61.419 MB
% 0.20/0.42 % Net memory used: 61.272 MB
%------------------------------------------------------------------------------