TSTP Solution File: SET722+4 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET722+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 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 20:40:15 EDT 2024
% Result : Theorem 19.51s 2.86s
% Output : CNFRefutation 19.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 5 unt; 0 def)
% Number of atoms : 155 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 177 ( 63 ~; 67 |; 38 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-7 aty)
% Number of variables : 150 ( 130 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [G,F,A,B,C,X,Z] :
( ( member(X,A)
& member(Z,C) )
=> ( apply(compose_function(G,F,A,B,C),X,Z)
<=> ? [Y] :
( member(Y,B)
& apply(F,X,Y)
& apply(G,Y,Z) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [F,A,B] :
( surjective(F,A,B)
<=> ! [Y] :
( member(Y,B)
=> ? [E] :
( member(E,A)
& apply(F,E,Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [F,G,A,B,C] :
( ( maps(F,A,B)
& maps(G,B,C)
& surjective(compose_function(G,F,A,B,C),A,C) )
=> surjective(G,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [F,G,A,B,C] :
( ( maps(F,A,B)
& maps(G,B,C)
& surjective(compose_function(G,F,A,B,C),A,C) )
=> surjective(G,B,C) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f111,plain,
! [G,F,A,B,C,X,Z] :
( ~ member(X,A)
| ~ member(Z,C)
| ( apply(compose_function(G,F,A,B,C),X,Z)
<=> ? [Y] :
( member(Y,B)
& apply(F,X,Y)
& apply(G,Y,Z) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f112,plain,
! [G,F,A,B,C,X,Z] :
( ~ member(X,A)
| ~ member(Z,C)
| ( ( ~ apply(compose_function(G,F,A,B,C),X,Z)
| ? [Y] :
( member(Y,B)
& apply(F,X,Y)
& apply(G,Y,Z) ) )
& ( apply(compose_function(G,F,A,B,C),X,Z)
| ! [Y] :
( ~ member(Y,B)
| ~ apply(F,X,Y)
| ~ apply(G,Y,Z) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f111]) ).
fof(f113,plain,
! [A,C,X,Z] :
( ~ member(X,A)
| ~ member(Z,C)
| ( ! [G,F,B] :
( ~ apply(compose_function(G,F,A,B,C),X,Z)
| ? [Y] :
( member(Y,B)
& apply(F,X,Y)
& apply(G,Y,Z) ) )
& ! [G,F,B] :
( apply(compose_function(G,F,A,B,C),X,Z)
| ! [Y] :
( ~ member(Y,B)
| ~ apply(F,X,Y)
| ~ apply(G,Y,Z) ) ) ) ),
inference(miniscoping,[status(esa)],[f112]) ).
fof(f114,plain,
! [A,C,X,Z] :
( ~ member(X,A)
| ~ member(Z,C)
| ( ! [G,F,B] :
( ~ apply(compose_function(G,F,A,B,C),X,Z)
| ( member(sk0_11(B,F,G,Z,X,C,A),B)
& apply(F,X,sk0_11(B,F,G,Z,X,C,A))
& apply(G,sk0_11(B,F,G,Z,X,C,A),Z) ) )
& ! [G,F,B] :
( apply(compose_function(G,F,A,B,C),X,Z)
| ! [Y] :
( ~ member(Y,B)
| ~ apply(F,X,Y)
| ~ apply(G,Y,Z) ) ) ) ),
inference(skolemization,[status(esa)],[f113]) ).
fof(f115,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| ~ apply(compose_function(X4,X5,X1,X6,X3),X0,X2)
| member(sk0_11(X6,X5,X4,X2,X0,X3,X1),X6) ),
inference(cnf_transformation,[status(esa)],[f114]) ).
fof(f117,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| ~ apply(compose_function(X4,X5,X1,X6,X3),X0,X2)
| apply(X4,sk0_11(X6,X5,X4,X2,X0,X3,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f114]) ).
fof(f148,plain,
! [F,A,B] :
( surjective(F,A,B)
<=> ! [Y] :
( ~ member(Y,B)
| ? [E] :
( member(E,A)
& apply(F,E,Y) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f149,plain,
! [F,A,B] :
( ( ~ surjective(F,A,B)
| ! [Y] :
( ~ member(Y,B)
| ? [E] :
( member(E,A)
& apply(F,E,Y) ) ) )
& ( surjective(F,A,B)
| ? [Y] :
( member(Y,B)
& ! [E] :
( ~ member(E,A)
| ~ apply(F,E,Y) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f148]) ).
fof(f150,plain,
( ! [F,A,B] :
( ~ surjective(F,A,B)
| ! [Y] :
( ~ member(Y,B)
| ? [E] :
( member(E,A)
& apply(F,E,Y) ) ) )
& ! [F,A,B] :
( surjective(F,A,B)
| ? [Y] :
( member(Y,B)
& ! [E] :
( ~ member(E,A)
| ~ apply(F,E,Y) ) ) ) ),
inference(miniscoping,[status(esa)],[f149]) ).
fof(f151,plain,
( ! [F,A,B] :
( ~ surjective(F,A,B)
| ! [Y] :
( ~ member(Y,B)
| ( member(sk0_19(Y,B,A,F),A)
& apply(F,sk0_19(Y,B,A,F),Y) ) ) )
& ! [F,A,B] :
( surjective(F,A,B)
| ( member(sk0_20(B,A,F),B)
& ! [E] :
( ~ member(E,A)
| ~ apply(F,E,sk0_20(B,A,F)) ) ) ) ),
inference(skolemization,[status(esa)],[f150]) ).
fof(f152,plain,
! [X0,X1,X2,X3] :
( ~ surjective(X0,X1,X2)
| ~ member(X3,X2)
| member(sk0_19(X3,X2,X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f151]) ).
fof(f153,plain,
! [X0,X1,X2,X3] :
( ~ surjective(X0,X1,X2)
| ~ member(X3,X2)
| apply(X0,sk0_19(X3,X2,X1,X0),X3) ),
inference(cnf_transformation,[status(esa)],[f151]) ).
fof(f154,plain,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
| member(sk0_20(X2,X1,X0),X2) ),
inference(cnf_transformation,[status(esa)],[f151]) ).
fof(f155,plain,
! [X0,X1,X2,X3] :
( surjective(X0,X1,X2)
| ~ member(X3,X1)
| ~ apply(X0,X3,sk0_20(X2,X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f151]) ).
fof(f244,plain,
? [F,G,A,B,C] :
( maps(F,A,B)
& maps(G,B,C)
& surjective(compose_function(G,F,A,B,C),A,C)
& ~ surjective(G,B,C) ),
inference(pre_NNF_transformation,[status(esa)],[f30]) ).
fof(f245,plain,
? [G,B,C] :
( ? [F,A] :
( maps(F,A,B)
& maps(G,B,C)
& surjective(compose_function(G,F,A,B,C),A,C) )
& ~ surjective(G,B,C) ),
inference(miniscoping,[status(esa)],[f244]) ).
fof(f246,plain,
( maps(sk0_42,sk0_43,sk0_40)
& maps(sk0_39,sk0_40,sk0_41)
& surjective(compose_function(sk0_39,sk0_42,sk0_43,sk0_40,sk0_41),sk0_43,sk0_41)
& ~ surjective(sk0_39,sk0_40,sk0_41) ),
inference(skolemization,[status(esa)],[f245]) ).
fof(f249,plain,
surjective(compose_function(sk0_39,sk0_42,sk0_43,sk0_40,sk0_41),sk0_43,sk0_41),
inference(cnf_transformation,[status(esa)],[f246]) ).
fof(f250,plain,
~ surjective(sk0_39,sk0_40,sk0_41),
inference(cnf_transformation,[status(esa)],[f246]) ).
fof(f379,plain,
! [X0] :
( ~ member(X0,sk0_41)
| member(sk0_19(X0,sk0_41,sk0_43,compose_function(sk0_39,sk0_42,sk0_43,sk0_40,sk0_41)),sk0_43) ),
inference(resolution,[status(thm)],[f152,f249]) ).
fof(f398,plain,
! [X0] :
( ~ member(X0,sk0_41)
| apply(compose_function(sk0_39,sk0_42,sk0_43,sk0_40,sk0_41),sk0_19(X0,sk0_41,sk0_43,compose_function(sk0_39,sk0_42,sk0_43,sk0_40,sk0_41)),X0) ),
inference(resolution,[status(thm)],[f153,f249]) ).
fof(f399,plain,
! [X0,X1] :
( apply(compose_function(sk0_39,sk0_42,sk0_43,sk0_40,sk0_41),sk0_19(sk0_20(sk0_41,X0,X1),sk0_41,sk0_43,compose_function(sk0_39,sk0_42,sk0_43,sk0_40,sk0_41)),sk0_20(sk0_41,X0,X1))
| surjective(X1,X0,sk0_41) ),
inference(resolution,[status(thm)],[f398,f154]) ).
fof(f2154,plain,
! [X0,X1] :
( ~ member(sk0_19(sk0_20(sk0_41,X0,X1),sk0_41,sk0_43,compose_function(sk0_39,sk0_42,sk0_43,sk0_40,sk0_41)),sk0_43)
| ~ member(sk0_20(sk0_41,X0,X1),sk0_41)
| member(sk0_11(sk0_40,sk0_42,sk0_39,sk0_20(sk0_41,X0,X1),sk0_19(sk0_20(sk0_41,X0,X1),sk0_41,sk0_43,compose_function(sk0_39,sk0_42,sk0_43,sk0_40,sk0_41)),sk0_41,sk0_43),sk0_40)
| surjective(X1,X0,sk0_41) ),
inference(resolution,[status(thm)],[f115,f399]) ).
fof(f2155,plain,
! [X0,X1] :
( ~ member(sk0_20(sk0_41,X0,X1),sk0_41)
| member(sk0_11(sk0_40,sk0_42,sk0_39,sk0_20(sk0_41,X0,X1),sk0_19(sk0_20(sk0_41,X0,X1),sk0_41,sk0_43,compose_function(sk0_39,sk0_42,sk0_43,sk0_40,sk0_41)),sk0_41,sk0_43),sk0_40)
| surjective(X1,X0,sk0_41) ),
inference(forward_subsumption_resolution,[status(thm)],[f2154,f379]) ).
fof(f2221,plain,
! [X0,X1] :
( ~ member(sk0_19(sk0_20(sk0_41,X0,X1),sk0_41,sk0_43,compose_function(sk0_39,sk0_42,sk0_43,sk0_40,sk0_41)),sk0_43)
| ~ member(sk0_20(sk0_41,X0,X1),sk0_41)
| apply(sk0_39,sk0_11(sk0_40,sk0_42,sk0_39,sk0_20(sk0_41,X0,X1),sk0_19(sk0_20(sk0_41,X0,X1),sk0_41,sk0_43,compose_function(sk0_39,sk0_42,sk0_43,sk0_40,sk0_41)),sk0_41,sk0_43),sk0_20(sk0_41,X0,X1))
| surjective(X1,X0,sk0_41) ),
inference(resolution,[status(thm)],[f117,f399]) ).
fof(f2222,plain,
! [X0,X1] :
( ~ member(sk0_20(sk0_41,X0,X1),sk0_41)
| apply(sk0_39,sk0_11(sk0_40,sk0_42,sk0_39,sk0_20(sk0_41,X0,X1),sk0_19(sk0_20(sk0_41,X0,X1),sk0_41,sk0_43,compose_function(sk0_39,sk0_42,sk0_43,sk0_40,sk0_41)),sk0_41,sk0_43),sk0_20(sk0_41,X0,X1))
| surjective(X1,X0,sk0_41) ),
inference(forward_subsumption_resolution,[status(thm)],[f2221,f379]) ).
fof(f2533,plain,
! [X0,X1] :
( member(sk0_11(sk0_40,sk0_42,sk0_39,sk0_20(sk0_41,X0,X1),sk0_19(sk0_20(sk0_41,X0,X1),sk0_41,sk0_43,compose_function(sk0_39,sk0_42,sk0_43,sk0_40,sk0_41)),sk0_41,sk0_43),sk0_40)
| surjective(X1,X0,sk0_41) ),
inference(forward_subsumption_resolution,[status(thm)],[f2155,f154]) ).
fof(f2791,plain,
! [X0,X1] :
( apply(sk0_39,sk0_11(sk0_40,sk0_42,sk0_39,sk0_20(sk0_41,X0,X1),sk0_19(sk0_20(sk0_41,X0,X1),sk0_41,sk0_43,compose_function(sk0_39,sk0_42,sk0_43,sk0_40,sk0_41)),sk0_41,sk0_43),sk0_20(sk0_41,X0,X1))
| surjective(X1,X0,sk0_41) ),
inference(forward_subsumption_resolution,[status(thm)],[f2222,f154]) ).
fof(f4498,plain,
! [X0] :
( surjective(sk0_39,X0,sk0_41)
| ~ member(sk0_11(sk0_40,sk0_42,sk0_39,sk0_20(sk0_41,X0,sk0_39),sk0_19(sk0_20(sk0_41,X0,sk0_39),sk0_41,sk0_43,compose_function(sk0_39,sk0_42,sk0_43,sk0_40,sk0_41)),sk0_41,sk0_43),X0)
| surjective(sk0_39,X0,sk0_41) ),
inference(resolution,[status(thm)],[f155,f2791]) ).
fof(f4499,plain,
! [X0] :
( surjective(sk0_39,X0,sk0_41)
| ~ member(sk0_11(sk0_40,sk0_42,sk0_39,sk0_20(sk0_41,X0,sk0_39),sk0_19(sk0_20(sk0_41,X0,sk0_39),sk0_41,sk0_43,compose_function(sk0_39,sk0_42,sk0_43,sk0_40,sk0_41)),sk0_41,sk0_43),X0) ),
inference(duplicate_literals_removal,[status(esa)],[f4498]) ).
fof(f4906,plain,
( spl0_4
<=> surjective(sk0_39,sk0_40,sk0_41) ),
introduced(split_symbol_definition) ).
fof(f4907,plain,
( surjective(sk0_39,sk0_40,sk0_41)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f4906]) ).
fof(f4909,plain,
( surjective(sk0_39,sk0_40,sk0_41)
| surjective(sk0_39,sk0_40,sk0_41) ),
inference(resolution,[status(thm)],[f4499,f2533]) ).
fof(f4910,plain,
spl0_4,
inference(split_clause,[status(thm)],[f4909,f4906]) ).
fof(f4923,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f4907,f250]) ).
fof(f4924,plain,
~ spl0_4,
inference(contradiction_clause,[status(thm)],[f4923]) ).
fof(f4925,plain,
$false,
inference(sat_refutation,[status(thm)],[f4910,f4924]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET722+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.15/0.34 % Computer : n020.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Mon Apr 29 21:30:32 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % Drodi V3.6.0
% 19.51/2.86 % Refutation found
% 19.51/2.86 % SZS status Theorem for theBenchmark: Theorem is valid
% 19.51/2.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 20.07/2.90 % Elapsed time: 2.534985 seconds
% 20.07/2.90 % CPU time: 19.987282 seconds
% 20.07/2.90 % Total memory used: 185.098 MB
% 20.07/2.90 % Net memory used: 181.639 MB
%------------------------------------------------------------------------------