TSTP Solution File: SET734+4 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET734+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n007.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 20:40:16 EDT 2024
% Result : Theorem 19.85s 2.87s
% Output : CNFRefutation 19.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 6 unt; 0 def)
% Number of atoms : 168 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 208 ( 81 ~; 71 |; 44 &)
% ( 7 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 2 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-7 aty)
% Number of variables : 162 ( 142 !; 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(f16,axiom,
! [F,A] :
( identity(F,A)
<=> ! [X] :
( member(X,A)
=> apply(F,X,X) ) ),
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] :
( ( maps(G,A,B)
& maps(F,B,A)
& identity(compose_function(G,F,B,A,B),B) )
=> surjective(G,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [F,G,A,B] :
( ( maps(G,A,B)
& maps(F,B,A)
& identity(compose_function(G,F,B,A,B),B) )
=> surjective(G,A,B) ),
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(f130,plain,
! [F,A] :
( identity(F,A)
<=> ! [X] :
( ~ member(X,A)
| apply(F,X,X) ) ),
inference(pre_NNF_transformation,[status(esa)],[f16]) ).
fof(f131,plain,
! [F,A] :
( ( ~ identity(F,A)
| ! [X] :
( ~ member(X,A)
| apply(F,X,X) ) )
& ( identity(F,A)
| ? [X] :
( member(X,A)
& ~ apply(F,X,X) ) ) ),
inference(NNF_transformation,[status(esa)],[f130]) ).
fof(f132,plain,
( ! [F,A] :
( ~ identity(F,A)
| ! [X] :
( ~ member(X,A)
| apply(F,X,X) ) )
& ! [F,A] :
( identity(F,A)
| ? [X] :
( member(X,A)
& ~ apply(F,X,X) ) ) ),
inference(miniscoping,[status(esa)],[f131]) ).
fof(f133,plain,
( ! [F,A] :
( ~ identity(F,A)
| ! [X] :
( ~ member(X,A)
| apply(F,X,X) ) )
& ! [F,A] :
( identity(F,A)
| ( member(sk0_15(A,F),A)
& ~ apply(F,sk0_15(A,F),sk0_15(A,F)) ) ) ),
inference(skolemization,[status(esa)],[f132]) ).
fof(f134,plain,
! [X0,X1,X2] :
( ~ identity(X0,X1)
| ~ member(X2,X1)
| apply(X0,X2,X2) ),
inference(cnf_transformation,[status(esa)],[f133]) ).
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(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] :
( maps(G,A,B)
& maps(F,B,A)
& identity(compose_function(G,F,B,A,B),B)
& ~ surjective(G,A,B) ),
inference(pre_NNF_transformation,[status(esa)],[f30]) ).
fof(f245,plain,
? [G,A,B] :
( ? [F] :
( maps(G,A,B)
& maps(F,B,A)
& identity(compose_function(G,F,B,A,B),B) )
& ~ surjective(G,A,B) ),
inference(miniscoping,[status(esa)],[f244]) ).
fof(f246,plain,
( maps(sk0_39,sk0_40,sk0_41)
& maps(sk0_42,sk0_41,sk0_40)
& identity(compose_function(sk0_39,sk0_42,sk0_41,sk0_40,sk0_41),sk0_41)
& ~ surjective(sk0_39,sk0_40,sk0_41) ),
inference(skolemization,[status(esa)],[f245]) ).
fof(f249,plain,
identity(compose_function(sk0_39,sk0_42,sk0_41,sk0_40,sk0_41),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(f265,plain,
member(sk0_20(sk0_41,sk0_40,sk0_39),sk0_41),
inference(resolution,[status(thm)],[f154,f250]) ).
fof(f272,plain,
! [X0] :
( ~ identity(X0,sk0_41)
| apply(X0,sk0_20(sk0_41,sk0_40,sk0_39),sk0_20(sk0_41,sk0_40,sk0_39)) ),
inference(resolution,[status(thm)],[f265,f134]) ).
fof(f378,plain,
( spl0_12
<=> member(sk0_20(sk0_41,sk0_40,sk0_39),sk0_41) ),
introduced(split_symbol_definition) ).
fof(f380,plain,
( ~ member(sk0_20(sk0_41,sk0_40,sk0_39),sk0_41)
| spl0_12 ),
inference(component_clause,[status(thm)],[f378]) ).
fof(f387,plain,
( $false
| spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f380,f265]) ).
fof(f388,plain,
spl0_12,
inference(contradiction_clause,[status(thm)],[f387]) ).
fof(f785,plain,
! [X0] :
( ~ member(X0,sk0_40)
| ~ apply(sk0_39,X0,sk0_20(sk0_41,sk0_40,sk0_39)) ),
inference(resolution,[status(thm)],[f155,f250]) ).
fof(f1179,plain,
! [X0,X1,X2,X3,X4] :
( ~ member(sk0_11(X0,X1,sk0_39,sk0_20(sk0_41,sk0_40,sk0_39),X2,X3,X4),sk0_40)
| ~ member(X2,X4)
| ~ member(sk0_20(sk0_41,sk0_40,sk0_39),X3)
| ~ apply(compose_function(sk0_39,X1,X4,X0,X3),X2,sk0_20(sk0_41,sk0_40,sk0_39)) ),
inference(resolution,[status(thm)],[f785,f117]) ).
fof(f1292,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,X1)
| ~ member(sk0_20(sk0_41,sk0_40,sk0_39),X2)
| ~ apply(compose_function(sk0_39,X3,X1,sk0_40,X2),X0,sk0_20(sk0_41,sk0_40,sk0_39))
| ~ member(X0,X1)
| ~ member(sk0_20(sk0_41,sk0_40,sk0_39),X2)
| ~ apply(compose_function(sk0_39,X3,X1,sk0_40,X2),X0,sk0_20(sk0_41,sk0_40,sk0_39)) ),
inference(resolution,[status(thm)],[f1179,f115]) ).
fof(f1293,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,X1)
| ~ member(sk0_20(sk0_41,sk0_40,sk0_39),X2)
| ~ apply(compose_function(sk0_39,X3,X1,sk0_40,X2),X0,sk0_20(sk0_41,sk0_40,sk0_39)) ),
inference(duplicate_literals_removal,[status(esa)],[f1292]) ).
fof(f1897,plain,
! [X0,X1,X2] :
( ~ member(sk0_20(sk0_41,sk0_40,sk0_39),X0)
| ~ member(sk0_20(sk0_41,sk0_40,sk0_39),X1)
| ~ identity(compose_function(sk0_39,X2,X0,sk0_40,X1),sk0_41) ),
inference(resolution,[status(thm)],[f1293,f272]) ).
fof(f1920,plain,
( ~ member(sk0_20(sk0_41,sk0_40,sk0_39),sk0_41)
| ~ member(sk0_20(sk0_41,sk0_40,sk0_39),sk0_41) ),
inference(resolution,[status(thm)],[f1897,f249]) ).
fof(f1921,plain,
~ spl0_12,
inference(split_clause,[status(thm)],[f1920,f378]) ).
fof(f1923,plain,
$false,
inference(sat_refutation,[status(thm)],[f388,f1921]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET734+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 21:19:47 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 19.85/2.87 % Refutation found
% 19.85/2.87 % SZS status Theorem for theBenchmark: Theorem is valid
% 19.85/2.87 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 20.39/2.92 % Elapsed time: 2.552239 seconds
% 20.39/2.92 % CPU time: 20.082308 seconds
% 20.39/2.92 % Total memory used: 166.134 MB
% 20.39/2.92 % Net memory used: 162.354 MB
%------------------------------------------------------------------------------