TSTP Solution File: SWV411+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWV411+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n002.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 12:41:36 EDT 2023
% Result : Theorem 0.10s 0.35s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 8 unt; 0 def)
% Number of atoms : 87 ( 21 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 91 ( 35 ~; 31 |; 15 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 80 (; 71 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [U,V,W,X] :
( contains_slb(insert_slb(U,pair(V,X)),W)
<=> ( contains_slb(U,W)
| V = W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [U,V,W,X,Y] :
( pair_in_list(insert_slb(U,pair(V,X)),W,Y)
<=> ( pair_in_list(U,W,Y)
| ( V = W
& X = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
! [U] :
( ! [V] :
( contains_slb(U,V)
=> ? [W] : pair_in_list(U,V,W) )
=> ! [X,Y,Z] :
( contains_slb(insert_slb(U,pair(Y,Z)),X)
=> ? [X1] : pair_in_list(insert_slb(U,pair(Y,Z)),X,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [U] :
( ! [V] :
( contains_slb(U,V)
=> ? [W] : pair_in_list(U,V,W) )
=> ! [X,Y,Z] :
( contains_slb(insert_slb(U,pair(Y,Z)),X)
=> ? [X1] : pair_in_list(insert_slb(U,pair(Y,Z)),X,X1) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f35,plain,
! [U,V,W,X] :
( ( ~ contains_slb(insert_slb(U,pair(V,X)),W)
| contains_slb(U,W)
| V = W )
& ( contains_slb(insert_slb(U,pair(V,X)),W)
| ( ~ contains_slb(U,W)
& V != W ) ) ),
inference(NNF_transformation,[status(esa)],[f9]) ).
fof(f36,plain,
( ! [U,V,W] :
( ! [X] : ~ contains_slb(insert_slb(U,pair(V,X)),W)
| contains_slb(U,W)
| V = W )
& ! [U,V,W] :
( ! [X] : contains_slb(insert_slb(U,pair(V,X)),W)
| ( ~ contains_slb(U,W)
& V != W ) ) ),
inference(miniscoping,[status(esa)],[f35]) ).
fof(f37,plain,
! [X0,X1,X2,X3] :
( ~ contains_slb(insert_slb(X0,pair(X1,X2)),X3)
| contains_slb(X0,X3)
| X1 = X3 ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f41,plain,
! [U,V,W,X,Y] :
( ( ~ pair_in_list(insert_slb(U,pair(V,X)),W,Y)
| pair_in_list(U,W,Y)
| ( V = W
& X = Y ) )
& ( pair_in_list(insert_slb(U,pair(V,X)),W,Y)
| ( ~ pair_in_list(U,W,Y)
& ( V != W
| X != Y ) ) ) ),
inference(NNF_transformation,[status(esa)],[f11]) ).
fof(f42,plain,
( ! [U,V,W,X,Y] :
( ~ pair_in_list(insert_slb(U,pair(V,X)),W,Y)
| pair_in_list(U,W,Y)
| ( V = W
& X = Y ) )
& ! [U,V,W,X,Y] :
( pair_in_list(insert_slb(U,pair(V,X)),W,Y)
| ( ~ pair_in_list(U,W,Y)
& ( V != W
| X != Y ) ) ) ),
inference(miniscoping,[status(esa)],[f41]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X2)),X3,X4)
| ~ pair_in_list(X0,X3,X4) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f46,plain,
! [X0,X1,X2,X3,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X2)),X3,X4)
| X1 != X3
| X2 != X4 ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f62,plain,
? [U] :
( ! [V] :
( ~ contains_slb(U,V)
| ? [W] : pair_in_list(U,V,W) )
& ? [X,Y,Z] :
( contains_slb(insert_slb(U,pair(Y,Z)),X)
& ! [X1] : ~ pair_in_list(insert_slb(U,pair(Y,Z)),X,X1) ) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f63,plain,
( ! [V] :
( ~ contains_slb(sk0_0,V)
| pair_in_list(sk0_0,V,sk0_1(V)) )
& contains_slb(insert_slb(sk0_0,pair(sk0_3,sk0_4)),sk0_2)
& ! [X1] : ~ pair_in_list(insert_slb(sk0_0,pair(sk0_3,sk0_4)),sk0_2,X1) ),
inference(skolemization,[status(esa)],[f62]) ).
fof(f64,plain,
! [X0] :
( ~ contains_slb(sk0_0,X0)
| pair_in_list(sk0_0,X0,sk0_1(X0)) ),
inference(cnf_transformation,[status(esa)],[f63]) ).
fof(f65,plain,
contains_slb(insert_slb(sk0_0,pair(sk0_3,sk0_4)),sk0_2),
inference(cnf_transformation,[status(esa)],[f63]) ).
fof(f66,plain,
! [X0] : ~ pair_in_list(insert_slb(sk0_0,pair(sk0_3,sk0_4)),sk0_2,X0),
inference(cnf_transformation,[status(esa)],[f63]) ).
fof(f68,plain,
! [X0,X1,X2] : pair_in_list(insert_slb(X0,pair(X1,X2)),X1,X2),
inference(destructive_equality_resolution,[status(esa)],[f46]) ).
fof(f69,plain,
( spl0_0
<=> contains_slb(sk0_0,sk0_2) ),
introduced(split_symbol_definition) ).
fof(f70,plain,
( contains_slb(sk0_0,sk0_2)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,plain,
( spl0_1
<=> sk0_3 = sk0_2 ),
introduced(split_symbol_definition) ).
fof(f73,plain,
( sk0_3 = sk0_2
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f72]) ).
fof(f75,plain,
( contains_slb(sk0_0,sk0_2)
| sk0_3 = sk0_2 ),
inference(resolution,[status(thm)],[f37,f65]) ).
fof(f76,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f75,f69,f72]) ).
fof(f77,plain,
! [X0] : ~ pair_in_list(sk0_0,sk0_2,X0),
inference(resolution,[status(thm)],[f45,f66]) ).
fof(f78,plain,
~ contains_slb(sk0_0,sk0_2),
inference(resolution,[status(thm)],[f77,f64]) ).
fof(f125,plain,
( $false
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f70,f78]) ).
fof(f126,plain,
~ spl0_0,
inference(contradiction_clause,[status(thm)],[f125]) ).
fof(f130,plain,
! [X0] :
( ~ pair_in_list(insert_slb(sk0_0,pair(sk0_2,sk0_4)),sk0_2,X0)
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f73,f66]) ).
fof(f133,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f130,f68]) ).
fof(f134,plain,
~ spl0_1,
inference(contradiction_clause,[status(thm)],[f133]) ).
fof(f135,plain,
$false,
inference(sat_refutation,[status(thm)],[f76,f126,f134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWV411+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.34 % Computer : n002.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8042.1875MB
% 0.10/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Tue May 30 11:58:28 EDT 2023
% 0.10/0.34 % CPUTime :
% 0.10/0.34 % Drodi V3.5.1
% 0.10/0.35 % Refutation found
% 0.10/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.57 % Elapsed time: 0.012741 seconds
% 0.16/0.57 % CPU time: 0.014321 seconds
% 0.16/0.57 % Memory used: 3.682 MB
%------------------------------------------------------------------------------