%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV411+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:47:36 PM UTC 2026
% Result : Theorem 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 8 unt; 2 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)
<=> ( V = W
| contains_slb(U,W) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [U,V,W,X,Y] :
( pair_in_list(insert_slb(U,pair(V,X)),W,Y)
<=> ( ( X = Y
& V = W )
| pair_in_list(U,W,Y) ) ),
file('/export/starexec/sandbox/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/sandbox/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] :
( ( ( V != W
& ~ contains_slb(U,W) )
| contains_slb(insert_slb(U,pair(V,X)),W) )
& ( V = W
| contains_slb(U,W)
| ~ contains_slb(insert_slb(U,pair(V,X)),W) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f36,plain,
( ! [U,V,W] :
( ( V != W
& ~ contains_slb(U,W) )
| ! [X] : contains_slb(insert_slb(U,pair(V,X)),W) )
& ! [U,V,W] :
( V = W
| contains_slb(U,W)
| ! [X] : ~ contains_slb(insert_slb(U,pair(V,X)),W) ) ),
inference(miniscoping,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0,X1,X2,X3] :
( X1 = X3
| contains_slb(X0,X3)
| ~ contains_slb(insert_slb(X0,pair(X1,X2)),X3) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f41,plain,
! [U,V,W,X,Y] :
( ( ( ( X != Y
| V != W )
& ~ pair_in_list(U,W,Y) )
| pair_in_list(insert_slb(U,pair(V,X)),W,Y) )
& ( ( X = Y
& V = W )
| pair_in_list(U,W,Y)
| ~ pair_in_list(insert_slb(U,pair(V,X)),W,Y) ) ),
inference(NNF_transformation,[status(thm)],[f11]) ).
fof(f42,plain,
( ! [U,V,W,X,Y] :
( ( ( X != Y
| V != W )
& ~ pair_in_list(U,W,Y) )
| pair_in_list(insert_slb(U,pair(V,X)),W,Y) )
& ! [U,V,W,X,Y] :
( ( X = Y
& V = W )
| pair_in_list(U,W,Y)
| ~ pair_in_list(insert_slb(U,pair(V,X)),W,Y) ) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4] :
( ~ pair_in_list(X0,X3,X4)
| pair_in_list(insert_slb(X0,pair(X1,X2)),X3,X4) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f46,plain,
! [X0,X1,X2,X3,X4] :
( X2 != X4
| X1 != X3
| pair_in_list(insert_slb(X0,pair(X1,X2)),X3,X4) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f62,plain,
? [U] :
( ? [X,Y,Z] :
( ! [X1] : ~ pair_in_list(insert_slb(U,pair(Y,Z)),X,X1)
& contains_slb(insert_slb(U,pair(Y,Z)),X) )
& ! [V] :
( ? [W] : pair_in_list(U,V,W)
| ~ contains_slb(U,V) ) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f63,plain,
( ! [X1] : ~ pair_in_list(insert_slb(sK0_skl,pair(sK3_skl,sK4_skl)),sK2_skl,X1)
& contains_slb(insert_slb(sK0_skl,pair(sK3_skl,sK4_skl)),sK2_skl)
& ! [V] :
( pair_in_list(sK0_skl,V,sK1_skl(V))
| ~ contains_slb(sK0_skl,V) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl]),skolemize(U,sK0_skl),skolemize(W,sK1_skl(V)),skolemize(X,sK2_skl),skolemize(Y,sK3_skl),skolemize(Z,sK4_skl)],[f62]) ).
fof(f64,plain,
! [X0] :
( pair_in_list(sK0_skl,X0,sK1_skl(X0))
| ~ contains_slb(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f65,plain,
contains_slb(insert_slb(sK0_skl,pair(sK3_skl,sK4_skl)),sK2_skl),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f66,plain,
! [X0] : ~ pair_in_list(insert_slb(sK0_skl,pair(sK3_skl,sK4_skl)),sK2_skl,X0),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f68,plain,
! [X0,X1,X2] : pair_in_list(insert_slb(X0,pair(X1,X2)),X1,X2),
inference(destructive_equality_resolution,[status(thm)],[f46]) ).
fof(f69,plain,
( sK3_skl = sK2_skl
| contains_slb(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f37,f65]) ).
fof(f71,definition,
( sQ0_spl
<=> contains_slb(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( ~ sQ0_spl
| contains_slb(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,definition,
( sQ1_spl
<=> sK3_skl = sK2_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( ~ sQ1_spl
| sK3_skl = sK2_skl ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f71,f74]) ).
fof(f79,plain,
! [X0] : ~ pair_in_list(sK0_skl,sK2_skl,X0),
inference(resolution,[status(thm)],[f45,f66]) ).
fof(f80,plain,
~ contains_slb(sK0_skl,sK2_skl),
inference(resolution,[status(thm)],[f79,f64]) ).
fof(f81,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f80,f72]) ).
fof(f82,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f81]) ).
fof(f84,plain,
! [X0] :
( ~ sQ1_spl
| ~ pair_in_list(insert_slb(sK0_skl,pair(sK3_skl,sK4_skl)),sK3_skl,X0) ),
inference(backward_demodulation,[status(thm)],[f75,f66]) ).
fof(f90,plain,
( ~ sQ1_spl
| $false ),
inference(resolution,[status(thm)],[f84,f68]) ).
fof(f91,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f90]) ).
fof(f92,plain,
$false,
inference(sat_refutation,[status(thm)],[f77,f82,f91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV411+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 08:45:03 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.11/0.39 % Refutation found
% 0.11/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.42 % Elapsed time: 0.057060 seconds
% 0.11/0.42 % CPU time: 0.161740 seconds
% 0.11/0.42 % Total memory used: 101.981 MB
% 0.11/0.42 % Net memory used: 101.728 MB
%------------------------------------------------------------------------------