%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC200+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 02:40:22 PM UTC 2026
% Result : Theorem 0.17s 0.55s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 70 ( 12 unt; 8 def)
% Number of atoms : 226 ( 42 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 254 ( 98 ~; 97 |; 32 &)
% ( 12 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 9 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 57 ( 45 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
? [U] :
( ? [V] :
( U != V
& ssItem(V) )
& ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssList(W)
=> ( memberP(cons(V,W),U)
<=> ( memberP(W,U)
| U = V ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ? [Y] :
( ! [Z] :
( ssItem(Z)
=> ( Y = Z
| ~ memberP(U,Z) ) )
& ssItem(Y) )
| ~ singletonP(W)
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ? [Y] :
( ! [Z] :
( ssItem(Z)
=> ( Y = Z
| ~ memberP(U,Z) ) )
& ssItem(Y) )
| ~ singletonP(W)
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f102,plain,
( sK0_skl != sK1_skl
& ssItem(sK1_skl)
& ssItem(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl)],[f2]) ).
fof(f104,plain,
ssItem(sK1_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f113,plain,
! [U] :
( ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f114,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ? [V] :
( cons(V,nil) = U
& ssItem(V) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ( cons(sK4_skl(U),nil) = U
& ssItem(sK4_skl(U)) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114]) ).
fof(f116,plain,
! [X0] :
( ssItem(sK4_skl(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0] :
( cons(sK4_skl(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f273,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( memberP(cons(V,W),U)
<=> ( memberP(W,U)
| U = V ) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f274,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( ( ( ~ memberP(W,U)
& U != V )
| memberP(cons(V,W),U) )
& ( memberP(W,U)
| U = V
| ~ memberP(cons(V,W),U) ) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f273]) ).
fof(f275,plain,
! [X0,X1,X2] :
( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f278,plain,
! [U] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f279,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f278]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ! [Y] :
( ? [Z] :
( Y != Z
& memberP(U,Z)
& ssItem(Z) )
| ~ ssItem(Y) )
& singletonP(W)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
( ! [Y] :
( ( Y != sK51_skl(Y)
& memberP(sK47_skl,sK51_skl(Y))
& ssItem(sK51_skl(Y)) )
| ~ ssItem(Y) )
& singletonP(sK49_skl)
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& ssList(sK50_skl)
& ssList(sK49_skl)
& ssList(sK48_skl)
& ssList(sK47_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl,sK51_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Z,sK51_skl(Y))],[f415]) ).
fof(f417,plain,
ssList(sK47_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f422,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f423,plain,
singletonP(sK49_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
! [X0] :
( ssItem(sK51_skl(X0))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f425,plain,
! [X0] :
( memberP(sK47_skl,sK51_skl(X0))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f426,plain,
! [X0] :
( X0 != sK51_skl(X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f460,plain,
singletonP(sK47_skl),
inference(forward_demodulation,[status(thm)],[f422,f423]) ).
fof(f461,plain,
! [X0] :
( ~ singletonP(X0)
| ~ ssList(X0)
| sK4_skl(X0) != sK51_skl(sK4_skl(X0)) ),
inference(resolution,[status(thm)],[f426,f116]) ).
fof(f465,plain,
( cons(sK4_skl(sK47_skl),nil) = sK47_skl
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f117,f460]) ).
fof(f467,definition,
( sQ0_spl
<=> ssList(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f469,plain,
( sQ0_spl
| ~ ssList(sK47_skl) ),
inference(component_clause,[status(thm)],[f467]) ).
fof(f470,definition,
( sQ1_spl
<=> cons(sK4_skl(sK47_skl),nil) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f471,plain,
( ~ sQ1_spl
| cons(sK4_skl(sK47_skl),nil) = sK47_skl ),
inference(component_clause,[status(thm)],[f470]) ).
fof(f473,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f465,f467,f470]) ).
fof(f475,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f469,f417]) ).
fof(f476,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f475]) ).
fof(f495,plain,
( ~ ssList(sK47_skl)
| sK4_skl(sK47_skl) != sK51_skl(sK4_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f461,f460]) ).
fof(f497,definition,
( sQ5_spl
<=> sK4_skl(sK47_skl) = sK51_skl(sK4_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f499,plain,
( sQ5_spl
| sK4_skl(sK47_skl) != sK51_skl(sK4_skl(sK47_skl)) ),
inference(component_clause,[status(thm)],[f497]) ).
fof(f500,plain,
( ~ sQ0_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f495,f497,f467]) ).
fof(f503,plain,
! [X0] :
( ~ sQ1_spl
| memberP(nil,X0)
| X0 = sK4_skl(sK47_skl)
| ~ memberP(sK47_skl,X0)
| ~ ssList(nil)
| ~ ssItem(sK4_skl(sK47_skl))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f471,f275]) ).
fof(f508,definition,
( sQ7_spl
<=> singletonP(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f510,plain,
( sQ7_spl
| ~ singletonP(sK47_skl) ),
inference(component_clause,[status(thm)],[f508]) ).
fof(f511,definition,
( sQ8_spl
<=> ssItem(sK4_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f512,plain,
( ~ sQ8_spl
| ssItem(sK4_skl(sK47_skl)) ),
inference(component_clause,[status(thm)],[f511]) ).
fof(f513,plain,
( sQ8_spl
| ~ ssItem(sK4_skl(sK47_skl)) ),
inference(component_clause,[status(thm)],[f511]) ).
fof(f515,definition,
! [X0] :
( sQ9_spl
<=> ( memberP(nil,X0)
| X0 = sK4_skl(sK47_skl)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f516,plain,
! [X0] :
( ~ sQ9_spl
| memberP(nil,X0)
| X0 = sK4_skl(sK47_skl)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f515]) ).
fof(f518,definition,
( sQ10_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f520,plain,
( sQ10_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f518]) ).
fof(f521,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f503,f515,f511,f518,f470]) ).
fof(f536,plain,
( sQ8_spl
| ~ singletonP(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f513,f116]) ).
fof(f537,plain,
( sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f536,f467,f508,f511]) ).
fof(f538,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f520,f223]) ).
fof(f539,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f538]) ).
fof(f540,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f510,f460]) ).
fof(f541,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f540]) ).
fof(f542,plain,
! [X0] :
( ~ sQ9_spl
| X0 = sK4_skl(sK47_skl)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f516,f279]) ).
fof(f586,definition,
( sQ16_spl
<=> ssItem(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f588,plain,
( sQ16_spl
| ~ ssItem(sK1_skl) ),
inference(component_clause,[status(thm)],[f586]) ).
fof(f609,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f588,f104]) ).
fof(f610,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f609]) ).
fof(f638,plain,
! [X0] :
( ~ sQ9_spl
| ~ ssItem(X0)
| sK51_skl(X0) = sK4_skl(sK47_skl)
| ~ ssItem(sK51_skl(X0)) ),
inference(resolution,[status(thm)],[f542,f425]) ).
fof(f639,plain,
! [X0] :
( ~ sQ9_spl
| ~ ssItem(X0)
| sK51_skl(X0) = sK4_skl(sK47_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f638,f424]) ).
fof(f692,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sK51_skl(sK4_skl(sK47_skl)) = sK4_skl(sK47_skl) ),
inference(resolution,[status(thm)],[f639,f512]) ).
fof(f696,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f692,f499]) ).
fof(f697,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f696]) ).
fof(f698,plain,
$false,
inference(sat_refutation,[status(thm)],[f473,f476,f500,f521,f537,f539,f541,f610,f697]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC200+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.45 % Computer : n006.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Mon Sep 21 08:03:57 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.50 % Drodi V4.1.1
% 0.17/0.55 % Refutation found
% 0.17/0.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.59 % Elapsed time: 0.120766 seconds
% 0.17/0.59 % CPU time: 0.381606 seconds
% 0.17/0.59 % Total memory used: 81.869 MB
% 0.17/0.59 % Net memory used: 81.642 MB
%------------------------------------------------------------------------------