%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC046+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 02:39:43 PM UTC 2026
% Result : Theorem 10.43s 1.98s
% Output : CNFRefutation 10.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 65 ( 11 unt; 7 def)
% Number of atoms : 226 ( 44 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 251 ( 90 ~; 95 |; 40 &)
% ( 9 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 63 ( 50 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f20,axiom,
! [U] :
( ssList(U)
=> ( ? [V] :
( ? [W] :
( cons(W,V) = U
& ssItem(W) )
& ssList(V) )
| nil = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ? [Y] :
( ( ( ( ? [Z] :
( segmentP(X,app(app(cons(Y,nil),Z),cons(Y,nil)))
& ssList(Z) )
| ~ memberP(X,Y) )
& memberP(W,Y) )
| ( memberP(X,Y)
& ! [Z] :
( ssList(Z)
=> ~ segmentP(X,app(app(cons(Y,nil),Z),cons(Y,nil))) )
& ~ memberP(W,Y) ) )
& ssItem(Y) )
| nil = U
| U != W
| V != X
| nil != V ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ? [Y] :
( ( ( ( ? [Z] :
( segmentP(X,app(app(cons(Y,nil),Z),cons(Y,nil)))
& ssList(Z) )
| ~ memberP(X,Y) )
& memberP(W,Y) )
| ( memberP(X,Y)
& ! [Z] :
( ssList(Z)
=> ~ segmentP(X,app(app(cons(Y,nil),Z),cons(Y,nil))) )
& ~ memberP(W,Y) ) )
& ssItem(Y) )
| nil = U
| U != W
| V != X
| nil != V ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f229,plain,
! [U] :
( ? [V] :
( ? [W] :
( cons(W,V) = U
& ssItem(W) )
& ssList(V) )
| nil = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f230,plain,
! [U] :
( ( cons(sK44_skl(U),sK43_skl(U)) = U
& ssItem(sK44_skl(U))
& ssList(sK43_skl(U)) )
| nil = U
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43_skl,sK44_skl]),skolemize(V,sK43_skl(U)),skolemize(W,sK44_skl(U))],[f229]) ).
fof(f231,plain,
! [X0] :
( ssList(sK43_skl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f232,plain,
! [X0] :
( ssItem(sK44_skl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f233,plain,
! [X0] :
( cons(sK44_skl(X0),sK43_skl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f244,plain,
! [U] :
( ! [V] :
( ssList(app(U,V))
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f245,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f244]) ).
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(f276,plain,
! [X0,X1,X2] :
( 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] :
( ~ segmentP(X,app(app(cons(Y,nil),Z),cons(Y,nil)))
| ~ ssList(Z) )
& memberP(X,Y) )
| ~ memberP(W,Y) )
& ( ~ memberP(X,Y)
| ? [Z] :
( segmentP(X,app(app(cons(Y,nil),Z),cons(Y,nil)))
& ssList(Z) )
| memberP(W,Y) ) )
| ~ ssItem(Y) )
& nil != U
& U = W
& V = X
& nil = V
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
( ! [Y] :
( ( ( ( ! [Z] :
( ~ segmentP(sK50_skl,app(app(cons(Y,nil),Z),cons(Y,nil)))
| ~ ssList(Z) )
& memberP(sK50_skl,Y) )
| ~ memberP(sK49_skl,Y) )
& ( ~ memberP(sK50_skl,Y)
| ( segmentP(sK50_skl,app(app(cons(Y,nil),sK51_skl(Y)),cons(Y,nil)))
& ssList(sK51_skl(Y)) )
| memberP(sK49_skl,Y) ) )
| ~ ssItem(Y) )
& nil != sK47_skl
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& nil = sK48_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(f421,plain,
nil = sK48_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f422,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f423,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
nil != sK47_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f427,plain,
! [X0] :
( memberP(sK50_skl,X0)
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f446,plain,
! [X1,X2] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f276]) ).
fof(f447,plain,
! [X0,X1] :
( memberP(cons(X0,X1),X0)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f446]) ).
fof(f461,plain,
nil = sK50_skl,
inference(forward_demodulation,[status(thm)],[f421,f422]) ).
fof(f464,plain,
! [X0] :
( memberP(sK50_skl,X0)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f423,f427]) ).
fof(f465,plain,
! [X0] :
( memberP(nil,X0)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f461,f464]) ).
fof(f473,plain,
! [X0] :
( ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f465,f279]) ).
fof(f490,definition,
( sQ3_spl
<=> ssList(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f492,plain,
( sQ3_spl
| ~ ssList(sK47_skl) ),
inference(component_clause,[status(thm)],[f490]) ).
fof(f518,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f492,f417]) ).
fof(f519,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f518]) ).
fof(f567,plain,
! [X0] :
( ssList(app(X0,sK47_skl))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f245,f417]) ).
fof(f585,plain,
ssList(app(sK47_skl,sK47_skl)),
inference(resolution,[status(thm)],[f567,f417]) ).
fof(f2243,definition,
( sQ136_spl
<=> nil = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f2244,plain,
( ~ sQ136_spl
| nil = sK47_skl ),
inference(component_clause,[status(thm)],[f2243]) ).
fof(f3344,plain,
( ~ sQ136_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2244,f424]) ).
fof(f3345,plain,
~ sQ136_spl,
inference(contradiction_clause,[status(thm)],[f3344]) ).
fof(f3487,definition,
( sQ234_spl
<=> ssList(app(sK47_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f3489,plain,
( sQ234_spl
| ~ ssList(app(sK47_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f3487]) ).
fof(f3701,plain,
( cons(sK44_skl(sK47_skl),sK43_skl(sK47_skl)) = sK47_skl
| nil = sK47_skl ),
inference(resolution,[status(thm)],[f233,f417]) ).
fof(f3723,definition,
( sQ249_spl
<=> cons(sK44_skl(sK47_skl),sK43_skl(sK47_skl)) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f3724,plain,
( ~ sQ249_spl
| cons(sK44_skl(sK47_skl),sK43_skl(sK47_skl)) = sK47_skl ),
inference(component_clause,[status(thm)],[f3723]) ).
fof(f3726,plain,
( sQ249_spl
| sQ136_spl ),
inference(split_clause,[status(thm)],[f3701,f2243,f3723]) ).
fof(f4055,plain,
( sQ234_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3489,f585]) ).
fof(f4056,plain,
sQ234_spl,
inference(contradiction_clause,[status(thm)],[f4055]) ).
fof(f4776,definition,
( sQ327_spl
<=> ssItem(sK44_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ327_spl])],[split_symbol_definition]) ).
fof(f4778,plain,
( sQ327_spl
| ~ ssItem(sK44_skl(sK47_skl)) ),
inference(component_clause,[status(thm)],[f4776]) ).
fof(f4782,definition,
( sQ329_spl
<=> ssList(sK43_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ329_spl])],[split_symbol_definition]) ).
fof(f4784,plain,
( sQ329_spl
| ~ ssList(sK43_skl(sK47_skl)) ),
inference(component_clause,[status(thm)],[f4782]) ).
fof(f4923,plain,
( sQ327_spl
| nil = sK47_skl
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f4778,f232]) ).
fof(f4924,plain,
( sQ327_spl
| sQ136_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4923,f490,f2243,f4776]) ).
fof(f4925,plain,
( sQ329_spl
| nil = sK47_skl
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f4784,f231]) ).
fof(f4926,plain,
( sQ329_spl
| sQ136_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4925,f490,f2243,f4782]) ).
fof(f6046,plain,
( ~ sQ249_spl
| memberP(sK47_skl,sK44_skl(sK47_skl))
| ~ ssList(sK43_skl(sK47_skl))
| ~ ssItem(sK44_skl(sK47_skl)) ),
inference(paramodulation,[status(thm)],[f3724,f447]) ).
fof(f6048,definition,
( sQ454_spl
<=> memberP(sK47_skl,sK44_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ454_spl])],[split_symbol_definition]) ).
fof(f6049,plain,
( ~ sQ454_spl
| memberP(sK47_skl,sK44_skl(sK47_skl)) ),
inference(component_clause,[status(thm)],[f6048]) ).
fof(f6051,plain,
( ~ sQ249_spl
| sQ454_spl
| ~ sQ329_spl
| ~ sQ327_spl ),
inference(split_clause,[status(thm)],[f6046,f4776,f4782,f6048,f3723]) ).
fof(f6056,plain,
( ~ sQ454_spl
| ~ ssItem(sK44_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f6049,f473]) ).
fof(f6057,plain,
( ~ sQ454_spl
| ~ sQ327_spl ),
inference(split_clause,[status(thm)],[f6056,f4776,f6048]) ).
fof(f6058,plain,
$false,
inference(sat_refutation,[status(thm)],[f519,f3345,f3726,f4056,f4924,f4926,f6051,f6057]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC046+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 07:51:28 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 10.43/1.98 % Refutation found
% 10.43/1.98 % SZS status Theorem for theBenchmark: Theorem is valid
% 10.43/1.98 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 10.43/2.02 % Elapsed time: 1.638887 seconds
% 10.43/2.02 % CPU time: 12.723178 seconds
% 10.43/2.02 % Total memory used: 178.774 MB
% 10.43/2.02 % Net memory used: 172.493 MB
%------------------------------------------------------------------------------