%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC355+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 : n020.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 02:40:54 PM UTC 2026
% Result : Theorem 41.97s 5.73s
% Output : CNFRefutation 41.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 65 ( 18 unt; 1 def)
% Number of atoms : 244 ( 48 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 286 ( 107 ~; 100 |; 57 &)
% ( 5 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 123 ( 102 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = U
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( segmentP(V,U)
| ! [Y] :
( ssItem(Y)
=> app(W,cons(Y,nil)) != X )
| ~ neq(V,nil) ) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( segmentP(V,U)
| ! [Y] :
( ssItem(Y)
=> app(W,cons(Y,nil)) != X )
| ~ neq(V,nil) ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f125,plain,
! [U] :
( ! [V] :
( ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f126,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(W,V) != U
| ~ ssList(W) )
| rearsegP(U,V) )
& ( ? [W] :
( app(W,V) = U
& ssList(W) )
| ~ rearsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(W,V) != U
| ~ ssList(W) )
| rearsegP(U,V) )
& ( ( app(sK6_skl(V,U),V) = U
& ssList(sK6_skl(V,U)) )
| ~ rearsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(W,sK6_skl(V,U))],[f126]) ).
fof(f128,plain,
! [X0,X1] :
( ssList(sK6_skl(X1,X0))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f129,plain,
! [X0,X1] :
( app(sK6_skl(X1,X0),X1) = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f131,plain,
! [U] :
( ! [V] :
( ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f132,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ( app(app(sK7_skl(V,U),V),sK8_skl(V,U)) = U
& ssList(sK8_skl(V,U))
& ssList(sK7_skl(V,U)) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132]) ).
fof(f137,plain,
! [X0,X1,X2,X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f221,plain,
! [U] :
( ! [V] :
( ssList(cons(V,U))
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f222,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f304,plain,
! [U] :
( rearsegP(U,U)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f305,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f304]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| ( ~ segmentP(V,U)
& ? [Y] :
( app(W,cons(Y,nil)) = X
& ssItem(Y) )
& neq(V,nil) ) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [U,V,W,X] :
( sP0_prd(X,W,V,U)
<=> ( ~ segmentP(V,U)
& ? [Y] :
( app(W,cons(Y,nil)) = X
& ssItem(Y) )
& neq(V,nil) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| sP0_prd(X,W,V,U) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ( ~ neq(sK50_skl,nil)
& neq(sK48_skl,nil) )
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_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]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl)],[f417]) ).
fof(f419,plain,
ssList(sK47_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f420,plain,
ssList(sK48_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f423,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f424,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f425,plain,
( neq(sK48_skl,nil)
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
( ~ neq(sK50_skl,nil)
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
! [U,V,W,X] :
( ( segmentP(V,U)
| ! [Y] :
( app(W,cons(Y,nil)) != X
| ~ ssItem(Y) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ( ( ~ segmentP(V,U)
& ? [Y] :
( app(W,cons(Y,nil)) = X
& ssItem(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f428,plain,
( ! [U,V,W,X] :
( segmentP(V,U)
| ! [Y] :
( app(W,cons(Y,nil)) != X
| ~ ssItem(Y) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( ~ segmentP(V,U)
& ? [Y] :
( app(W,cons(Y,nil)) = X
& ssItem(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(miniscoping,[status(thm)],[f427]) ).
fof(f429,plain,
( ! [U,V,W,X] :
( segmentP(V,U)
| ! [Y] :
( app(W,cons(Y,nil)) != X
| ~ ssItem(Y) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( ~ segmentP(V,U)
& app(W,cons(sK51_skl(X,W,V,U),nil)) = X
& ssItem(sK51_skl(X,W,V,U))
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51_skl]),skolemize(Y,sK51_skl(X,W,V,U))],[f428]) ).
fof(f430,plain,
! [X0,X1,X2,X3] :
( neq(X2,nil)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f431,plain,
! [X0,X1,X2,X3] :
( ssItem(sK51_skl(X0,X1,X2,X3))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f432,plain,
! [X0,X1,X2,X3] :
( app(X1,cons(sK51_skl(X0,X1,X2,X3),nil)) = X0
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f433,plain,
! [X0,X1,X2,X3] :
( ~ segmentP(X2,X3)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f451,plain,
( neq(sK48_skl,nil)
| sP0_prd(sK48_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f425]) ).
fof(f452,plain,
( neq(sK48_skl,nil)
| sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f451]) ).
fof(f453,plain,
neq(sK48_skl,nil),
inference(forward_subsumption_resolution,[status(thm)],[f452,f430]) ).
fof(f458,plain,
! [X0,X1,X2] :
( app(app(X1,X0),X2) != sK48_skl
| ~ ssList(X2)
| ~ ssList(X1)
| segmentP(sK48_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f137,f420]) ).
fof(f469,plain,
( ~ neq(sK50_skl,nil)
| sP0_prd(sK48_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f426]) ).
fof(f470,plain,
( ~ neq(sK50_skl,nil)
| sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f469]) ).
fof(f471,plain,
( ~ neq(sK48_skl,nil)
| sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f470]) ).
fof(f472,plain,
sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl),
inference(forward_subsumption_resolution,[status(thm)],[f471,f453]) ).
fof(f474,plain,
~ segmentP(sK48_skl,sK47_skl),
inference(resolution,[status(thm)],[f472,f433]) ).
fof(f478,plain,
! [X0] :
( ssList(cons(X0,nil))
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f222,f223]) ).
fof(f521,plain,
ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl)),
inference(resolution,[status(thm)],[f431,f472]) ).
fof(f565,plain,
rearsegP(sK47_skl,sK47_skl),
inference(resolution,[status(thm)],[f305,f419]) ).
fof(f574,plain,
( ssList(sK6_skl(sK47_skl,sK47_skl))
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f128,f565]) ).
fof(f577,plain,
( ssList(sK6_skl(sK47_skl,sK47_skl))
| ~ ssList(sK47_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f574]) ).
fof(f578,plain,
ssList(sK6_skl(sK47_skl,sK47_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f577,f419]) ).
fof(f583,plain,
( app(sK6_skl(sK47_skl,sK47_skl),sK47_skl) = sK47_skl
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f129,f565]) ).
fof(f586,plain,
( app(sK6_skl(sK47_skl,sK47_skl),sK47_skl) = sK47_skl
| ~ ssList(sK47_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f583]) ).
fof(f587,plain,
app(sK6_skl(sK47_skl,sK47_skl),sK47_skl) = sK47_skl,
inference(forward_subsumption_resolution,[status(thm)],[f586,f419]) ).
fof(f592,plain,
app(sK47_skl,cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil)) = sK48_skl,
inference(resolution,[status(thm)],[f432,f472]) ).
fof(f953,plain,
! [X0,X1] :
( app(app(X0,sK47_skl),X1) != sK48_skl
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(sK48_skl,sK47_skl) ),
inference(resolution,[status(thm)],[f458,f419]) ).
fof(f954,plain,
! [X0,X1] :
( app(app(X0,sK47_skl),X1) != sK48_skl
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f953,f474]) ).
fof(f2239,plain,
ssList(cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil)),
inference(resolution,[status(thm)],[f521,f478]) ).
fof(f30421,plain,
! [X0] :
( app(app(sK6_skl(sK47_skl,sK47_skl),sK47_skl),X0) != sK48_skl
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f954,f578]) ).
fof(f30429,plain,
! [X0] :
( app(sK47_skl,X0) != sK48_skl
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f587,f30421]) ).
fof(f33464,plain,
app(sK47_skl,cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil)) != sK48_skl,
inference(resolution,[status(thm)],[f2239,f30429]) ).
fof(f33619,plain,
sK48_skl != sK48_skl,
inference(forward_demodulation,[status(thm)],[f592,f33464]) ).
fof(f33620,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f33619]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC355+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n020.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 08:19:17 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.37 % Drodi V4.1.1
% 41.97/5.73 % Refutation found
% 41.97/5.73 % SZS status Theorem for theBenchmark: Theorem is valid
% 41.97/5.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 41.97/5.77 % Elapsed time: 5.410850 seconds
% 41.97/5.77 % CPU time: 42.435575 seconds
% 41.97/5.77 % Total memory used: 321.732 MB
% 41.97/5.77 % Net memory used: 300.951 MB
%------------------------------------------------------------------------------