%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC037+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 : n003.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 02:39:41 PM UTC 2026
% Result : Theorem 0.14s 5.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 16 unt; 1 def)
% Number of atoms : 154 ( 50 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 174 ( 60 ~; 51 |; 45 &)
% ( 5 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 55 ( 45 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [U] :
( ssList(U)
=> ( segmentP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [Y] :
( ssList(Y)
=> ( ~ segmentP(W,Y)
| ~ segmentP(X,Y)
| ~ neq(Y,nil) ) ) )
| 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)
=> ( ( ( nil != W
| nil != X )
& ! [Y] :
( ssList(Y)
=> ( ~ segmentP(W,Y)
| ~ segmentP(X,Y)
| ~ neq(Y,nil) ) ) )
| nil = U
| U != W
| V != X
| nil != V ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f217,plain,
! [U] :
( ! [V] :
( ( neq(U,V)
<=> U != V )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f218,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f217]) ).
fof(f219,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f324,plain,
! [U] :
( ( segmentP(nil,U)
<=> nil = U )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f58]) ).
fof(f325,plain,
! [U] :
( ( ( nil != U
| segmentP(nil,U) )
& ( nil = U
| ~ segmentP(nil,U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f324]) ).
fof(f326,plain,
! [X0] :
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f325]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [Y] :
( segmentP(W,Y)
& segmentP(X,Y)
& neq(Y,nil)
& ssList(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,definition,
! [W,X,Y] :
( sP0_prd(Y,X,W)
<=> ( segmentP(W,Y)
& segmentP(X,Y)
& neq(Y,nil)
& ssList(Y) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [Y] : sP0_prd(Y,X,W) )
& nil != U
& U = W
& V = X
& nil = V
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ( nil = sK49_skl
& nil = sK50_skl )
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) )
& 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(Y,sK51_skl)],[f417]) ).
fof(f423,plain,
nil = sK48_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f424,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f425,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
nil != sK47_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f428,plain,
( nil = sK49_skl
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f429,plain,
! [W,X,Y] :
( ( ~ segmentP(W,Y)
| ~ segmentP(X,Y)
| ~ neq(Y,nil)
| ~ ssList(Y)
| sP0_prd(Y,X,W) )
& ( ( segmentP(W,Y)
& segmentP(X,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ sP0_prd(Y,X,W) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f430,plain,
( ! [W,X,Y] :
( ~ segmentP(W,Y)
| ~ segmentP(X,Y)
| ~ neq(Y,nil)
| ~ ssList(Y)
| sP0_prd(Y,X,W) )
& ! [W,X,Y] :
( ( segmentP(W,Y)
& segmentP(X,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ sP0_prd(Y,X,W) ) ),
inference(miniscoping,[status(thm)],[f429]) ).
fof(f431,plain,
! [X0,X1,X2] :
( ssList(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f430]) ).
fof(f432,plain,
! [X0,X1,X2] :
( neq(X0,nil)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f430]) ).
fof(f433,plain,
! [X0,X1,X2] :
( segmentP(X1,X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f430]) ).
fof(f451,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f219]) ).
fof(f452,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f451]) ).
fof(f468,plain,
nil = sK50_skl,
inference(forward_demodulation,[status(thm)],[f423,f424]) ).
fof(f470,plain,
nil != sK49_skl,
inference(forward_demodulation,[status(thm)],[f425,f426]) ).
fof(f490,plain,
( nil = sK49_skl
| sP0_prd(sK51_skl,nil,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f468,f428]) ).
fof(f491,plain,
sP0_prd(sK51_skl,nil,sK49_skl),
inference(forward_subsumption_resolution,[status(thm)],[f490,f470]) ).
fof(f492,plain,
neq(sK51_skl,nil),
inference(resolution,[status(thm)],[f491,f432]) ).
fof(f494,plain,
segmentP(nil,sK51_skl),
inference(resolution,[status(thm)],[f491,f433]) ).
fof(f495,plain,
ssList(sK51_skl),
inference(resolution,[status(thm)],[f491,f431]) ).
fof(f502,plain,
( nil = sK51_skl
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f494,f326]) ).
fof(f504,plain,
nil = sK51_skl,
inference(forward_subsumption_resolution,[status(thm)],[f502,f495]) ).
fof(f508,plain,
neq(nil,nil),
inference(backward_demodulation,[status(thm)],[f504,f492]) ).
fof(f514,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[f508,f452]) ).
fof(f516,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f514,f223]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC037+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n003.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 07:52:07 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.39 % Drodi V4.1.1
% 0.14/5.40 % Refutation found
% 0.14/5.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.43 % Elapsed time: 0.053936 seconds
% 0.14/5.43 % CPU time: 0.144333 seconds
% 0.14/5.43 % Total memory used: 62.473 MB
% 0.14/5.43 % Net memory used: 62.360 MB
%------------------------------------------------------------------------------