%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC029+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 : 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 02:39:39 PM UTC 2026
% Result : Theorem 0.07s 5.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 57 ( 13 unt; 1 def)
% Number of atoms : 220 ( 106 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 259 ( 96 ~; 85 |; 53 &)
% ( 5 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 65 ( 53 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
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(f21,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> nil != cons(V,U) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f83,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil = app(U,V)
<=> ( nil = U
& nil = V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil = V
| nil != U )
& ( nil = U
| nil != V ) )
| ( neq(X,nil)
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(Z,cons(Y,nil)) != W
| app(cons(Y,nil),Z) != X ) ) ) )
| ( nil = X
& nil != W )
| 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)
=> ( ( ( nil = V
| nil != U )
& ( nil = U
| nil != V ) )
| ( neq(X,nil)
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(Z,cons(Y,nil)) != W
| app(cons(Y,nil),Z) != X ) ) ) )
| ( nil = X
& nil != W )
| U != W
| V != X ) ) ) ) ),
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(f220,plain,
! [X0,X1] :
( X0 = X1
| neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
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(f234,plain,
! [U] :
( ! [V] :
( nil != cons(V,U)
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f235,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f383,plain,
! [U] :
( ! [V] :
( ( nil = app(U,V)
<=> ( nil = U
& nil = V ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f83]) ).
fof(f384,plain,
! [U] :
( ! [V] :
( ( ( nil != U
| nil != V
| nil = app(U,V) )
& ( ( nil = U
& nil = V )
| nil != app(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f383]) ).
fof(f385,plain,
! [X0,X1] :
( nil = X1
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil != V
& nil = U )
| ( nil != U
& nil = V ) )
& ( ~ neq(X,nil)
| ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = W
& app(cons(Y,nil),Z) = X
& ssList(Z) )
& ssItem(Y) ) )
& ( nil != X
| nil = W )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [U,V] :
( sP0_prd(V,U)
<=> ( nil != U
& nil = V ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil != V
& nil = U )
| sP0_prd(V,U) )
& ( ~ neq(X,nil)
| ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = W
& app(cons(Y,nil),Z) = X
& ssList(Z) )
& ssItem(Y) ) )
& ( nil != X
| nil = W )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ( nil != sK48_skl
& nil = sK47_skl )
| sP0_prd(sK48_skl,sK47_skl) )
& ( ~ neq(sK50_skl,nil)
| ( app(sK52_skl,cons(sK51_skl,nil)) = sK49_skl
& app(cons(sK51_skl,nil),sK52_skl) = sK50_skl
& ssList(sK52_skl)
& ssItem(sK51_skl) ) )
& ( nil != sK50_skl
| nil = 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,sK52_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl),skolemize(Z,sK52_skl)],[f417]) ).
fof(f422,plain,
ssList(sK50_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,
( nil != sK50_skl
| nil = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
( ~ neq(sK50_skl,nil)
| ssItem(sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
( ~ neq(sK50_skl,nil)
| ssList(sK52_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f429,plain,
( ~ neq(sK50_skl,nil)
| app(sK52_skl,cons(sK51_skl,nil)) = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f430,plain,
( nil = sK47_skl
| sP0_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f431,plain,
( nil != sK48_skl
| sP0_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f432,plain,
! [U,V] :
( ( nil = U
| nil != V
| sP0_prd(V,U) )
& ( ( nil != U
& nil = V )
| ~ sP0_prd(V,U) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f433,plain,
( ! [U,V] :
( nil = U
| nil != V
| sP0_prd(V,U) )
& ! [U,V] :
( ( nil != U
& nil = V )
| ~ sP0_prd(V,U) ) ),
inference(miniscoping,[status(thm)],[f432]) ).
fof(f434,plain,
! [X0,X1] :
( nil = X0
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f435,plain,
! [X0,X1] :
( nil != X1
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f467,plain,
! [X0] : ~ sP0_prd(X0,nil),
inference(destructive_equality_resolution,[status(thm)],[f435]) ).
fof(f475,plain,
( nil != sK50_skl
| nil = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f424,f425]) ).
fof(f484,plain,
( nil = sK47_skl
| sP0_prd(sK50_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f430]) ).
fof(f485,plain,
( nil = sK50_skl
| nil = sK47_skl ),
inference(resolution,[status(thm)],[f484,f434]) ).
fof(f486,plain,
nil = sK47_skl,
inference(forward_subsumption_resolution,[status(thm)],[f485,f475]) ).
fof(f489,plain,
nil = sK49_skl,
inference(backward_demodulation,[status(thm)],[f486,f424]) ).
fof(f493,plain,
( nil != sK48_skl
| sP0_prd(sK50_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f431]) ).
fof(f494,plain,
( nil != sK48_skl
| sP0_prd(sK50_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f486,f493]) ).
fof(f495,plain,
( nil != sK50_skl
| sP0_prd(sK50_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f423,f494]) ).
fof(f496,plain,
nil != sK50_skl,
inference(forward_subsumption_resolution,[status(thm)],[f495,f467]) ).
fof(f525,plain,
( ~ neq(sK50_skl,nil)
| app(sK52_skl,cons(sK51_skl,nil)) = nil ),
inference(forward_demodulation,[status(thm)],[f489,f429]) ).
fof(f527,plain,
( nil = cons(sK51_skl,nil)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| ~ neq(sK50_skl,nil) ),
inference(resolution,[status(thm)],[f525,f385]) ).
fof(f529,plain,
( nil = cons(sK51_skl,nil)
| ~ ssList(cons(sK51_skl,nil))
| ~ neq(sK50_skl,nil) ),
inference(forward_subsumption_resolution,[status(thm)],[f527,f427]) ).
fof(f532,plain,
( ~ ssItem(sK51_skl)
| ~ ssList(nil)
| nil = cons(sK51_skl,nil)
| ~ neq(sK50_skl,nil) ),
inference(resolution,[status(thm)],[f529,f222]) ).
fof(f533,plain,
( ~ ssItem(sK51_skl)
| ~ ssList(nil)
| ~ neq(sK50_skl,nil) ),
inference(forward_subsumption_resolution,[status(thm)],[f532,f235]) ).
fof(f546,plain,
~ neq(sK50_skl,nil),
inference(backward_subsumption_resolution,[status(thm)],[f426,f547]) ).
fof(f547,plain,
( ~ ssItem(sK51_skl)
| ~ neq(sK50_skl,nil) ),
inference(forward_subsumption_resolution,[status(thm)],[f533,f223]) ).
fof(f552,plain,
( sK50_skl = nil
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f546,f220]) ).
fof(f554,plain,
( sK50_skl = nil
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[status(thm)],[f552,f422]) ).
fof(f561,plain,
nil != nil,
inference(backward_demodulation,[status(thm)],[f564,f496]) ).
fof(f564,plain,
sK50_skl = nil,
inference(forward_subsumption_resolution,[status(thm)],[f554,f223]) ).
fof(f566,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f561]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC029+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/5.36 % Computer : n005.cluster.edu
% 0.07/5.36 % Model : x86_64 x86_64
% 0.07/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/5.36 % Memory : 8046.5625MB
% 0.07/5.36 % OS : Linux 6.8.0-71-generic
% 0.07/5.36 % CPULimit : 300
% 0.07/5.36 % WCLimit : 300
% 0.07/5.36 % DateTime : Mon Sep 21 07:50:09 UTC 2026
% 0.07/5.36 % CPUTime :
% 0.07/5.37 % Drodi V4.1.1
% 0.07/5.39 % Refutation found
% 0.07/5.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.42 % Elapsed time: 0.049401 seconds
% 0.13/5.42 % CPU time: 0.162248 seconds
% 0.13/5.42 % Total memory used: 97.312 MB
% 0.13/5.42 % Net memory used: 97.161 MB
%------------------------------------------------------------------------------