%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC030+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 : n015.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 02:39:40 PM UTC 2026
% Result : Theorem 0.13s 5.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 5
% Syntax : Number of formulae : 70 ( 22 unt; 1 def)
% Number of atoms : 226 ( 135 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 246 ( 90 ~; 90 |; 45 &)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 62 ( 50 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f82,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> app(app(U,V),W) = app(U,app(V,W)) ) ) ),
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(f84,axiom,
! [U] :
( ssList(U)
=> app(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 = V
| nil != U )
& ( nil = U
| nil != V ) )
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(Z,Y) != W
| app(Y,Z) != X ) ) )
| 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 ) )
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(Z,Y) != W
| app(Y,Z) != X ) ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f381,plain,
! [U] :
( ! [V] :
( ! [W] :
( app(app(U,V),W) = app(U,app(V,W))
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f82]) ).
fof(f382,plain,
! [X0,X1,X2] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f381]) ).
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(f386,plain,
! [X0,X1] :
( nil = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f388,plain,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f84]) ).
fof(f389,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f388]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil != V
& nil = U )
| ( nil != U
& nil = V ) )
& ? [Y] :
( ? [Z] :
( app(Z,Y) = W
& app(Y,Z) = X
& ssList(Z) )
& ssList(Y) )
& 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) )
& ? [Y] :
( ? [Z] :
( app(Z,Y) = W
& app(Y,Z) = X
& ssList(Z) )
& ssList(Y) )
& 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) )
& app(sK52_skl,sK51_skl) = sK49_skl
& app(sK51_skl,sK52_skl) = sK50_skl
& ssList(sK52_skl)
& ssList(sK51_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(f419,plain,
ssList(sK47_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,
ssList(sK51_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
ssList(sK52_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
app(sK51_skl,sK52_skl) = sK50_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f428,plain,
app(sK52_skl,sK51_skl) = sK49_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f429,plain,
( nil = sK47_skl
| sP0_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f430,plain,
( nil != sK48_skl
| sP0_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f431,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(f432,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)],[f431]) ).
fof(f433,plain,
! [X0,X1] :
( nil = X0
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f432]) ).
fof(f434,plain,
! [X0,X1] :
( nil != X1
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f432]) ).
fof(f466,plain,
! [X0] : ~ sP0_prd(X0,nil),
inference(destructive_equality_resolution,[status(thm)],[f434]) ).
fof(f471,plain,
app(sK51_skl,sK52_skl) = sK48_skl,
inference(forward_demodulation,[status(thm)],[f423,f427]) ).
fof(f473,plain,
app(sK52_skl,sK51_skl) = sK47_skl,
inference(forward_demodulation,[status(thm)],[f424,f428]) ).
fof(f475,plain,
( nil = sK48_skl
| nil = sK47_skl ),
inference(resolution,[status(thm)],[f429,f433]) ).
fof(f519,plain,
( nil = sK51_skl
| nil != sK47_skl
| ~ ssList(sK51_skl)
| ~ ssList(sK52_skl) ),
inference(paramodulation,[status(thm)],[f473,f385]) ).
fof(f520,plain,
( nil = sK52_skl
| nil != sK48_skl
| ~ ssList(sK52_skl)
| ~ ssList(sK51_skl) ),
inference(paramodulation,[status(thm)],[f471,f385]) ).
fof(f522,plain,
( nil = sK51_skl
| nil != sK47_skl
| ~ ssList(sK51_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f519,f426]) ).
fof(f523,plain,
( nil = sK52_skl
| nil != sK48_skl
| ~ ssList(sK52_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f520,f425]) ).
fof(f524,plain,
( nil = sK51_skl
| nil != sK47_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f522,f425]) ).
fof(f525,plain,
( nil = sK52_skl
| nil != sK48_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f523,f426]) ).
fof(f529,plain,
( nil = sK52_skl
| nil != sK47_skl
| ~ ssList(sK51_skl)
| ~ ssList(sK52_skl) ),
inference(paramodulation,[status(thm)],[f473,f386]) ).
fof(f532,plain,
( nil = sK52_skl
| nil != sK47_skl
| ~ ssList(sK51_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f529,f426]) ).
fof(f534,plain,
( nil = sK52_skl
| nil != sK47_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f532,f425]) ).
fof(f536,plain,
! [X0] :
( app(sK47_skl,X0) = app(sK52_skl,app(sK51_skl,X0))
| ~ ssList(X0)
| ~ ssList(sK51_skl)
| ~ ssList(sK52_skl) ),
inference(paramodulation,[status(thm)],[f473,f382]) ).
fof(f538,plain,
! [X0] :
( app(sK47_skl,X0) = app(sK52_skl,app(sK51_skl,X0))
| ~ ssList(X0)
| ~ ssList(sK51_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f536,f426]) ).
fof(f546,plain,
! [X0] :
( app(sK47_skl,X0) = app(sK52_skl,app(sK51_skl,X0))
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f538,f425]) ).
fof(f547,plain,
( app(sK47_skl,sK52_skl) = app(sK52_skl,sK48_skl)
| ~ ssList(sK52_skl) ),
inference(paramodulation,[status(thm)],[f471,f546]) ).
fof(f548,plain,
app(sK47_skl,sK52_skl) = app(sK52_skl,sK48_skl),
inference(forward_subsumption_resolution,[status(thm)],[f547,f426]) ).
fof(f549,plain,
( nil = sK47_skl
| app(sK47_skl,sK52_skl) = app(sK52_skl,nil) ),
inference(paramodulation,[status(thm)],[f475,f548]) ).
fof(f570,plain,
( nil = sK47_skl
| app(sK47_skl,sK52_skl) = sK52_skl
| ~ ssList(sK52_skl) ),
inference(paramodulation,[status(thm)],[f549,f389]) ).
fof(f580,plain,
( nil = sK47_skl
| app(sK47_skl,sK52_skl) = sK52_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f570,f426]) ).
fof(f591,plain,
( nil = sK47_skl
| nil = sK47_skl
| nil != sK52_skl
| ~ ssList(sK52_skl)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f580,f386]) ).
fof(f600,plain,
( nil = sK47_skl
| nil != sK52_skl
| ~ ssList(sK52_skl)
| ~ ssList(sK47_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f591]) ).
fof(f601,plain,
( nil = sK47_skl
| nil != sK52_skl
| ~ ssList(sK52_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f600,f419]) ).
fof(f643,plain,
( nil = sK47_skl
| nil != sK52_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f601,f426]) ).
fof(f645,plain,
( nil != sK48_skl
| nil = sK47_skl ),
inference(resolution,[status(thm)],[f643,f525]) ).
fof(f646,plain,
nil = sK47_skl,
inference(forward_subsumption_resolution,[status(thm)],[f645,f475]) ).
fof(f659,plain,
( nil = sK52_skl
| nil != nil ),
inference(backward_demodulation,[status(thm)],[f646,f534]) ).
fof(f660,plain,
( nil = sK51_skl
| nil != nil ),
inference(backward_demodulation,[status(thm)],[f646,f524]) ).
fof(f662,plain,
( nil != sK48_skl
| sP0_prd(sK48_skl,nil) ),
inference(backward_demodulation,[status(thm)],[f646,f430]) ).
fof(f665,plain,
app(sK52_skl,sK51_skl) = nil,
inference(backward_demodulation,[status(thm)],[f646,f473]) ).
fof(f669,plain,
nil = sK52_skl,
inference(trivial_equality_resolution,[status(thm)],[f659]) ).
fof(f670,plain,
nil = sK51_skl,
inference(trivial_equality_resolution,[status(thm)],[f660]) ).
fof(f671,plain,
nil != sK48_skl,
inference(forward_subsumption_resolution,[status(thm)],[f662,f466]) ).
fof(f676,plain,
app(sK51_skl,nil) = sK48_skl,
inference(backward_demodulation,[status(thm)],[f669,f471]) ).
fof(f681,plain,
app(nil,sK51_skl) = nil,
inference(forward_demodulation,[status(thm)],[f669,f665]) ).
fof(f682,plain,
app(nil,nil) = nil,
inference(forward_demodulation,[status(thm)],[f670,f681]) ).
fof(f706,plain,
app(nil,nil) = sK48_skl,
inference(forward_demodulation,[status(thm)],[f670,f676]) ).
fof(f707,plain,
nil = sK48_skl,
inference(forward_demodulation,[status(thm)],[f682,f706]) ).
fof(f708,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f707,f671]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC030+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n015.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Mon Sep 21 07:53:27 UTC 2026
% 0.10/5.36 % CPUTime :
% 0.10/5.38 % Drodi V4.1.1
% 0.13/5.40 % Refutation found
% 0.13/5.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.42 % Elapsed time: 0.048748 seconds
% 0.13/5.42 % CPU time: 0.150359 seconds
% 0.13/5.42 % Total memory used: 28.831 MB
% 0.13/5.42 % Net memory used: 28.694 MB
%------------------------------------------------------------------------------