%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC068-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 02:39:50 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 22
% Syntax : Number of formulae : 67 ( 17 unt; 9 def)
% Number of atoms : 190 ( 43 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 243 ( 120 ~; 114 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 10 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 43 ( 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [U] :
( segmentP(U,U)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f73,axiom,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [U,V] :
( ssList(app(V,U))
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f100,axiom,
! [U,V] :
( V = U
| neq(V,U)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f145,axiom,
! [U,V] :
( app(U,V) = nil
| ~ ssList(U)
| ~ ssList(V)
| nil != V
| nil != U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f173,axiom,
! [U,V,W,X] :
( segmentP(X,V)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| app(app(U,V),W) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f187,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f190,negated_conjecture,
app(sk4,sk4) = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
! [A] :
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
( nil != sk1
| nil != sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f202,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f251,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f268,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f280,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f297,plain,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f356,plain,
! [X0,X1] :
( app(X0,X1) = nil
| ~ ssList(X0)
| ~ ssList(X1)
| nil != X1
| nil != X0 ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f400,plain,
! [V,X] :
( segmentP(X,V)
| ~ ssList(X)
| ~ ssList(V)
| ! [U] :
( ~ ssList(U)
| ! [W] :
( ~ ssList(W)
| app(app(U,V),W) != X ) ) ),
inference(miniscoping,[status(thm)],[f173]) ).
fof(f401,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| app(app(X0,X1),X2) != X3 ),
inference(cnf_transformation,[status(thm)],[f400]) ).
fof(f426,plain,
ssList(sk2),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f429,plain,
app(sk4,sk4) = sk3,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f430,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f431,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f432,plain,
! [X0] :
( ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f433,plain,
( nil != sk1
| nil != sk2 ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f441,definition,
( sQ2_spl
<=> nil = sk2 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f444,definition,
( sQ3_spl
<=> nil = sk1 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f447,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f433,f441,f444]) ).
fof(f458,plain,
app(sk4,sk2) = sk3,
inference(backward_demodulation,[status(thm)],[f430,f429]) ).
fof(f460,plain,
app(sk2,sk2) = sk3,
inference(forward_demodulation,[status(thm)],[f430,f458]) ).
fof(f465,definition,
( sQ4_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f467,plain,
( sQ4_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f465]) ).
fof(f473,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f467,f202]) ).
fof(f474,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f473]) ).
fof(f475,plain,
app(sk2,sk2) = sk1,
inference(forward_demodulation,[status(thm)],[f431,f460]) ).
fof(f476,plain,
( ssList(sk1)
| ~ ssList(sk2)
| ~ ssList(sk2) ),
inference(paramodulation,[status(thm)],[f475,f280]) ).
fof(f477,definition,
( sQ6_spl
<=> ssList(sk2) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f479,plain,
( sQ6_spl
| ~ ssList(sk2) ),
inference(component_clause,[status(thm)],[f477]) ).
fof(f480,definition,
( sQ7_spl
<=> ssList(sk1) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f483,plain,
( sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f476,f477,f480]) ).
fof(f484,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f479,f426]) ).
fof(f485,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f484]) ).
fof(f486,plain,
! [X0] :
( ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f297,f432]) ).
fof(f489,definition,
! [X0] :
( sQ8_spl
<=> ( ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ ssList(X0)
| X0 = nil
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f490,plain,
! [X0] :
( ~ sQ8_spl
| ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ ssList(X0)
| X0 = nil
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f489]) ).
fof(f492,plain,
( sQ8_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f486,f465,f489]) ).
fof(f493,plain,
! [X0] :
( ~ sQ8_spl
| ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| X0 = nil
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f490]) ).
fof(f511,plain,
( ~ sQ8_spl
| ~ ssList(sk2)
| ~ segmentP(sk1,sk2)
| sk2 = nil
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f493,f251]) ).
fof(f516,definition,
( sQ12_spl
<=> segmentP(sk1,sk2) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f519,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| sQ2_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f511,f477,f441,f516,f489]) ).
fof(f562,plain,
( sk1 = nil
| ~ ssList(sk2)
| ~ ssList(sk2)
| nil != sk2
| nil != sk2 ),
inference(paramodulation,[status(thm)],[f475,f356]) ).
fof(f563,definition,
! [X0] :
( sQ15_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0)
| nil != X0 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f564,plain,
! [X0] :
( ~ sQ15_spl
| ~ ssList(X0)
| ~ ssList(X0)
| nil != X0 ),
inference(component_clause,[status(thm)],[f563]) ).
fof(f571,plain,
( sQ3_spl
| ~ sQ6_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f562,f441,f477,f444]) ).
fof(f572,plain,
! [X0] :
( ~ sQ15_spl
| ~ ssList(X0)
| nil != X0 ),
inference(duplicate_literals_removal,[status(thm)],[f564]) ).
fof(f605,plain,
( ~ sQ15_spl
| nil != nil ),
inference(resolution,[status(thm)],[f572,f202]) ).
fof(f607,plain,
( ~ sQ15_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f605]) ).
fof(f608,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f607]) ).
fof(f781,plain,
! [X0,X1] :
( segmentP(X1,sk2)
| ~ ssList(X1)
| ~ ssList(sk2)
| ~ ssList(sk2)
| ~ ssList(X0)
| app(sk1,X0) != X1 ),
inference(paramodulation,[status(thm)],[f475,f401]) ).
fof(f793,definition,
! [X0,X1] :
( sQ44_spl
<=> ( segmentP(X1,sk2)
| ~ ssList(X1)
| ~ ssList(X0)
| app(sk1,X0) != X1 ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f794,plain,
! [X0,X1] :
( ~ sQ44_spl
| segmentP(X1,sk2)
| ~ ssList(X1)
| ~ ssList(X0)
| app(sk1,X0) != X1 ),
inference(component_clause,[status(thm)],[f793]) ).
fof(f796,plain,
( ~ sQ6_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f781,f793,f477]) ).
fof(f883,plain,
( ~ sQ44_spl
| ~ ssList(sk1)
| segmentP(sk1,sk2)
| ~ ssList(sk1)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f794,f268]) ).
fof(f897,plain,
( ~ sQ44_spl
| sQ12_spl
| ~ sQ7_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f883,f465,f480,f516,f793]) ).
fof(f903,plain,
$false,
inference(sat_refutation,[status(thm)],[f447,f474,f483,f485,f492,f519,f571,f608,f796,f897]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC068-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 07:52:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.45 % Elapsed time: 0.074494 seconds
% 0.13/0.45 % CPU time: 0.243697 seconds
% 0.13/0.45 % Total memory used: 110.714 MB
% 0.13/0.45 % Net memory used: 110.445 MB
%------------------------------------------------------------------------------