%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC331-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 02:40:49 PM UTC 2026
% Result : Unsatisfiable 64.95s 8.66s
% Output : CNFRefutation 64.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 31
% Syntax : Number of formulae : 109 ( 46 unt; 16 def)
% Number of atoms : 192 ( 11 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 143 ( 60 ~; 67 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 17 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [U] : ssList(skaf77(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [U] :
( segmentP(U,U)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f59,axiom,
! [U] :
( rearsegP(U,U)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f61,axiom,
! [U] :
( frontsegP(U,U)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f74,axiom,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f172,axiom,
! [U,V,W,X] :
( segmentP(app(app(X,U),W),V)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X)
| ~ ssList(W)
| ~ segmentP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f186,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f187,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f190,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
ssList(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
app(sk3,sk5) = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
equalelemsP(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( ~ equalelemsP(sk1)
| ~ segmentP(sk2,sk1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f205,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f215,plain,
! [X0] : ssList(skaf77(X0)),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f254,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f256,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f258,plain,
! [X0] :
( ~ ssList(X0)
| frontsegP(X0,X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f272,plain,
! [X0] :
( ~ ssList(X0)
| X0 = app(nil,X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f402,plain,
! [X0,X1,X2,X3] :
( ~ ssList(X3)
| ~ ssList(X0)
| segmentP(app(app(X3,X0),X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f428,plain,
ssList(sk1),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f429,plain,
ssList(sk2),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f432,plain,
sk4 = sk2,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f433,plain,
sk3 = sk1,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f434,plain,
ssList(sk5),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f435,plain,
sk4 = app(sk3,sk5),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f436,plain,
equalelemsP(sk3),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f440,plain,
( ~ equalelemsP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f455,definition,
( sQ4_spl
<=> segmentP(sk2,sk1) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f458,definition,
( sQ5_spl
<=> equalelemsP(sk1) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f460,plain,
( sQ5_spl
| ~ equalelemsP(sk1) ),
inference(component_clause,[status(thm)],[f458]) ).
fof(f461,plain,
( ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f440,f455,f458]) ).
fof(f498,plain,
segmentP(nil,nil),
inference(resolution,[status(thm)],[f254,f205]) ).
fof(f508,plain,
equalelemsP(sk1),
inference(forward_demodulation,[status(thm)],[f433,f436]) ).
fof(f509,plain,
segmentP(sk1,sk1),
inference(resolution,[status(thm)],[f428,f254]) ).
fof(f511,plain,
sk1 = app(nil,sk1),
inference(resolution,[status(thm)],[f428,f272]) ).
fof(f571,definition,
( sQ12_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f573,plain,
( sQ12_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f571]) ).
fof(f577,plain,
app(sk1,sk5) = sk4,
inference(forward_demodulation,[status(thm)],[f433,f435]) ).
fof(f580,plain,
segmentP(sk2,sk2),
inference(resolution,[status(thm)],[f429,f254]) ).
fof(f600,plain,
app(sk1,sk5) = sk2,
inference(forward_demodulation,[status(thm)],[f432,f577]) ).
fof(f606,definition,
( sQ16_spl
<=> ssList(sk5) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f608,plain,
( sQ16_spl
| ~ ssList(sk5) ),
inference(component_clause,[status(thm)],[f606]) ).
fof(f617,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f608,f434]) ).
fof(f618,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f617]) ).
fof(f653,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X1)
| segmentP(app(app(X1,X0),X2),sk1)
| ~ segmentP(X0,sk1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f402,f428]) ).
fof(f736,definition,
( sQ25_spl
<=> ssList(sk1) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f738,plain,
( sQ25_spl
| ~ ssList(sk1) ),
inference(component_clause,[status(thm)],[f736]) ).
fof(f740,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f573,f205]) ).
fof(f741,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f740]) ).
fof(f749,plain,
( sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f738,f428]) ).
fof(f750,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f749]) ).
fof(f776,definition,
( sQ28_spl
<=> segmentP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f778,plain,
( sQ28_spl
| ~ segmentP(nil,nil) ),
inference(component_clause,[status(thm)],[f776]) ).
fof(f783,definition,
( sQ30_spl
<=> segmentP(sk2,sk2) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f785,plain,
( sQ30_spl
| ~ segmentP(sk2,sk2) ),
inference(component_clause,[status(thm)],[f783]) ).
fof(f791,definition,
( sQ32_spl
<=> segmentP(sk1,sk1) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f793,plain,
( sQ32_spl
| ~ segmentP(sk1,sk1) ),
inference(component_clause,[status(thm)],[f791]) ).
fof(f822,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f460,f508]) ).
fof(f823,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f822]) ).
fof(f915,definition,
! [X1] :
( sQ37_spl
<=> ~ ssList(X1) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f916,plain,
! [X0] :
( ~ sQ37_spl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f915]) ).
fof(f1617,definition,
( sQ57_spl
<=> rearsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f1619,plain,
( sQ57_spl
| ~ rearsegP(nil,nil) ),
inference(component_clause,[status(thm)],[f1617]) ).
fof(f1624,definition,
( sQ59_spl
<=> rearsegP(sk5,sk5) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f1626,plain,
( sQ59_spl
| ~ rearsegP(sk5,sk5) ),
inference(component_clause,[status(thm)],[f1624]) ).
fof(f1711,plain,
frontsegP(sk2,sk2),
inference(resolution,[status(thm)],[f258,f429]) ).
fof(f1712,plain,
frontsegP(sk5,sk5),
inference(resolution,[status(thm)],[f258,f434]) ).
fof(f1713,plain,
frontsegP(sk1,sk1),
inference(resolution,[status(thm)],[f258,f428]) ).
fof(f1714,plain,
frontsegP(nil,nil),
inference(resolution,[status(thm)],[f258,f205]) ).
fof(f1806,plain,
( sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f793,f509]) ).
fof(f1807,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f1806]) ).
fof(f1937,definition,
( sQ73_spl
<=> frontsegP(sk2,sk2) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1939,plain,
( sQ73_spl
| ~ frontsegP(sk2,sk2) ),
inference(component_clause,[status(thm)],[f1937]) ).
fof(f1944,definition,
( sQ75_spl
<=> frontsegP(sk5,sk5) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f1946,plain,
( sQ75_spl
| ~ frontsegP(sk5,sk5) ),
inference(component_clause,[status(thm)],[f1944]) ).
fof(f1951,definition,
( sQ77_spl
<=> frontsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1953,plain,
( sQ77_spl
| ~ frontsegP(nil,nil) ),
inference(component_clause,[status(thm)],[f1951]) ).
fof(f1958,definition,
( sQ79_spl
<=> frontsegP(sk1,sk1) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f1960,plain,
( sQ79_spl
| ~ frontsegP(sk1,sk1) ),
inference(component_clause,[status(thm)],[f1958]) ).
fof(f3368,plain,
rearsegP(sk5,sk5),
inference(resolution,[status(thm)],[f256,f434]) ).
fof(f3370,plain,
rearsegP(nil,nil),
inference(resolution,[status(thm)],[f256,f205]) ).
fof(f3371,plain,
( sQ59_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3368,f1626]) ).
fof(f3372,plain,
sQ59_spl,
inference(contradiction_clause,[status(thm)],[f3371]) ).
fof(f3895,definition,
! [X0] :
( sQ177_spl
<=> ( ~ ssList(X0)
| segmentP(app(sk1,X0),sk1) ) ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f3896,plain,
! [X0] :
( ~ sQ177_spl
| segmentP(app(sk1,X0),sk1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3895]) ).
fof(f4079,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(app(sk1,X0),sk1)
| ~ ssList(sk1)
| ~ segmentP(sk1,sk1)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f511,f653]) ).
fof(f4102,plain,
( sQ177_spl
| ~ sQ25_spl
| ~ sQ32_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f4079,f571,f791,f736,f3895]) ).
fof(f4923,plain,
( sQ77_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1953,f1714]) ).
fof(f4924,plain,
sQ77_spl,
inference(contradiction_clause,[status(thm)],[f4923]) ).
fof(f4925,plain,
( sQ73_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1939,f1711]) ).
fof(f4926,plain,
sQ73_spl,
inference(contradiction_clause,[status(thm)],[f4925]) ).
fof(f4927,plain,
( sQ79_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1960,f1713]) ).
fof(f4928,plain,
sQ79_spl,
inference(contradiction_clause,[status(thm)],[f4927]) ).
fof(f4929,plain,
( sQ75_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1946,f1712]) ).
fof(f4930,plain,
sQ75_spl,
inference(contradiction_clause,[status(thm)],[f4929]) ).
fof(f5189,plain,
( sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f778,f498]) ).
fof(f5190,plain,
sQ28_spl,
inference(contradiction_clause,[status(thm)],[f5189]) ).
fof(f5191,plain,
( sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f785,f580]) ).
fof(f5192,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f5191]) ).
fof(f7035,plain,
( sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1619,f3370]) ).
fof(f7036,plain,
sQ57_spl,
inference(contradiction_clause,[status(thm)],[f7035]) ).
fof(f7056,plain,
( ~ sQ37_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f215,f916]) ).
fof(f7074,plain,
~ sQ37_spl,
inference(contradiction_clause,[status(thm)],[f7056]) ).
fof(f14477,plain,
( ~ sQ177_spl
| segmentP(sk2,sk1)
| ~ ssList(sk5) ),
inference(paramodulation,[status(thm)],[f600,f3896]) ).
fof(f14479,plain,
( ~ sQ177_spl
| sQ4_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f14477,f606,f455,f3895]) ).
fof(f14481,plain,
$false,
inference(sat_refutation,[status(thm)],[f461,f618,f741,f750,f823,f1807,f3372,f4102,f4924,f4926,f4928,f4930,f5190,f5192,f7036,f7074,f14479]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC331-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 08:16:41 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 64.95/8.66 % Refutation found
% 64.95/8.66 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 64.95/8.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.24/8.72 % Elapsed time: 8.324191 seconds
% 4.24/8.72 % CPU time: 65.675508 seconds
% 4.24/8.72 % Total memory used: 486.090 MB
% 4.24/8.72 % Net memory used: 449.931 MB
%------------------------------------------------------------------------------