%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC101-1 : 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 02:39:58 PM UTC 2026
% Result : Unsatisfiable 0.07s 0.37s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 22
% Syntax : Number of formulae : 70 ( 16 unt; 10 def)
% Number of atoms : 150 ( 29 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 147 ( 67 ~; 70 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 11 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 21 ( 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [U,V] :
( ssList(app(V,U))
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f100,axiom,
! [U,V] :
( V = U
| neq(V,U)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f144,axiom,
! [U,V,W] :
( frontsegP(W,U)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != W ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f188,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f190,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
ssList(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
app(sk3,sk5) = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
( nil != sk3
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( nil != sk1
| nil != sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f206,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f284,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f301,plain,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f358,plain,
! [U,W] :
( frontsegP(W,U)
| ~ ssList(W)
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| app(U,V) != W ) ),
inference(miniscoping,[status(thm)],[f144]) ).
fof(f359,plain,
! [X0,X1,X2] :
( frontsegP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != X2 ),
inference(cnf_transformation,[status(thm)],[f358]) ).
fof(f431,plain,
ssList(sk3),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f433,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f434,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f435,plain,
ssList(sk5),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f436,plain,
app(sk3,sk5) = sk4,
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f440,plain,
( nil != sk3
| nil = sk4 ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f441,plain,
( nil != sk1
| nil != sk2 ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f442,plain,
( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f450,definition,
( sQ2_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f451,plain,
( ~ sQ2_spl
| nil = sk4 ),
inference(component_clause,[status(thm)],[f450]) ).
fof(f453,definition,
( sQ3_spl
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f456,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f440,f450,f453]) ).
fof(f457,definition,
( sQ4_spl
<=> nil = sk2 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f459,plain,
( sQ4_spl
| nil != sk2 ),
inference(component_clause,[status(thm)],[f457]) ).
fof(f460,definition,
( sQ5_spl
<=> nil = sk1 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f462,plain,
( sQ5_spl
| nil != sk1 ),
inference(component_clause,[status(thm)],[f460]) ).
fof(f463,plain,
( ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f441,f457,f460]) ).
fof(f464,definition,
( sQ6_spl
<=> neq(sk1,nil) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f466,plain,
( sQ6_spl
| ~ neq(sk1,nil) ),
inference(component_clause,[status(thm)],[f464]) ).
fof(f467,definition,
( sQ7_spl
<=> frontsegP(sk2,sk1) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f469,plain,
( sQ7_spl
| ~ frontsegP(sk2,sk1) ),
inference(component_clause,[status(thm)],[f467]) ).
fof(f470,plain,
( ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f442,f464,f467]) ).
fof(f486,plain,
! [X0,X1] :
( frontsegP(app(X1,X0),X1)
| ~ ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f359]) ).
fof(f502,plain,
( sQ4_spl
| nil != sk4 ),
inference(forward_demodulation,[status(thm)],[f433,f459]) ).
fof(f503,plain,
( ~ sQ2_spl
| sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f451,f502]) ).
fof(f504,plain,
( ~ sQ2_spl
| sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f503]) ).
fof(f505,plain,
( sQ5_spl
| nil != sk3 ),
inference(forward_demodulation,[status(thm)],[f434,f462]) ).
fof(f518,plain,
( sQ6_spl
| ~ neq(sk3,nil) ),
inference(forward_demodulation,[status(thm)],[f434,f466]) ).
fof(f540,definition,
( sQ10_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f542,plain,
( sQ10_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f540]) ).
fof(f547,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f542,f206]) ).
fof(f548,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f547]) ).
fof(f550,definition,
( sQ12_spl
<=> ssList(sk5) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f552,plain,
( sQ12_spl
| ~ ssList(sk5) ),
inference(component_clause,[status(thm)],[f550]) ).
fof(f553,definition,
( sQ13_spl
<=> ssList(sk3) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f555,plain,
( sQ13_spl
| ~ ssList(sk3) ),
inference(component_clause,[status(thm)],[f553]) ).
fof(f557,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f555,f431]) ).
fof(f558,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f557]) ).
fof(f559,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f552,f435]) ).
fof(f560,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f559]) ).
fof(f570,plain,
( sQ6_spl
| sk3 = nil
| ~ ssList(sk3)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f301,f518]) ).
fof(f573,plain,
( sQ6_spl
| sQ3_spl
| ~ sQ13_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f570,f540,f553,f453,f464]) ).
fof(f574,plain,
( sQ5_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f505,f453,f460]) ).
fof(f575,plain,
( sQ7_spl
| ~ frontsegP(sk4,sk1) ),
inference(forward_demodulation,[status(thm)],[f433,f469]) ).
fof(f576,plain,
( sQ7_spl
| ~ frontsegP(sk4,sk3) ),
inference(forward_demodulation,[status(thm)],[f434,f575]) ).
fof(f639,plain,
! [X0,X1] :
( frontsegP(app(X1,X0),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f486,f284]) ).
fof(f641,plain,
( frontsegP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(sk5) ),
inference(paramodulation,[status(thm)],[f436,f639]) ).
fof(f644,definition,
( sQ18_spl
<=> frontsegP(sk4,sk3) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f645,plain,
( ~ sQ18_spl
| frontsegP(sk4,sk3) ),
inference(component_clause,[status(thm)],[f644]) ).
fof(f647,plain,
( sQ18_spl
| ~ sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f641,f550,f553,f644]) ).
fof(f648,plain,
( ~ sQ18_spl
| sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f645,f576]) ).
fof(f649,plain,
( ~ sQ18_spl
| sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f648]) ).
fof(f650,plain,
$false,
inference(sat_refutation,[status(thm)],[f456,f463,f470,f504,f548,f558,f560,f573,f574,f647,f649]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC101-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n015.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 07:58:52 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.36 % Drodi V4.1.1
% 0.07/0.37 % Refutation found
% 0.07/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.07/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.056511 seconds
% 0.14/0.41 % CPU time: 0.101645 seconds
% 0.14/0.41 % Total memory used: 24.331 MB
% 0.14/0.41 % Net memory used: 24.302 MB
%------------------------------------------------------------------------------