%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC018-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 02:39:36 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 34
% Syntax : Number of formulae : 107 ( 18 unt; 15 def)
% Number of atoms : 283 ( 48 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 342 ( 166 ~; 161 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 16 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 53 ( 53 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,axiom,
! [U] :
( frontsegP(U,nil)
| ~ 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(f83,axiom,
! [U] :
( frontsegP(nil,U)
| ~ ssList(U)
| nil != 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(f115,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f118,axiom,
! [U,V] :
( nil = U
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f129,axiom,
! [U,V] :
( V = U
| ~ ssList(V)
| ~ ssList(U)
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f188,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f189,negated_conjecture,
ssList(sk4),
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(f196,negated_conjecture,
( nil != sk3
| nil = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
! [A] :
( ~ frontsegP(sk1,A)
| ~ frontsegP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f199,negated_conjecture,
( neq(sk2,nil)
| nil != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f208,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f260,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f261,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f284,plain,
! [X0] :
( frontsegP(nil,X0)
| ~ ssList(X0)
| nil != X0 ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f286,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f303,plain,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f321,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ~ neq(U,V)
| U != V ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f322,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f321]) ).
fof(f327,plain,
! [U] :
( nil = U
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f118]) ).
fof(f328,plain,
! [X0,X1] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f327]) ).
fof(f342,plain,
! [X0,X1] :
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f360,plain,
! [U,W] :
( frontsegP(W,U)
| ~ ssList(W)
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| app(U,V) != W ) ),
inference(miniscoping,[status(thm)],[f144]) ).
fof(f361,plain,
! [X0,X1,X2] :
( frontsegP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != X2 ),
inference(cnf_transformation,[status(thm)],[f360]) ).
fof(f433,plain,
ssList(sk3),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f434,plain,
ssList(sk4),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f435,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f436,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f437,plain,
ssList(sk5),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f438,plain,
app(sk3,sk5) = sk4,
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f442,plain,
( nil != sk3
| nil = sk4 ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f444,plain,
! [X0] :
( ~ frontsegP(sk1,X0)
| ~ frontsegP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0)
| nil = sk2 ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f445,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f454,definition,
( sQ2_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f455,plain,
( ~ sQ2_spl
| nil = sk4 ),
inference(component_clause,[status(thm)],[f454]) ).
fof(f457,definition,
( sQ3_spl
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f460,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f442,f454,f457]) ).
fof(f461,definition,
( sQ4_spl
<=> nil = sk2 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f462,plain,
( ~ sQ4_spl
| nil = sk2 ),
inference(component_clause,[status(thm)],[f461]) ).
fof(f464,definition,
( sQ5_spl
<=> neq(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f465,plain,
( ~ sQ5_spl
| neq(sk2,nil) ),
inference(component_clause,[status(thm)],[f464]) ).
fof(f468,definition,
! [X0] :
( sQ6_spl
<=> ( ~ frontsegP(sk1,X0)
| ~ frontsegP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f469,plain,
! [X0] :
( ~ sQ6_spl
| ~ frontsegP(sk1,X0)
| ~ frontsegP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f468]) ).
fof(f471,plain,
( sQ6_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f444,f461,f468]) ).
fof(f472,definition,
( sQ7_spl
<=> nil = sk1 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f474,plain,
( sQ7_spl
| nil != sk1 ),
inference(component_clause,[status(thm)],[f472]) ).
fof(f475,plain,
( sQ5_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f445,f472,f464]) ).
fof(f479,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(destructive_equality_resolution,[status(thm)],[f284]) ).
fof(f484,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f322]) ).
fof(f485,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f484]) ).
fof(f492,plain,
! [X0,X1] :
( frontsegP(app(X1,X0),X1)
| ~ ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f361]) ).
fof(f508,plain,
( sQ7_spl
| nil != sk3 ),
inference(forward_demodulation,[status(thm)],[f436,f474]) ).
fof(f512,plain,
( ~ sQ4_spl
| nil = sk4 ),
inference(forward_demodulation,[status(thm)],[f435,f462]) ).
fof(f533,definition,
( sQ8_spl
<=> ssList(sk4) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f541,plain,
( ~ sQ5_spl
| neq(sk4,nil) ),
inference(forward_demodulation,[status(thm)],[f435,f465]) ).
fof(f542,plain,
! [X0] :
( ~ sQ6_spl
| ~ frontsegP(sk1,X0)
| ~ frontsegP(sk4,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f435,f469]) ).
fof(f543,plain,
! [X0] :
( ~ sQ6_spl
| ~ frontsegP(sk3,X0)
| ~ frontsegP(sk4,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f436,f542]) ).
fof(f544,definition,
( sQ10_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f546,plain,
( sQ10_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f544]) ).
fof(f547,definition,
( sQ11_spl
<=> frontsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f548,plain,
( ~ sQ11_spl
| frontsegP(nil,nil) ),
inference(component_clause,[status(thm)],[f547]) ).
fof(f550,plain,
( sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f479,f544,f547]) ).
fof(f557,plain,
( ssList(sk4)
| ~ ssList(sk3)
| ~ ssList(sk5) ),
inference(paramodulation,[status(thm)],[f438,f286]) ).
fof(f558,definition,
( sQ12_spl
<=> ssList(sk5) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f560,plain,
( sQ12_spl
| ~ ssList(sk5) ),
inference(component_clause,[status(thm)],[f558]) ).
fof(f561,definition,
( sQ13_spl
<=> ssList(sk3) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f563,plain,
( sQ13_spl
| ~ ssList(sk3) ),
inference(component_clause,[status(thm)],[f561]) ).
fof(f564,plain,
( sQ8_spl
| ~ sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f557,f558,f561,f533]) ).
fof(f565,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f563,f433]) ).
fof(f566,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f565]) ).
fof(f567,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f560,f437]) ).
fof(f568,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f567]) ).
fof(f570,plain,
( ~ sQ6_spl
| ~ ssList(sk3)
| ~ frontsegP(sk4,sk3)
| ~ neq(sk3,nil)
| ~ ssList(sk3) ),
inference(resolution,[status(thm)],[f543,f261]) ).
fof(f578,definition,
( sQ16_spl
<=> neq(sk3,nil) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f580,plain,
( sQ16_spl
| ~ neq(sk3,nil) ),
inference(component_clause,[status(thm)],[f578]) ).
fof(f581,definition,
( sQ17_spl
<=> frontsegP(sk4,sk3) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f584,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| ~ sQ16_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f570,f561,f578,f581,f468]) ).
fof(f585,plain,
( ~ sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f512,f454,f461]) ).
fof(f587,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| neq(sk4,sk4) ),
inference(backward_demodulation,[status(thm)],[f455,f541]) ).
fof(f604,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ ssList(sk4) ),
inference(resolution,[status(thm)],[f587,f485]) ).
fof(f605,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f604,f434]) ).
fof(f606,plain,
( ~ sQ5_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f605]) ).
fof(f614,plain,
( sQ16_spl
| sk3 = nil
| ~ ssList(sk3)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f303,f580]) ).
fof(f617,plain,
( sQ16_spl
| sQ3_spl
| ~ sQ13_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f614,f544,f561,f457,f578]) ).
fof(f618,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f546,f208]) ).
fof(f619,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f618]) ).
fof(f658,definition,
( sQ18_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f666,plain,
( nil = sk3
| ~ ssList(sk3)
| ~ ssList(sk5)
| sk4 != nil ),
inference(paramodulation,[status(thm)],[f438,f328]) ).
fof(f669,plain,
( sQ3_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f666,f454,f558,f561,f457]) ).
fof(f708,plain,
( ~ sQ11_spl
| nil = nil
| ~ ssList(nil)
| ~ ssList(nil)
| ~ frontsegP(nil,nil) ),
inference(resolution,[status(thm)],[f342,f548]) ).
fof(f709,plain,
! [X0] :
( ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(nil,X0) ),
inference(resolution,[status(thm)],[f342,f260]) ).
fof(f711,plain,
( sQ18_spl
| ~ sQ10_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f708,f547,f544,f658]) ).
fof(f712,definition,
! [X0] :
( sQ25_spl
<=> ( ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f715,plain,
( ~ sQ10_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f709,f712,f544]) ).
fof(f717,plain,
! [X0,X1] :
( frontsegP(app(X1,X0),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f492,f286]) ).
fof(f719,plain,
( frontsegP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(sk5) ),
inference(paramodulation,[status(thm)],[f438,f717]) ).
fof(f722,plain,
( sQ17_spl
| ~ sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f719,f558,f561,f581]) ).
fof(f723,plain,
( sQ7_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f508,f457,f472]) ).
fof(f724,plain,
$false,
inference(sat_refutation,[status(thm)],[f460,f471,f475,f550,f564,f566,f568,f584,f585,f606,f617,f619,f669,f711,f715,f722,f723]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC018-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 07:55:00 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.060927 seconds
% 0.13/0.43 % CPU time: 0.170622 seconds
% 0.13/0.43 % Total memory used: 105.644 MB
% 0.13/0.43 % Net memory used: 105.522 MB
%------------------------------------------------------------------------------