%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC182-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 02:40:18 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.44s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 24
% Syntax : Number of formulae : 86 ( 21 unt; 11 def)
% Number of atoms : 189 ( 34 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 193 ( 90 ~; 92 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 12 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f71,axiom,
! [U] :
( ~ ssItem(U)
| ~ memberP(nil,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(f85,axiom,
! [U,V] :
( ssList(app(V,U))
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f86,axiom,
! [U,V] :
( ssList(cons(U,V))
| ~ ssList(V)
| ~ ssItem(U) ),
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(f188,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f190,negated_conjecture,
nil = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( memberP(sk7,sk5)
| memberP(sk6,sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f268,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f272,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f283,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f284,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f324,plain,
! [U] :
( nil = U
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f118]) ).
fof(f325,plain,
! [X0,X1] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f324]) ).
fof(f430,plain,
ssList(sk3),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f432,plain,
nil = sk3,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f434,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f435,plain,
ssItem(sk5),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f436,plain,
ssList(sk6),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f437,plain,
ssList(sk7),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f438,plain,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f439,plain,
( memberP(sk7,sk5)
| memberP(sk6,sk5) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f447,definition,
( sQ2_spl
<=> memberP(sk6,sk5) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f448,plain,
( ~ sQ2_spl
| memberP(sk6,sk5) ),
inference(component_clause,[status(thm)],[f447]) ).
fof(f449,plain,
( sQ2_spl
| ~ memberP(sk6,sk5) ),
inference(component_clause,[status(thm)],[f447]) ).
fof(f450,definition,
( sQ3_spl
<=> memberP(sk7,sk5) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f451,plain,
( ~ sQ3_spl
| memberP(sk7,sk5) ),
inference(component_clause,[status(thm)],[f450]) ).
fof(f453,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f439,f447,f450]) ).
fof(f486,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(sk3,X0) ),
inference(forward_demodulation,[status(thm)],[f432,f268]) ).
fof(f488,plain,
! [X0] :
( app(sk3,X0) = X0
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f432,f272]) ).
fof(f497,plain,
app(app(sk6,cons(sk5,sk3)),sk7) = sk1,
inference(forward_demodulation,[status(thm)],[f432,f438]) ).
fof(f498,plain,
app(app(sk6,cons(sk5,sk3)),sk7) = sk3,
inference(forward_demodulation,[status(thm)],[f434,f497]) ).
fof(f500,definition,
( sQ4_spl
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f502,plain,
( sQ4_spl
| ~ ssList(sk7) ),
inference(component_clause,[status(thm)],[f500]) ).
fof(f503,definition,
( sQ5_spl
<=> ssList(app(sk6,cons(sk5,sk3))) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f505,plain,
( sQ5_spl
| ~ ssList(app(sk6,cons(sk5,sk3))) ),
inference(component_clause,[status(thm)],[f503]) ).
fof(f506,definition,
( sQ6_spl
<=> ssList(sk3) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f508,plain,
( sQ6_spl
| ~ ssList(sk3) ),
inference(component_clause,[status(thm)],[f506]) ).
fof(f515,plain,
! [X0,X1] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != sk3 ),
inference(forward_demodulation,[status(thm)],[f432,f325]) ).
fof(f516,plain,
! [X0,X1] :
( sk3 = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != sk3 ),
inference(forward_demodulation,[status(thm)],[f432,f515]) ).
fof(f517,plain,
( sk3 = app(sk6,cons(sk5,sk3))
| ~ ssList(app(sk6,cons(sk5,sk3)))
| ~ ssList(sk7) ),
inference(resolution,[status(thm)],[f516,f498]) ).
fof(f521,definition,
( sQ7_spl
<=> sk3 = app(sk6,cons(sk5,sk3)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f522,plain,
( ~ sQ7_spl
| sk3 = app(sk6,cons(sk5,sk3)) ),
inference(component_clause,[status(thm)],[f521]) ).
fof(f524,plain,
( sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f517,f500,f503,f521]) ).
fof(f531,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f502,f437]) ).
fof(f532,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f531]) ).
fof(f533,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f508,f430]) ).
fof(f534,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f533]) ).
fof(f535,plain,
( sQ5_spl
| ~ ssList(sk6)
| ~ ssList(cons(sk5,sk3)) ),
inference(resolution,[status(thm)],[f505,f283]) ).
fof(f536,definition,
( sQ9_spl
<=> ssList(cons(sk5,sk3)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f538,plain,
( sQ9_spl
| ~ ssList(cons(sk5,sk3)) ),
inference(component_clause,[status(thm)],[f536]) ).
fof(f539,definition,
( sQ10_spl
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f541,plain,
( sQ10_spl
| ~ ssList(sk6) ),
inference(component_clause,[status(thm)],[f539]) ).
fof(f542,plain,
( sQ5_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f535,f536,f539,f503]) ).
fof(f543,plain,
( sQ9_spl
| ~ ssList(sk3)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f538,f284]) ).
fof(f544,definition,
( sQ11_spl
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f546,plain,
( sQ11_spl
| ~ ssItem(sk5) ),
inference(component_clause,[status(thm)],[f544]) ).
fof(f547,plain,
( sQ9_spl
| ~ sQ6_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f543,f544,f506,f536]) ).
fof(f548,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f541,f436]) ).
fof(f549,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f548]) ).
fof(f550,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f546,f435]) ).
fof(f551,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f550]) ).
fof(f552,plain,
( ~ sQ7_spl
| app(sk3,sk7) = sk3 ),
inference(backward_demodulation,[status(thm)],[f522,f498]) ).
fof(f553,plain,
( ~ sQ7_spl
| sk3 = sk6
| ~ ssList(sk6)
| ~ ssList(cons(sk5,sk3)) ),
inference(resolution,[status(thm)],[f522,f516]) ).
fof(f556,definition,
( sQ12_spl
<=> sk3 = sk6 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f557,plain,
( ~ sQ12_spl
| sk3 = sk6 ),
inference(component_clause,[status(thm)],[f556]) ).
fof(f559,plain,
( ~ sQ7_spl
| sQ12_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f553,f536,f539,f556,f521]) ).
fof(f574,plain,
! [X0] :
( ~ sQ12_spl
| app(sk6,X0) = X0
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f557,f488]) ).
fof(f576,plain,
! [X0] :
( ~ sQ12_spl
| ~ ssItem(X0)
| ~ memberP(sk6,X0) ),
inference(backward_demodulation,[status(thm)],[f557,f486]) ).
fof(f585,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| app(sk6,sk7) = sk3 ),
inference(forward_demodulation,[status(thm)],[f557,f552]) ).
fof(f586,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| app(sk6,sk7) = sk6 ),
inference(forward_demodulation,[status(thm)],[f557,f585]) ).
fof(f589,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f576,f448]) ).
fof(f590,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f589,f544,f556,f447]) ).
fof(f599,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| sk6 = sk7
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f586,f574]) ).
fof(f601,definition,
( sQ14_spl
<=> sk6 = sk7 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f602,plain,
( ~ sQ14_spl
| sk6 = sk7 ),
inference(component_clause,[status(thm)],[f601]) ).
fof(f604,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| sQ14_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f599,f500,f601,f556,f521]) ).
fof(f607,plain,
( sQ2_spl
| ~ sQ14_spl
| ~ memberP(sk7,sk5) ),
inference(backward_demodulation,[status(thm)],[f602,f449]) ).
fof(f624,plain,
( sQ2_spl
| ~ sQ14_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f607,f451]) ).
fof(f625,plain,
( sQ2_spl
| ~ sQ14_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f624]) ).
fof(f626,plain,
$false,
inference(sat_refutation,[status(thm)],[f453,f524,f532,f534,f542,f547,f549,f551,f559,f590,f604,f625]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC182-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.38 % Computer : n015.cluster.edu
% 0.15/0.38 % Model : x86_64 x86_64
% 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38 % Memory : 8046.5625MB
% 0.15/0.38 % OS : Linux 6.8.0-71-generic
% 0.15/0.38 % CPULimit : 300
% 0.15/0.38 % WCLimit : 300
% 0.15/0.38 % DateTime : Mon Sep 21 08:05:51 UTC 2026
% 0.15/0.39 % CPUTime :
% 0.19/0.43 % Drodi V4.1.1
% 0.19/0.44 % Refutation found
% 0.19/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.51 % Elapsed time: 0.103357 seconds
% 0.19/0.51 % CPU time: 0.125897 seconds
% 0.19/0.51 % Total memory used: 13.688 MB
% 0.19/0.51 % Net memory used: 13.658 MB
%------------------------------------------------------------------------------