%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC229-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 02:40:27 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.80s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 29
% Syntax : Number of formulae : 95 ( 27 unt; 12 def)
% Number of atoms : 227 ( 47 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 263 ( 131 ~; 120 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 13 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 46 ( 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [U] : ssItem(skaf44(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71,axiom,
! [U] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f73,axiom,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f74,axiom,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f80,axiom,
! [U] :
( nil = U
| ~ ssList(U)
| ~ segmentP(nil,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(f101,axiom,
! [U] :
( cons(skaf44(U),nil) = U
| ~ ssList(U)
| ~ singletonP(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f186,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f187,negated_conjecture,
ssList(sk2),
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,
segmentP(sk4,sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
nil != sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
! [A,B,C] :
( ssItem(sk5(C,B,A))
| app(app(B,cons(A,nil)),C) != sk1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
! [A,B,C] :
( memberP(B,sk5(C,B,A))
| app(app(B,cons(A,nil)),C) != sk1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f199,negated_conjecture,
( ~ neq(sk4,nil)
| singletonP(sk3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f207,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f246,plain,
! [X0] : ssItem(skaf44(X0)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f270,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f273,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f274,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f280,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f302,plain,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f303,plain,
! [X0] :
( cons(skaf44(X0),nil) = X0
| ~ ssList(X0)
| ~ singletonP(X0) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f430,plain,
ssList(sk1),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f431,plain,
ssList(sk2),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f434,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f435,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f436,plain,
segmentP(sk4,sk3),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f437,plain,
nil != sk1,
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f438,plain,
! [X0,X1,X2] :
( ssItem(sk5(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sk1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f439,plain,
! [X0,X1,X2] :
( memberP(X1,sk5(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sk1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f443,plain,
( ~ neq(sk4,nil)
| singletonP(sk3) ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f451,definition,
( sQ2_spl
<=> singletonP(sk3) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f452,plain,
( ~ sQ2_spl
| singletonP(sk3) ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f454,definition,
( sQ3_spl
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f456,plain,
( sQ3_spl
| ~ neq(sk4,nil) ),
inference(component_clause,[status(thm)],[f454]) ).
fof(f457,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f443,f451,f454]) ).
fof(f489,plain,
( ~ sQ2_spl
| singletonP(sk1) ),
inference(forward_demodulation,[status(thm)],[f435,f452]) ).
fof(f490,plain,
segmentP(sk2,sk3),
inference(forward_demodulation,[status(thm)],[f434,f436]) ).
fof(f491,plain,
segmentP(sk2,sk1),
inference(forward_demodulation,[status(thm)],[f435,f490]) ).
fof(f493,plain,
! [X0,X1] :
( app(app(nil,cons(X1,nil)),X0) != sk1
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssItem(X1)
| ~ ssItem(sk5(X0,nil,X1)) ),
inference(resolution,[status(thm)],[f270,f439]) ).
fof(f497,definition,
( sQ5_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f499,plain,
( sQ5_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f497]) ).
fof(f501,definition,
! [X0,X1] :
( sQ6_spl
<=> ( app(app(nil,cons(X1,nil)),X0) != sk1
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sk5(X0,nil,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f502,plain,
! [X0,X1] :
( ~ sQ6_spl
| app(app(nil,cons(X1,nil)),X0) != sk1
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sk5(X0,nil,X1)) ),
inference(component_clause,[status(thm)],[f501]) ).
fof(f504,plain,
( ~ sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f493,f501,f497]) ).
fof(f505,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f499,f207]) ).
fof(f506,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f505]) ).
fof(f511,plain,
app(sk1,nil) = sk1,
inference(resolution,[status(thm)],[f273,f430]) ).
fof(f516,plain,
app(nil,sk1) = sk1,
inference(resolution,[status(thm)],[f274,f430]) ).
fof(f558,definition,
( sQ10_spl
<=> ssList(sk1) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f560,plain,
( sQ10_spl
| ~ ssList(sk1) ),
inference(component_clause,[status(thm)],[f558]) ).
fof(f562,definition,
( sQ11_spl
<=> ssList(sk2) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f564,plain,
( sQ11_spl
| ~ ssList(sk2) ),
inference(component_clause,[status(thm)],[f562]) ).
fof(f595,plain,
! [X0,X1] :
( ~ sQ6_spl
| app(app(nil,cons(X0,nil)),X1) != sk1
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssItem(X0)
| app(app(nil,cons(X0,nil)),X1) != sk1
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f502,f438]) ).
fof(f596,definition,
! [X0,X1] :
( sQ14_spl
<=> ( app(app(nil,cons(X0,nil)),X1) != sk1
| ~ ssList(X1)
| ~ ssItem(X0)
| app(app(nil,cons(X0,nil)),X1) != sk1
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f597,plain,
! [X0,X1] :
( ~ sQ14_spl
| app(app(nil,cons(X0,nil)),X1) != sk1
| ~ ssList(X1)
| ~ ssItem(X0)
| app(app(nil,cons(X0,nil)),X1) != sk1
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f596]) ).
fof(f599,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f595,f596,f497,f501]) ).
fof(f600,plain,
! [X0,X1] :
( ~ sQ14_spl
| app(app(nil,cons(X0,nil)),X1) != sk1
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f597]) ).
fof(f845,definition,
( sQ23_spl
<=> nil = sk2 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f846,plain,
( ~ sQ23_spl
| nil = sk2 ),
inference(component_clause,[status(thm)],[f845]) ).
fof(f852,definition,
( sQ25_spl
<=> nil = sk1 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f853,plain,
( ~ sQ25_spl
| nil = sk1 ),
inference(component_clause,[status(thm)],[f852]) ).
fof(f944,plain,
( ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f853,f437]) ).
fof(f945,plain,
~ sQ25_spl,
inference(contradiction_clause,[status(thm)],[f944]) ).
fof(f951,plain,
( ~ sQ23_spl
| segmentP(nil,sk1) ),
inference(backward_demodulation,[status(thm)],[f846,f491]) ).
fof(f958,plain,
( ~ sQ23_spl
| nil = sk1
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f951,f280]) ).
fof(f959,plain,
( ~ sQ23_spl
| sQ25_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f958,f558,f852,f845]) ).
fof(f960,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f560,f430]) ).
fof(f961,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f960]) ).
fof(f1015,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f431,f564]) ).
fof(f1016,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f1015]) ).
fof(f1352,plain,
( ~ sQ2_spl
| cons(skaf44(sk1),nil) = sk1
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f303,f489]) ).
fof(f1354,definition,
( sQ37_spl
<=> cons(skaf44(sk1),nil) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f1355,plain,
( ~ sQ37_spl
| cons(skaf44(sk1),nil) = sk1 ),
inference(component_clause,[status(thm)],[f1354]) ).
fof(f1357,plain,
( ~ sQ2_spl
| sQ37_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f1352,f558,f1354,f451]) ).
fof(f1358,plain,
( sQ3_spl
| ~ neq(sk2,nil) ),
inference(forward_demodulation,[status(thm)],[f434,f456]) ).
fof(f1360,plain,
( sQ3_spl
| sk2 = nil
| ~ ssList(sk2)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1358,f302]) ).
fof(f1368,plain,
( sQ3_spl
| sQ23_spl
| ~ sQ11_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1360,f497,f562,f845,f454]) ).
fof(f2629,plain,
! [X0] :
( ~ sQ37_spl
| ~ sQ14_spl
| app(app(nil,sk1),X0) != sk1
| ~ ssList(X0)
| ~ ssItem(skaf44(sk1)) ),
inference(paramodulation,[status(thm)],[f1355,f600]) ).
fof(f2637,definition,
( sQ78_spl
<=> ssItem(skaf44(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f2639,plain,
( sQ78_spl
| ~ ssItem(skaf44(sk1)) ),
inference(component_clause,[status(thm)],[f2637]) ).
fof(f2683,definition,
! [X0] :
( sQ90_spl
<=> ( app(app(nil,sk1),X0) != sk1
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f2684,plain,
! [X0] :
( ~ sQ90_spl
| app(app(nil,sk1),X0) != sk1
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2683]) ).
fof(f2686,plain,
( ~ sQ37_spl
| ~ sQ14_spl
| sQ90_spl
| ~ sQ78_spl ),
inference(split_clause,[status(thm)],[f2629,f2637,f2683,f596,f1354]) ).
fof(f2712,plain,
( sQ78_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2639,f246]) ).
fof(f2713,plain,
sQ78_spl,
inference(contradiction_clause,[status(thm)],[f2712]) ).
fof(f2715,plain,
! [X0] :
( ~ sQ90_spl
| app(sk1,X0) != sk1
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f516,f2684]) ).
fof(f3330,plain,
( ~ sQ90_spl
| app(sk1,nil) != sk1 ),
inference(resolution,[status(thm)],[f2715,f207]) ).
fof(f3332,plain,
( ~ sQ90_spl
| sk1 != sk1 ),
inference(forward_demodulation,[status(thm)],[f511,f3330]) ).
fof(f3333,plain,
( ~ sQ90_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3332]) ).
fof(f3334,plain,
~ sQ90_spl,
inference(contradiction_clause,[status(thm)],[f3333]) ).
fof(f3335,plain,
$false,
inference(sat_refutation,[status(thm)],[f457,f504,f506,f599,f945,f959,f961,f1016,f1357,f1368,f2686,f2713,f3334]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC229-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n017.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
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 08:01:57 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.19/0.80 % Refutation found
% 0.19/0.80 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/0.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.83 % Elapsed time: 0.453283 seconds
% 0.19/0.83 % CPU time: 3.256234 seconds
% 0.19/0.83 % Total memory used: 145.212 MB
% 0.19/0.83 % Net memory used: 142.914 MB
%------------------------------------------------------------------------------