%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC364-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 02:40:57 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.58s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 23
% Syntax : Number of formulae : 70 ( 13 unt; 11 def)
% Number of atoms : 173 ( 22 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 198 ( 95 ~; 92 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 12 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 31 ( 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f73,axiom,
! [U] :
( app(U,nil) = 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(f173,axiom,
! [U,V,W,X] :
( segmentP(X,V)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| app(app(U,V),W) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f186,negated_conjecture,
ssList(sk1),
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,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk3) = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f199,negated_conjecture,
( ~ neq(sk4,nil)
| ~ segmentP(sk2,sk1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f207,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f273,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f285,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f286,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f405,plain,
! [V,X] :
( segmentP(X,V)
| ~ ssList(X)
| ~ ssList(V)
| ! [U] :
( ~ ssList(U)
| ! [W] :
( ~ ssList(W)
| app(app(U,V),W) != X ) ) ),
inference(miniscoping,[status(thm)],[f173]) ).
fof(f406,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| app(app(X0,X1),X2) != X3 ),
inference(cnf_transformation,[status(thm)],[f405]) ).
fof(f430,plain,
ssList(sk1),
inference(cnf_transformation,[status(thm)],[f186]) ).
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,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f441,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f442,plain,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk3) = sk4 ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f443,plain,
( ~ neq(sk4,nil)
| ~ segmentP(sk2,sk1) ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f451,definition,
( sQ2_spl
<=> neq(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f452,plain,
( ~ sQ2_spl
| neq(sk2,nil) ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f454,plain,
sQ2_spl,
inference(split_clause,[status(thm)],[f436,f451]) ).
fof(f455,definition,
( sQ3_spl
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( sQ3_spl
| ~ neq(sk4,nil) ),
inference(component_clause,[status(thm)],[f455]) ).
fof(f459,definition,
( sQ4_spl
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f463,definition,
( sQ5_spl
<=> app(cons(sk5,nil),sk3) = sk4 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f464,plain,
( ~ sQ5_spl
| app(cons(sk5,nil),sk3) = sk4 ),
inference(component_clause,[status(thm)],[f463]) ).
fof(f467,definition,
( sQ6_spl
<=> segmentP(sk2,sk1) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f471,plain,
( ~ sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f441,f459,f455]) ).
fof(f472,plain,
( ~ sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f442,f463,f455]) ).
fof(f473,plain,
( ~ sQ3_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f443,f467,f455]) ).
fof(f486,plain,
( sQ3_spl
| ~ neq(sk2,nil) ),
inference(forward_demodulation,[status(thm)],[f434,f457]) ).
fof(f487,plain,
( sQ3_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f486,f452]) ).
fof(f488,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f487]) ).
fof(f489,plain,
( ~ sQ5_spl
| app(cons(sk5,nil),sk1) = sk4 ),
inference(forward_demodulation,[status(thm)],[f435,f464]) ).
fof(f490,plain,
( ~ sQ5_spl
| app(cons(sk5,nil),sk1) = sk2 ),
inference(forward_demodulation,[status(thm)],[f434,f489]) ).
fof(f495,definition,
( sQ7_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f497,plain,
( sQ7_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f495]) ).
fof(f503,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f497,f207]) ).
fof(f504,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f503]) ).
fof(f505,plain,
( ~ sQ5_spl
| ssList(sk2)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk1) ),
inference(paramodulation,[status(thm)],[f490,f285]) ).
fof(f506,definition,
( sQ9_spl
<=> ssList(sk1) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f508,plain,
( sQ9_spl
| ~ ssList(sk1) ),
inference(component_clause,[status(thm)],[f506]) ).
fof(f509,definition,
( sQ10_spl
<=> ssList(cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f511,plain,
( sQ10_spl
| ~ ssList(cons(sk5,nil)) ),
inference(component_clause,[status(thm)],[f509]) ).
fof(f512,definition,
( sQ11_spl
<=> ssList(sk2) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f515,plain,
( ~ sQ5_spl
| sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f505,f506,f509,f512,f463]) ).
fof(f532,plain,
( sQ10_spl
| ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f511,f286]) ).
fof(f533,plain,
( sQ10_spl
| ~ sQ7_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f532,f459,f495,f509]) ).
fof(f534,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f508,f430]) ).
fof(f535,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f534]) ).
fof(f574,definition,
! [X0] :
( sQ19_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0)
| nil != X0 ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f575,plain,
! [X0] :
( ~ sQ19_spl
| ~ ssList(X0)
| ~ ssList(X0)
| nil != X0 ),
inference(component_clause,[status(thm)],[f574]) ).
fof(f583,plain,
! [X0] :
( ~ sQ19_spl
| ~ ssList(X0)
| nil != X0 ),
inference(duplicate_literals_removal,[status(thm)],[f575]) ).
fof(f610,plain,
( ~ sQ19_spl
| nil != nil ),
inference(resolution,[status(thm)],[f583,f207]) ).
fof(f613,plain,
( ~ sQ19_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f610]) ).
fof(f614,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f613]) ).
fof(f817,plain,
! [X0,X1] :
( ~ sQ5_spl
| segmentP(X1,sk1)
| ~ ssList(X1)
| ~ ssList(sk1)
| ~ ssList(cons(sk5,nil))
| ~ ssList(X0)
| app(sk2,X0) != X1 ),
inference(paramodulation,[status(thm)],[f490,f406]) ).
fof(f825,definition,
! [X0,X1] :
( sQ51_spl
<=> ( segmentP(X1,sk1)
| ~ ssList(X1)
| ~ ssList(X0)
| app(sk2,X0) != X1 ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f826,plain,
! [X0,X1] :
( ~ sQ51_spl
| segmentP(X1,sk1)
| ~ ssList(X1)
| ~ ssList(X0)
| app(sk2,X0) != X1 ),
inference(component_clause,[status(thm)],[f825]) ).
fof(f828,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f817,f825,f509,f506,f463]) ).
fof(f907,plain,
( ~ sQ51_spl
| ~ ssList(sk2)
| segmentP(sk2,sk1)
| ~ ssList(sk2)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f826,f273]) ).
fof(f915,plain,
( ~ sQ51_spl
| sQ6_spl
| ~ sQ11_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f907,f495,f512,f467,f825]) ).
fof(f922,plain,
$false,
inference(sat_refutation,[status(thm)],[f454,f471,f472,f473,f488,f504,f515,f533,f535,f614,f828,f915]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC364-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.51 % Computer : n009.cluster.edu
% 0.08/0.51 % Model : x86_64 x86_64
% 0.08/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.51 % Memory : 8046.5625MB
% 0.08/0.51 % OS : Linux 6.8.0-71-generic
% 0.08/0.51 % CPULimit : 300
% 0.08/0.51 % WCLimit : 300
% 0.08/0.51 % DateTime : Mon Sep 21 08:18:58 UTC 2026
% 0.08/0.51 % CPUTime :
% 0.08/0.53 % Drodi V4.1.1
% 0.08/0.58 % Refutation found
% 0.08/0.58 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.61 % Elapsed time: 0.088873 seconds
% 0.08/0.61 % CPU time: 0.380489 seconds
% 0.08/0.61 % Total memory used: 115.007 MB
% 0.08/0.61 % Net memory used: 114.563 MB
%------------------------------------------------------------------------------