%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC198-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 02:40:21 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.41s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 60 ( 8 unt; 6 def)
% Number of atoms : 154 ( 34 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 173 ( 79 ~; 88 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 28 ( 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
ssItem(skac3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f71,axiom,
! [U] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f161,axiom,
! [U,V,W] :
( W = U
| memberP(V,W)
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(V)
| ~ memberP(cons(U,V),W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
! [A] :
( ssItem(sk5(A))
| ~ ssItem(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
! [A] :
( memberP(sk1,sk5(A))
| ~ ssItem(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
! [A] :
( A != sk5(A)
| ~ ssItem(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
( nil = sk4
| ssItem(sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
( nil = sk3
| ssItem(sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( nil = sk4
| cons(sk6,nil) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f200,negated_conjecture,
( nil = sk3
| cons(sk6,nil) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f210,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f211,plain,
ssItem(skac3),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f273,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f393,plain,
! [U,W] :
( W = U
| ! [V] :
( memberP(V,W)
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(V)
| ~ memberP(cons(U,V),W) ) ),
inference(miniscoping,[status(thm)],[f161]) ).
fof(f394,plain,
! [X0,X1,X2] :
( X2 = X0
| memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ memberP(cons(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f393]) ).
fof(f438,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f439,plain,
! [X0] :
( ssItem(sk5(X0))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f440,plain,
! [X0] :
( memberP(sk1,sk5(X0))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f441,plain,
! [X0] :
( X0 != sk5(X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f442,plain,
( nil = sk4
| ssItem(sk6) ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f443,plain,
( nil = sk3
| ssItem(sk6) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f444,plain,
( nil = sk4
| cons(sk6,nil) = sk3 ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f448,plain,
( nil = sk3
| cons(sk6,nil) = sk3 ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f459,definition,
( sQ2_spl
<=> ssItem(sk6) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f462,definition,
( sQ3_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f463,plain,
( ~ sQ3_spl
| nil = sk4 ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f465,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f442,f459,f462]) ).
fof(f466,definition,
( sQ4_spl
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f467,plain,
( ~ sQ4_spl
| nil = sk3 ),
inference(component_clause,[status(thm)],[f466]) ).
fof(f469,plain,
( sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f443,f459,f466]) ).
fof(f470,definition,
( sQ5_spl
<=> cons(sk6,nil) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f471,plain,
( ~ sQ5_spl
| cons(sk6,nil) = sk3 ),
inference(component_clause,[status(thm)],[f470]) ).
fof(f473,plain,
( sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f444,f470,f462]) ).
fof(f482,plain,
( sQ4_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f448,f470,f466]) ).
fof(f517,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| nil = sk4 ),
inference(backward_demodulation,[status(thm)],[f520,f467]) ).
fof(f518,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk1 = sk4 ),
inference(backward_demodulation,[status(thm)],[f520,f438]) ).
fof(f520,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk3 = sk4 ),
inference(forward_demodulation,[status(thm)],[f467,f463]) ).
fof(f521,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ ssItem(X0)
| ~ memberP(sk4,X0) ),
inference(forward_demodulation,[status(thm)],[f517,f273]) ).
fof(f522,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| memberP(sk4,sk5(X0))
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f518,f440]) ).
fof(f523,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ ssItem(sk5(X0))
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f522,f521]) ).
fof(f524,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f523,f439]) ).
fof(f533,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f211,f524]) ).
fof(f534,plain,
( ~ sQ4_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f533]) ).
fof(f535,plain,
! [X0] :
( memberP(sk3,sk5(X0))
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f438,f440]) ).
fof(f537,definition,
( sQ8_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f539,plain,
( sQ8_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f537]) ).
fof(f569,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f210,f539]) ).
fof(f570,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f569]) ).
fof(f588,plain,
! [X0] :
( ~ sQ5_spl
| X0 = sk6
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssItem(sk6)
| ~ ssList(nil)
| ~ memberP(sk3,X0) ),
inference(paramodulation,[status(thm)],[f471,f394]) ).
fof(f589,definition,
! [X0] :
( sQ13_spl
<=> ( X0 = sk6
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f590,plain,
! [X0] :
( ~ sQ13_spl
| X0 = sk6
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ),
inference(component_clause,[status(thm)],[f589]) ).
fof(f592,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ8_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f588,f589,f537,f459,f470]) ).
fof(f593,plain,
! [X0] :
( ~ sQ13_spl
| X0 = sk6
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f590,f273]) ).
fof(f595,plain,
! [X0] :
( ~ sQ13_spl
| ~ ssItem(X0)
| sk5(X0) = sk6
| ~ ssItem(sk5(X0)) ),
inference(resolution,[status(thm)],[f593,f535]) ).
fof(f597,plain,
! [X0] :
( ~ sQ13_spl
| ~ ssItem(X0)
| sk5(X0) = sk6 ),
inference(forward_subsumption_resolution,[status(thm)],[f595,f439]) ).
fof(f598,plain,
( ~ sQ13_spl
| ~ ssItem(sk6)
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f597,f441]) ).
fof(f599,plain,
( ~ sQ13_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f598,f459,f589]) ).
fof(f600,plain,
$false,
inference(sat_refutation,[status(thm)],[f465,f469,f473,f482,f534,f570,f592,f599]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC198-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 08:04:12 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 0.15/0.41 % Refutation found
% 0.15/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.44 % Elapsed time: 0.062432 seconds
% 0.15/0.44 % CPU time: 0.169999 seconds
% 0.15/0.44 % Total memory used: 109.420 MB
% 0.15/0.44 % Net memory used: 109.290 MB
%------------------------------------------------------------------------------