%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC242-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 02:40:30 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.47s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 20
% Syntax : Number of formulae : 56 ( 10 unt; 9 def)
% Number of atoms : 155 ( 28 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 185 ( 86 ~; 90 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 10 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 31 ( 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f103,axiom,
! [U,V] :
( leq(U,V)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
nil != sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f193,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/sandbox/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
! [A,B,C] :
( lt(A,sk5(C,B,A))
| app(app(B,cons(A,nil)),C) != sk1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
! [A,B,C] :
( ~ leq(A,sk5(C,B,A))
| app(app(B,cons(A,nil)),C) != sk1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
( ssItem(sk6)
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f199,negated_conjecture,
( ssList(sk7)
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f200,negated_conjecture,
( ssList(sk8)
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f201,negated_conjecture,
( app(app(sk7,cons(sk6,nil)),sk8) = sk3
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f210,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f308,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f438,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f439,plain,
nil != sk1,
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f440,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)],[f193]) ).
fof(f443,plain,
! [X0,X1,X2] :
( lt(X0,sk5(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sk1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f444,plain,
! [X0,X1,X2] :
( ~ leq(X0,sk5(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sk1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f445,plain,
( ssItem(sk6)
| nil = sk3 ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f446,plain,
( ssList(sk7)
| nil = sk3 ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f447,plain,
( ssList(sk8)
| nil = sk3 ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f448,plain,
( app(app(sk7,cons(sk6,nil)),sk8) = sk3
| nil = sk3 ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f457,definition,
( sQ2_spl
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f458,plain,
( ~ sQ2_spl
| nil = sk3 ),
inference(component_clause,[status(thm)],[f457]) ).
fof(f460,definition,
( sQ3_spl
<=> ssItem(sk6) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f463,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f445,f457,f460]) ).
fof(f464,definition,
( sQ4_spl
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f467,plain,
( sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f446,f457,f464]) ).
fof(f468,definition,
( sQ5_spl
<=> ssList(sk8) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f471,plain,
( sQ5_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f447,f457,f468]) ).
fof(f472,definition,
( sQ6_spl
<=> app(app(sk7,cons(sk6,nil)),sk8) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f473,plain,
( ~ sQ6_spl
| app(app(sk7,cons(sk6,nil)),sk8) = sk3 ),
inference(component_clause,[status(thm)],[f472]) ).
fof(f475,plain,
( sQ6_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f448,f457,f472]) ).
fof(f511,plain,
nil != sk3,
inference(forward_demodulation,[status(thm)],[f438,f439]) ).
fof(f512,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f458,f511]) ).
fof(f513,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f512]) ).
fof(f514,plain,
! [X0,X1,X2] :
( ssItem(sk5(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sk3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f438,f440]) ).
fof(f515,plain,
( ~ sQ6_spl
| ssItem(sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f514,f473]) ).
fof(f517,definition,
( sQ8_spl
<=> ssItem(sk5(sk8,sk7,sk6)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f520,plain,
( ~ sQ6_spl
| sQ8_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f515,f460,f464,f468,f517,f472]) ).
fof(f555,definition,
( sQ15_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f557,plain,
( sQ15_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f555]) ).
fof(f559,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f557,f210]) ).
fof(f560,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f559]) ).
fof(f561,plain,
! [X0,X1,X2] :
( lt(X0,sk5(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sk3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f438,f443]) ).
fof(f562,plain,
( ~ sQ6_spl
| lt(sk6,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f561,f473]) ).
fof(f564,definition,
( sQ16_spl
<=> lt(sk6,sk5(sk8,sk7,sk6)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f565,plain,
( ~ sQ16_spl
| lt(sk6,sk5(sk8,sk7,sk6)) ),
inference(component_clause,[status(thm)],[f564]) ).
fof(f567,plain,
( ~ sQ6_spl
| sQ16_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f562,f460,f464,f468,f564,f472]) ).
fof(f571,plain,
( ~ sQ16_spl
| leq(sk6,sk5(sk8,sk7,sk6))
| ~ ssItem(sk6)
| ~ ssItem(sk5(sk8,sk7,sk6)) ),
inference(resolution,[status(thm)],[f565,f308]) ).
fof(f572,definition,
( sQ17_spl
<=> leq(sk6,sk5(sk8,sk7,sk6)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f580,plain,
( ~ sQ16_spl
| sQ17_spl
| ~ sQ3_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f571,f517,f460,f572,f564]) ).
fof(f581,plain,
! [X0,X1,X2] :
( ~ leq(X0,sk5(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sk3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f438,f444]) ).
fof(f582,plain,
( ~ sQ6_spl
| ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f581,f473]) ).
fof(f584,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f582,f460,f464,f468,f572,f472]) ).
fof(f586,plain,
$false,
inference(sat_refutation,[status(thm)],[f463,f467,f471,f475,f513,f520,f560,f567,f580,f584]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC242-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n016.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Mon Sep 21 08:12:37 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.46 % Drodi V4.1.1
% 0.15/0.47 % Refutation found
% 0.15/0.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.53 % Elapsed time: 0.091169 seconds
% 0.15/0.53 % CPU time: 0.134337 seconds
% 0.15/0.53 % Total memory used: 17.179 MB
% 0.15/0.53 % Net memory used: 17.168 MB
%------------------------------------------------------------------------------