%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC220-1 : 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 02:40:26 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 25
% Syntax : Number of formulae : 67 ( 9 unt; 12 def)
% Number of atoms : 209 ( 32 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 263 ( 121 ~; 130 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 13 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 34 ( 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
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(f194,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/sandbox/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
! [A,B,C] :
( memberP(C,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] :
( 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(f197,negated_conjecture,
! [A,B,C] :
( ~ leq(sk5(C,B,A),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(f202,negated_conjecture,
! [A] :
( ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6)
| ~ ssItem(A)
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f210,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
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(f441,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)],[f194]) ).
fof(f442,plain,
! [X0,X1,X2] :
( memberP(X2,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,
! [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)],[f196]) ).
fof(f444,plain,
! [X0,X1,X2] :
( ~ leq(sk5(X2,X1,X0),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(f449,plain,
! [X0] :
( ~ leq(sk6,X0)
| ~ memberP(sk8,X0)
| ~ memberP(sk7,X0)
| leq(X0,sk6)
| ~ ssItem(X0)
| nil = sk3 ),
inference(cnf_transformation,[status(thm)],[f202]) ).
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(f476,definition,
! [X0] :
( sQ7_spl
<=> ( ~ leq(sk6,X0)
| ~ memberP(sk8,X0)
| ~ memberP(sk7,X0)
| leq(X0,sk6)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f477,plain,
! [X0] :
( ~ sQ7_spl
| ~ leq(sk6,X0)
| ~ memberP(sk8,X0)
| ~ memberP(sk7,X0)
| leq(X0,sk6)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f476]) ).
fof(f479,plain,
( sQ7_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f449,f457,f476]) ).
fof(f492,plain,
( ~ sQ2_spl
| sk1 = nil ),
inference(backward_demodulation,[status(thm)],[f458,f438]) ).
fof(f493,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f492,f439]) ).
fof(f494,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f493]) ).
fof(f498,definition,
( sQ8_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f500,plain,
( sQ8_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f498]) ).
fof(f506,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f500,f210]) ).
fof(f507,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f506]) ).
fof(f512,plain,
( ~ sQ6_spl
| app(app(sk7,cons(sk6,nil)),sk8) = sk1 ),
inference(forward_demodulation,[status(thm)],[f438,f473]) ).
fof(f513,plain,
( ~ sQ6_spl
| memberP(sk7,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f512,f441]) ).
fof(f514,plain,
( ~ sQ6_spl
| ssItem(sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f512,f440]) ).
fof(f520,definition,
( sQ10_spl
<=> memberP(sk7,sk5(sk8,sk7,sk6)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f521,plain,
( ~ sQ10_spl
| memberP(sk7,sk5(sk8,sk7,sk6)) ),
inference(component_clause,[status(thm)],[f520]) ).
fof(f523,plain,
( ~ sQ6_spl
| sQ10_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f513,f460,f464,f468,f520,f472]) ).
fof(f524,definition,
( sQ11_spl
<=> ssItem(sk5(sk8,sk7,sk6)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f527,plain,
( ~ sQ6_spl
| sQ11_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f514,f460,f464,f468,f524,f472]) ).
fof(f551,plain,
( ~ sQ6_spl
| memberP(sk8,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f442,f512]) ).
fof(f553,definition,
( sQ18_spl
<=> memberP(sk8,sk5(sk8,sk7,sk6)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f556,plain,
( ~ sQ6_spl
| sQ18_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f551,f460,f464,f468,f553,f472]) ).
fof(f566,plain,
( ~ sQ6_spl
| leq(sk6,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f443,f512]) ).
fof(f568,definition,
( sQ20_spl
<=> leq(sk6,sk5(sk8,sk7,sk6)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f571,plain,
( ~ sQ6_spl
| sQ20_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f566,f460,f464,f468,f568,f472]) ).
fof(f573,plain,
( ~ sQ6_spl
| ~ leq(sk5(sk8,sk7,sk6),sk6)
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f444,f512]) ).
fof(f575,definition,
( sQ21_spl
<=> leq(sk5(sk8,sk7,sk6),sk6) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f578,plain,
( ~ sQ6_spl
| ~ sQ21_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f573,f460,f464,f468,f575,f472]) ).
fof(f595,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ memberP(sk8,sk5(sk8,sk7,sk6))
| leq(sk5(sk8,sk7,sk6),sk6)
| ~ ssItem(sk5(sk8,sk7,sk6)) ),
inference(resolution,[status(thm)],[f477,f521]) ).
fof(f599,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ18_spl
| sQ21_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f595,f524,f575,f553,f568,f476,f520]) ).
fof(f612,plain,
$false,
inference(sat_refutation,[status(thm)],[f463,f467,f471,f475,f479,f494,f507,f523,f527,f556,f571,f578,f599]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC220-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n006.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 08:05:14 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.44 % Elapsed time: 0.064436 seconds
% 0.09/0.44 % CPU time: 0.176224 seconds
% 0.09/0.44 % Total memory used: 109.555 MB
% 0.09/0.44 % Net memory used: 109.419 MB
%------------------------------------------------------------------------------