%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC054-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 02:39:46 PM UTC 2026
% Result : Unsatisfiable 0.03s 0.41s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 28
% Syntax : Number of formulae : 85 ( 10 unt; 14 def)
% Number of atoms : 203 ( 31 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 221 ( 103 ~; 104 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 15 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 10 ( 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f79,axiom,
! [U] :
( segmentP(nil,U)
| ~ ssList(U)
| nil != U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f188,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f189,negated_conjecture,
ssList(sk4),
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,
( nil != sk4
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
( ~ neq(sk4,nil)
| neq(sk5,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
( ~ neq(sk4,nil)
| segmentP(sk4,sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
( ~ neq(sk4,nil)
| segmentP(sk3,sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( neq(sk2,nil)
| nil = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
! [A] :
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f199,negated_conjecture,
( neq(sk2,nil)
| nil != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f200,negated_conjecture,
! [A] :
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f280,plain,
! [X0] :
( segmentP(nil,X0)
| ~ ssList(X0)
| nil != X0 ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f433,plain,
ssList(sk3),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f434,plain,
ssList(sk4),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f435,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f436,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f437,plain,
( nil != sk4
| nil = sk3 ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f438,plain,
( ~ neq(sk4,nil)
| ssList(sk5) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f439,plain,
( ~ neq(sk4,nil)
| neq(sk5,nil) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f440,plain,
( ~ neq(sk4,nil)
| segmentP(sk4,sk5) ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f441,plain,
( ~ neq(sk4,nil)
| segmentP(sk3,sk5) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f442,plain,
( neq(sk2,nil)
| nil = sk2 ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f443,plain,
! [X0] :
( ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0)
| nil = sk2 ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f444,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f445,plain,
! [X0] :
( ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0)
| nil != sk1 ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f453,definition,
( sQ2_spl
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f454,plain,
( ~ sQ2_spl
| nil = sk3 ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f456,definition,
( sQ3_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f458,plain,
( sQ3_spl
| nil != sk4 ),
inference(component_clause,[status(thm)],[f456]) ).
fof(f459,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f437,f453,f456]) ).
fof(f460,definition,
( sQ4_spl
<=> ssList(sk5) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f463,definition,
( sQ5_spl
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f465,plain,
( sQ5_spl
| ~ neq(sk4,nil) ),
inference(component_clause,[status(thm)],[f463]) ).
fof(f466,plain,
( ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f438,f460,f463]) ).
fof(f467,definition,
( sQ6_spl
<=> neq(sk5,nil) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f470,plain,
( ~ sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f439,f467,f463]) ).
fof(f471,definition,
( sQ7_spl
<=> segmentP(sk4,sk5) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f472,plain,
( ~ sQ7_spl
| segmentP(sk4,sk5) ),
inference(component_clause,[status(thm)],[f471]) ).
fof(f474,plain,
( ~ sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f440,f471,f463]) ).
fof(f475,definition,
( sQ8_spl
<=> segmentP(sk3,sk5) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f478,plain,
( ~ sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f441,f475,f463]) ).
fof(f479,definition,
( sQ9_spl
<=> nil = sk2 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f480,plain,
( ~ sQ9_spl
| nil = sk2 ),
inference(component_clause,[status(thm)],[f479]) ).
fof(f482,definition,
( sQ10_spl
<=> neq(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f483,plain,
( ~ sQ10_spl
| neq(sk2,nil) ),
inference(component_clause,[status(thm)],[f482]) ).
fof(f485,plain,
( sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f442,f479,f482]) ).
fof(f486,definition,
! [X0] :
( sQ11_spl
<=> ( ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f487,plain,
! [X0] :
( ~ sQ11_spl
| ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f486]) ).
fof(f489,plain,
( sQ11_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f443,f479,f486]) ).
fof(f490,definition,
( sQ12_spl
<=> nil = sk1 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f492,plain,
( sQ12_spl
| nil != sk1 ),
inference(component_clause,[status(thm)],[f490]) ).
fof(f493,plain,
( sQ10_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f444,f490,f482]) ).
fof(f494,plain,
( sQ11_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f445,f490,f486]) ).
fof(f495,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(destructive_equality_resolution,[status(thm)],[f280]) ).
fof(f526,plain,
( sQ12_spl
| nil != sk3 ),
inference(forward_demodulation,[status(thm)],[f436,f492]) ).
fof(f527,plain,
( sQ12_spl
| ~ sQ9_spl
| sk4 != sk3 ),
inference(backward_demodulation,[status(thm)],[f529,f526]) ).
fof(f529,plain,
( ~ sQ9_spl
| nil = sk4 ),
inference(forward_demodulation,[status(thm)],[f435,f480]) ).
fof(f532,plain,
( ~ sQ2_spl
| ~ sQ9_spl
| sk4 = sk3 ),
inference(forward_demodulation,[status(thm)],[f529,f454]) ).
fof(f533,plain,
( sQ12_spl
| ~ sQ9_spl
| ~ sQ2_spl
| sk4 != sk4 ),
inference(forward_demodulation,[status(thm)],[f532,f527]) ).
fof(f534,plain,
( sQ12_spl
| ~ sQ9_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f533]) ).
fof(f535,plain,
( sQ12_spl
| ~ sQ9_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f534]) ).
fof(f536,plain,
( ~ sQ10_spl
| neq(sk4,nil) ),
inference(forward_demodulation,[status(thm)],[f435,f483]) ).
fof(f537,plain,
! [X0] :
( ~ sQ11_spl
| ~ segmentP(sk1,X0)
| ~ segmentP(sk4,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f435,f487]) ).
fof(f539,plain,
( ~ sQ10_spl
| sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f536,f465]) ).
fof(f540,plain,
( ~ sQ10_spl
| sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f539]) ).
fof(f541,plain,
( ~ sQ9_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f529,f458]) ).
fof(f542,plain,
( ~ sQ9_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f541]) ).
fof(f562,definition,
( sQ13_spl
<=> ssList(sk4) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f564,plain,
( sQ13_spl
| ~ ssList(sk4) ),
inference(component_clause,[status(thm)],[f562]) ).
fof(f602,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f564,f434]) ).
fof(f603,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f602]) ).
fof(f604,definition,
( sQ20_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f606,plain,
( sQ20_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f604]) ).
fof(f607,definition,
( sQ21_spl
<=> segmentP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f610,plain,
( sQ21_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f495,f604,f607]) ).
fof(f616,plain,
( sQ20_spl
| ~ sQ2_spl
| ~ ssList(sk3) ),
inference(forward_demodulation,[status(thm)],[f454,f606]) ).
fof(f617,plain,
( sQ20_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f616,f433]) ).
fof(f618,plain,
( sQ20_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f617]) ).
fof(f621,plain,
! [X0] :
( ~ sQ11_spl
| ~ segmentP(sk3,X0)
| ~ segmentP(sk4,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f436,f537]) ).
fof(f622,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ segmentP(sk3,sk5)
| ~ neq(sk5,nil)
| ~ ssList(sk5) ),
inference(resolution,[status(thm)],[f621,f472]) ).
fof(f626,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f622,f460,f467,f475,f486,f471]) ).
fof(f642,plain,
$false,
inference(sat_refutation,[status(thm)],[f459,f466,f470,f474,f478,f485,f489,f493,f494,f535,f540,f542,f603,f610,f618,f626]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC054-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.36 % Computer : n014.cluster.edu
% 0.03/0.36 % Model : x86_64 x86_64
% 0.03/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.36 % Memory : 8046.5625MB
% 0.03/0.36 % OS : Linux 6.8.0-71-generic
% 0.03/0.36 % CPULimit : 300
% 0.03/0.36 % WCLimit : 300
% 0.03/0.36 % DateTime : Mon Sep 21 07:51:50 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.38 % Drodi V4.1.1
% 0.03/0.41 % Refutation found
% 0.03/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.03/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.03/0.44 % Elapsed time: 0.071385 seconds
% 0.03/0.44 % CPU time: 0.178068 seconds
% 0.03/0.44 % Total memory used: 109.057 MB
% 0.03/0.44 % Net memory used: 108.914 MB
%------------------------------------------------------------------------------