%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC059-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 02:39:48 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.41s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 26
% Syntax : Number of formulae : 82 ( 11 unt; 13 def)
% Number of atoms : 195 ( 31 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 211 ( 98 ~; 100 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 14 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 12 ( 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f57,axiom,
! [U] :
( segmentP(U,U)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(sk3,nil)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
( segmentP(sk4,sk3)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
( neq(sk2,nil)
| nil = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
! [A] :
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( neq(sk2,nil)
| nil != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
! [A] :
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f255,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f278,plain,
! [X0] :
( segmentP(nil,X0)
| ~ ssList(X0)
| nil != X0 ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f431,plain,
ssList(sk3),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f432,plain,
ssList(sk4),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f433,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f434,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f435,plain,
( nil != sk4
| nil = sk3 ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f436,plain,
( neq(sk3,nil)
| ~ neq(sk4,nil) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f437,plain,
( segmentP(sk4,sk3)
| ~ neq(sk4,nil) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f438,plain,
( neq(sk2,nil)
| nil = sk2 ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f439,plain,
! [X0] :
( ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0)
| nil = sk2 ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f440,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f441,plain,
! [X0] :
( ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0)
| nil != sk1 ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f449,definition,
( sQ2_spl
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f450,plain,
( ~ sQ2_spl
| nil = sk3 ),
inference(component_clause,[status(thm)],[f449]) ).
fof(f452,definition,
( sQ3_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f454,plain,
( sQ3_spl
| nil != sk4 ),
inference(component_clause,[status(thm)],[f452]) ).
fof(f455,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f435,f449,f452]) ).
fof(f456,definition,
( sQ4_spl
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f458,plain,
( sQ4_spl
| ~ neq(sk4,nil) ),
inference(component_clause,[status(thm)],[f456]) ).
fof(f459,definition,
( sQ5_spl
<=> neq(sk3,nil) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f462,plain,
( sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f436,f456,f459]) ).
fof(f463,definition,
( sQ6_spl
<=> segmentP(sk4,sk3) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f466,plain,
( sQ6_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f437,f456,f463]) ).
fof(f467,definition,
( sQ7_spl
<=> nil = sk2 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f468,plain,
( ~ sQ7_spl
| nil = sk2 ),
inference(component_clause,[status(thm)],[f467]) ).
fof(f470,definition,
( sQ8_spl
<=> neq(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f471,plain,
( ~ sQ8_spl
| neq(sk2,nil) ),
inference(component_clause,[status(thm)],[f470]) ).
fof(f473,plain,
( sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f438,f467,f470]) ).
fof(f474,definition,
! [X0] :
( sQ9_spl
<=> ( ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f475,plain,
! [X0] :
( ~ sQ9_spl
| ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f474]) ).
fof(f477,plain,
( sQ9_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f439,f467,f474]) ).
fof(f478,definition,
( sQ10_spl
<=> nil = sk1 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f480,plain,
( sQ10_spl
| nil != sk1 ),
inference(component_clause,[status(thm)],[f478]) ).
fof(f481,plain,
( sQ8_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f440,f478,f470]) ).
fof(f482,plain,
( sQ9_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f441,f478,f474]) ).
fof(f483,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(destructive_equality_resolution,[status(thm)],[f278]) ).
fof(f514,plain,
( sQ10_spl
| nil != sk3 ),
inference(forward_demodulation,[status(thm)],[f434,f480]) ).
fof(f515,plain,
( sQ10_spl
| ~ sQ7_spl
| sk4 != sk3 ),
inference(backward_demodulation,[status(thm)],[f517,f514]) ).
fof(f517,plain,
( ~ sQ7_spl
| nil = sk4 ),
inference(forward_demodulation,[status(thm)],[f433,f468]) ).
fof(f520,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| sk4 = sk3 ),
inference(forward_demodulation,[status(thm)],[f517,f450]) ).
fof(f521,plain,
( sQ10_spl
| ~ sQ7_spl
| ~ sQ2_spl
| sk4 != sk4 ),
inference(forward_demodulation,[status(thm)],[f520,f515]) ).
fof(f522,plain,
( sQ10_spl
| ~ sQ7_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f521]) ).
fof(f523,plain,
( sQ10_spl
| ~ sQ7_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f522]) ).
fof(f524,plain,
( ~ sQ8_spl
| neq(sk4,nil) ),
inference(forward_demodulation,[status(thm)],[f433,f471]) ).
fof(f525,plain,
! [X0] :
( ~ sQ9_spl
| ~ segmentP(sk1,X0)
| ~ segmentP(sk4,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f433,f475]) ).
fof(f527,plain,
( ~ sQ8_spl
| sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f524,f458]) ).
fof(f528,plain,
( ~ sQ8_spl
| sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f527]) ).
fof(f529,plain,
( ~ sQ7_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f517,f454]) ).
fof(f530,plain,
( ~ sQ7_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f529]) ).
fof(f550,definition,
( sQ11_spl
<=> ssList(sk4) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f552,plain,
( sQ11_spl
| ~ ssList(sk4) ),
inference(component_clause,[status(thm)],[f550]) ).
fof(f590,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f552,f432]) ).
fof(f591,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f590]) ).
fof(f592,definition,
( sQ18_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f594,plain,
( sQ18_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f592]) ).
fof(f595,definition,
( sQ19_spl
<=> segmentP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f598,plain,
( sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f483,f592,f595]) ).
fof(f604,plain,
( sQ18_spl
| ~ sQ2_spl
| ~ ssList(sk3) ),
inference(forward_demodulation,[status(thm)],[f450,f594]) ).
fof(f605,plain,
( sQ18_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f604,f431]) ).
fof(f606,plain,
( sQ18_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f605]) ).
fof(f609,plain,
! [X0] :
( ~ sQ9_spl
| ~ segmentP(sk3,X0)
| ~ segmentP(sk4,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f434,f525]) ).
fof(f612,plain,
( ~ sQ9_spl
| ~ ssList(sk3)
| ~ segmentP(sk4,sk3)
| ~ neq(sk3,nil)
| ~ ssList(sk3) ),
inference(resolution,[status(thm)],[f609,f255]) ).
fof(f613,definition,
( sQ20_spl
<=> ssList(sk3) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f615,plain,
( sQ20_spl
| ~ ssList(sk3) ),
inference(component_clause,[status(thm)],[f613]) ).
fof(f624,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f612,f613,f459,f463,f474]) ).
fof(f625,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f615,f431]) ).
fof(f626,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f625]) ).
fof(f627,plain,
$false,
inference(sat_refutation,[status(thm)],[f455,f462,f466,f473,f477,f481,f482,f523,f528,f530,f591,f598,f606,f624,f626]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC059-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 07:47:26 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.39 % 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
% 0.15/0.45 % Elapsed time: 0.075478 seconds
% 0.15/0.45 % CPU time: 0.153388 seconds
% 0.15/0.45 % Total memory used: 40.875 MB
% 0.15/0.45 % Net memory used: 40.815 MB
%------------------------------------------------------------------------------