%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC116-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 02:40:02 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 29
% Syntax : Number of formulae : 94 ( 14 unt; 14 def)
% Number of atoms : 205 ( 36 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 209 ( 98 ~; 97 |; 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 : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 18 ( 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [U] :
( segmentP(U,nil)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f79,axiom,
! [U] :
( segmentP(nil,U)
| ~ ssList(U)
| nil != U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f80,axiom,
! [U] :
( nil = U
| ~ ssList(U)
| ~ segmentP(nil,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f100,axiom,
! [U,V] :
( V = U
| neq(V,U)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f115,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f188,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f189,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f190,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
( nil != sk4
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
( nil != sk1
| nil != sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
( neq(sk3,nil)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
( segmentP(sk4,sk3)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f204,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f252,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f276,plain,
! [X0] :
( segmentP(nil,X0)
| ~ ssList(X0)
| nil != X0 ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f277,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f299,plain,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f317,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ~ neq(U,V)
| U != V ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f318,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f317]) ).
fof(f429,plain,
ssList(sk3),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f430,plain,
ssList(sk4),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f431,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f432,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f433,plain,
( nil != sk4
| nil = sk3 ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f434,plain,
( nil != sk1
| nil != sk2 ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f435,plain,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f436,plain,
( neq(sk3,nil)
| ~ neq(sk4,nil) ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f437,plain,
( segmentP(sk4,sk3)
| ~ neq(sk4,nil) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f445,definition,
( sQ2_spl
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f446,plain,
( ~ sQ2_spl
| nil = sk3 ),
inference(component_clause,[status(thm)],[f445]) ).
fof(f448,definition,
( sQ3_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f449,plain,
( ~ sQ3_spl
| nil = sk4 ),
inference(component_clause,[status(thm)],[f448]) ).
fof(f451,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f433,f445,f448]) ).
fof(f452,definition,
( sQ4_spl
<=> nil = sk2 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f454,plain,
( sQ4_spl
| nil != sk2 ),
inference(component_clause,[status(thm)],[f452]) ).
fof(f455,definition,
( sQ5_spl
<=> nil = sk1 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( sQ5_spl
| nil != sk1 ),
inference(component_clause,[status(thm)],[f455]) ).
fof(f458,plain,
( ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f434,f452,f455]) ).
fof(f459,definition,
( sQ6_spl
<=> neq(sk1,nil) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f461,plain,
( sQ6_spl
| ~ neq(sk1,nil) ),
inference(component_clause,[status(thm)],[f459]) ).
fof(f462,definition,
( sQ7_spl
<=> segmentP(sk2,sk1) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f464,plain,
( sQ7_spl
| ~ segmentP(sk2,sk1) ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f465,plain,
( ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f435,f459,f462]) ).
fof(f466,definition,
( sQ8_spl
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f468,plain,
( sQ8_spl
| ~ neq(sk4,nil) ),
inference(component_clause,[status(thm)],[f466]) ).
fof(f469,definition,
( sQ9_spl
<=> neq(sk3,nil) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f470,plain,
( ~ sQ9_spl
| neq(sk3,nil) ),
inference(component_clause,[status(thm)],[f469]) ).
fof(f472,plain,
( sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f436,f466,f469]) ).
fof(f473,definition,
( sQ10_spl
<=> segmentP(sk4,sk3) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f474,plain,
( ~ sQ10_spl
| segmentP(sk4,sk3) ),
inference(component_clause,[status(thm)],[f473]) ).
fof(f476,plain,
( sQ10_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f437,f466,f473]) ).
fof(f477,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(destructive_equality_resolution,[status(thm)],[f276]) ).
fof(f484,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f318]) ).
fof(f485,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f484]) ).
fof(f508,plain,
( sQ4_spl
| nil != sk4 ),
inference(forward_demodulation,[status(thm)],[f431,f454]) ).
fof(f512,plain,
( sQ6_spl
| ~ neq(sk3,nil) ),
inference(forward_demodulation,[status(thm)],[f432,f461]) ).
fof(f522,definition,
( sQ11_spl
<=> ssList(sk3) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f524,plain,
( sQ11_spl
| ~ ssList(sk3) ),
inference(component_clause,[status(thm)],[f522]) ).
fof(f530,definition,
( sQ13_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f532,plain,
( sQ13_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f530]) ).
fof(f533,definition,
( sQ14_spl
<=> segmentP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f536,plain,
( sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f477,f530,f533]) ).
fof(f537,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f532,f204]) ).
fof(f538,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f537]) ).
fof(f540,plain,
( ~ ssList(nil)
| nil = nil
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f277,f252]) ).
fof(f542,definition,
( sQ15_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f546,plain,
( sQ15_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f540,f530,f542]) ).
fof(f548,plain,
( sQ8_spl
| sk4 = nil
| ~ ssList(sk4)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f299,f468]) ).
fof(f549,plain,
( sQ6_spl
| sk3 = nil
| ~ ssList(sk3)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f299,f512]) ).
fof(f552,definition,
( sQ16_spl
<=> ssList(sk4) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f554,plain,
( sQ16_spl
| ~ ssList(sk4) ),
inference(component_clause,[status(thm)],[f552]) ).
fof(f555,plain,
( sQ8_spl
| sQ3_spl
| ~ sQ16_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f548,f530,f552,f448,f466]) ).
fof(f556,plain,
( sQ6_spl
| sQ2_spl
| ~ sQ11_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f549,f530,f522,f445,f459]) ).
fof(f557,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f524,f429]) ).
fof(f558,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f557]) ).
fof(f559,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f554,f430]) ).
fof(f560,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f559]) ).
fof(f561,plain,
( sQ7_spl
| ~ segmentP(sk4,sk1) ),
inference(forward_demodulation,[status(thm)],[f431,f464]) ).
fof(f562,plain,
( sQ7_spl
| ~ segmentP(sk4,sk3) ),
inference(forward_demodulation,[status(thm)],[f432,f561]) ).
fof(f582,plain,
( ~ sQ9_spl
| ~ sQ2_spl
| neq(sk3,sk3) ),
inference(forward_demodulation,[status(thm)],[f446,f470]) ).
fof(f584,plain,
( ~ sQ9_spl
| ~ sQ2_spl
| ~ ssList(sk3) ),
inference(resolution,[status(thm)],[f582,f485]) ).
fof(f585,plain,
( ~ sQ9_spl
| ~ sQ2_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f584,f522,f445,f469]) ).
fof(f587,plain,
( ~ sQ10_spl
| sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f474,f562]) ).
fof(f588,plain,
( ~ sQ10_spl
| sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f587]) ).
fof(f589,plain,
( ~ sQ3_spl
| sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f449,f508]) ).
fof(f590,plain,
( ~ sQ3_spl
| sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f589]) ).
fof(f593,plain,
( sQ5_spl
| nil != sk3 ),
inference(forward_demodulation,[status(thm)],[f432,f457]) ).
fof(f609,plain,
( sQ5_spl
| ~ sQ2_spl
| sk3 != sk3 ),
inference(forward_demodulation,[status(thm)],[f446,f593]) ).
fof(f610,plain,
( sQ5_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f609]) ).
fof(f611,plain,
( sQ5_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f610]) ).
fof(f612,plain,
$false,
inference(sat_refutation,[status(thm)],[f451,f458,f465,f472,f476,f536,f538,f546,f555,f556,f558,f560,f585,f588,f590,f611]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC116-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.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 07:56:49 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.44 % Elapsed time: 0.067339 seconds
% 0.10/0.44 % CPU time: 0.084079 seconds
% 0.10/0.44 % Total memory used: 3.478 MB
% 0.10/0.44 % Net memory used: 3.470 MB
%------------------------------------------------------------------------------