%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC124-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 02:40:04 PM UTC 2026
% Result : Unsatisfiable 49.21s 6.70s
% Output : CNFRefutation 49.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 26
% Syntax : Number of formulae : 84 ( 25 unt; 11 def)
% Number of atoms : 186 ( 29 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 194 ( 92 ~; 91 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 12 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 33 ( 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [U] :
( segmentP(U,U)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f74,axiom,
! [U] :
( app(nil,U) = U
| ~ ssList(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(f172,axiom,
! [U,V,W,X] :
( segmentP(app(app(X,U),W),V)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X)
| ~ ssList(W)
| ~ segmentP(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f186,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f187,negated_conjecture,
ssList(sk2),
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,
neq(sk2,nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
ssList(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
app(sk3,sk5) = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( nil != sk3
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f206,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f255,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f273,plain,
! [X0] :
( ~ ssList(X0)
| X0 = app(nil,X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f301,plain,
! [X0,X1] :
( ~ ssList(X1)
| neq(X1,X0)
| X1 = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f319,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ~ neq(U,V)
| U != V ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f320,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f319]) ).
fof(f403,plain,
! [X0,X1,X2,X3] :
( ~ ssList(X0)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(X1,X3)
| segmentP(app(app(X0,X1),X2),X3) ),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f429,plain,
ssList(sk1),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f430,plain,
ssList(sk2),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f433,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f434,plain,
sk3 = sk1,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f435,plain,
neq(sk2,nil),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f436,plain,
ssList(sk5),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f437,plain,
app(sk3,sk5) = sk4,
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f441,plain,
( nil != sk3
| nil = sk4 ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f442,plain,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f450,definition,
( sQ2_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f451,plain,
( ~ sQ2_spl
| nil = sk4 ),
inference(component_clause,[status(thm)],[f450]) ).
fof(f453,definition,
( sQ3_spl
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f455,plain,
( sQ3_spl
| nil != sk3 ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f456,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f441,f450,f453]) ).
fof(f457,definition,
( sQ4_spl
<=> neq(sk1,nil) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f459,plain,
( sQ4_spl
| ~ neq(sk1,nil) ),
inference(component_clause,[status(thm)],[f457]) ).
fof(f460,definition,
( sQ5_spl
<=> segmentP(sk2,sk1) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f463,plain,
( ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f442,f457,f460]) ).
fof(f467,plain,
app(sk3,sk5) = sk2,
inference(forward_demodulation,[status(thm)],[f433,f437]) ).
fof(f497,plain,
sk2 = app(sk1,sk5),
inference(backward_demodulation,[status(thm)],[f434,f467]) ).
fof(f499,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f320]) ).
fof(f500,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f499]) ).
fof(f528,plain,
( ~ sQ2_spl
| neq(sk2,sk2) ),
inference(backward_demodulation,[status(thm)],[f550,f435]) ).
fof(f550,plain,
( ~ sQ2_spl
| nil = sk2 ),
inference(forward_demodulation,[status(thm)],[f433,f451]) ).
fof(f573,definition,
( sQ8_spl
<=> ssList(sk5) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f575,plain,
( sQ8_spl
| ~ ssList(sk5) ),
inference(component_clause,[status(thm)],[f573]) ).
fof(f579,definition,
( sQ10_spl
<=> ssList(sk1) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f581,plain,
( sQ10_spl
| ~ ssList(sk1) ),
inference(component_clause,[status(thm)],[f579]) ).
fof(f583,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f581,f429]) ).
fof(f584,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f583]) ).
fof(f585,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f575,f436]) ).
fof(f586,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f585]) ).
fof(f587,plain,
( ~ sQ2_spl
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f500,f528]) ).
fof(f588,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f587,f430]) ).
fof(f589,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f588]) ).
fof(f590,plain,
( sQ3_spl
| sk1 != nil ),
inference(forward_demodulation,[status(thm)],[f434,f455]) ).
fof(f613,definition,
( sQ12_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f615,plain,
( sQ12_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f613]) ).
fof(f621,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f615,f206]) ).
fof(f622,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f621]) ).
fof(f632,plain,
sk1 = app(nil,sk1),
inference(resolution,[status(thm)],[f273,f429]) ).
fof(f634,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(sk1)
| ~ segmentP(sk1,X1)
| segmentP(app(sk1,X0),X1) ),
inference(paramodulation,[status(thm)],[f632,f403]) ).
fof(f636,definition,
! [X0,X1] :
( sQ14_spl
<=> ( ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(sk1,X1)
| segmentP(app(sk1,X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f637,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ segmentP(sk1,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(sk1,X0),X1) ),
inference(component_clause,[status(thm)],[f636]) ).
fof(f639,plain,
( ~ sQ12_spl
| ~ sQ10_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f634,f636,f579,f613]) ).
fof(f685,definition,
( sQ22_spl
<=> ssList(sk2) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f687,plain,
( sQ22_spl
| ~ ssList(sk2) ),
inference(component_clause,[status(thm)],[f685]) ).
fof(f693,plain,
( sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f687,f430]) ).
fof(f694,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f693]) ).
fof(f696,plain,
! [X0] :
( ~ sQ14_spl
| ~ ssList(sk1)
| ~ ssList(X0)
| segmentP(app(sk1,X0),sk1)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f637,f255]) ).
fof(f697,definition,
! [X0] :
( sQ24_spl
<=> ( ~ ssList(X0)
| segmentP(app(sk1,X0),sk1) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f698,plain,
! [X0] :
( ~ sQ24_spl
| segmentP(app(sk1,X0),sk1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f697]) ).
fof(f700,plain,
( ~ sQ14_spl
| sQ24_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f696,f579,f697,f636]) ).
fof(f707,plain,
( ~ sQ24_spl
| ~ ssList(sk5)
| segmentP(sk2,sk1) ),
inference(paramodulation,[status(thm)],[f497,f698]) ).
fof(f708,plain,
( ~ sQ24_spl
| ~ sQ8_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f707,f460,f573,f697]) ).
fof(f821,plain,
( sQ4_spl
| ~ ssList(sk1)
| sk1 = nil
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f459,f301]) ).
fof(f822,definition,
( sQ42_spl
<=> sk1 = nil ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f823,plain,
( ~ sQ42_spl
| sk1 = nil ),
inference(component_clause,[status(thm)],[f822]) ).
fof(f825,plain,
( sQ4_spl
| ~ sQ10_spl
| sQ42_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f821,f613,f822,f579,f457]) ).
fof(f826,plain,
( ~ sQ42_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f823,f590]) ).
fof(f827,plain,
( ~ sQ42_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f826]) ).
fof(f828,plain,
$false,
inference(sat_refutation,[status(thm)],[f456,f463,f584,f586,f589,f622,f639,f694,f700,f708,f825,f827]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC124-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.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 07:57:25 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 49.21/6.70 % Refutation found
% 49.21/6.70 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 49.21/6.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 38.38/6.75 % Elapsed time: 6.381973 seconds
% 38.38/6.75 % CPU time: 50.313937 seconds
% 38.38/6.75 % Total memory used: 405.031 MB
% 38.38/6.75 % Net memory used: 379.370 MB
%------------------------------------------------------------------------------