%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC083-1 : 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 02:39:53 PM UTC 2026
% Result : Unsatisfiable 216.37s 28.08s
% Output : CNFRefutation 216.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 63
% Syntax : Number of formulae : 225 ( 59 unt; 39 def)
% Number of atoms : 517 ( 46 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 528 ( 236 ~; 253 |; 0 &)
% ( 39 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 45 ( 43 usr; 40 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 69 ( 69 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [U] : ssList(skaf53(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [U] : ssList(skaf51(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [U] : ssItem(skaf50(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [U] : ssItem(skaf44(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [U,V] : ssList(skaf46(U,V)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [U,V] : ssList(skaf45(U,V)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [U] :
( segmentP(U,U)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f73,axiom,
! [U] :
( app(U,nil) = 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(f85,axiom,
! [U,V] :
( ssList(app(V,U))
| ~ ssList(V)
| ~ 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(f173,axiom,
! [U,V,W,X] :
( segmentP(X,V)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| app(app(U,V),W) != X ),
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,
! [A] :
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
ssList(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
app(app(sk5,sk6),sk7) = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
app(sk5,sk7) = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f206,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f240,plain,
! [X0] : ssList(skaf53(X0)),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f242,plain,
! [X0] : ssList(skaf51(X0)),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f243,plain,
! [X0] : ssItem(skaf50(X0)),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f245,plain,
! [X0] : ssItem(skaf44(X0)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f248,plain,
! [X0,X1] : ssList(skaf46(X0,X1)),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f249,plain,
! [X0,X1] : ssList(skaf45(X0,X1)),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f255,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f272,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f273,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f284,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f301,plain,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f404,plain,
! [V,X] :
( segmentP(X,V)
| ~ ssList(X)
| ~ ssList(V)
| ! [U] :
( ~ ssList(U)
| ! [W] :
( ~ ssList(W)
| app(app(U,V),W) != X ) ) ),
inference(miniscoping,[status(thm)],[f173]) ).
fof(f405,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| app(app(X0,X1),X2) != X3 ),
inference(cnf_transformation,[status(thm)],[f404]) ).
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,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f435,plain,
neq(sk2,nil),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f436,plain,
! [X0] :
( ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f437,plain,
ssList(sk5),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f438,plain,
ssList(sk6),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f439,plain,
ssList(sk7),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f440,plain,
app(app(sk5,sk6),sk7) = sk3,
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f441,plain,
app(sk5,sk7) = sk4,
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f467,plain,
! [X0,X1,X2] :
( segmentP(app(app(X1,X2),X0),X2)
| ~ ssList(app(app(X1,X2),X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f405]) ).
fof(f480,plain,
app(sk5,sk7) = sk2,
inference(forward_demodulation,[status(thm)],[f433,f441]) ).
fof(f481,plain,
app(app(sk5,sk6),sk7) = sk1,
inference(forward_demodulation,[status(thm)],[f434,f440]) ).
fof(f482,plain,
( ~ segmentP(sk1,sk2)
| ~ segmentP(sk2,sk2)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f436,f435]) ).
fof(f483,definition,
( sQ2_spl
<=> ssList(sk2) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f486,definition,
( sQ3_spl
<=> segmentP(sk2,sk2) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f488,plain,
( sQ3_spl
| ~ segmentP(sk2,sk2) ),
inference(component_clause,[status(thm)],[f486]) ).
fof(f489,definition,
( sQ4_spl
<=> segmentP(sk1,sk2) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f492,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f482,f483,f486,f489]) ).
fof(f495,definition,
( sQ5_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f497,plain,
( sQ5_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f495]) ).
fof(f503,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f497,f206]) ).
fof(f504,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f503]) ).
fof(f505,plain,
( ssList(sk1)
| ~ ssList(app(sk5,sk6))
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f481,f284]) ).
fof(f506,plain,
( ssList(sk2)
| ~ ssList(sk5)
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f480,f284]) ).
fof(f507,definition,
( sQ7_spl
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f509,plain,
( sQ7_spl
| ~ ssList(sk7) ),
inference(component_clause,[status(thm)],[f507]) ).
fof(f510,definition,
( sQ8_spl
<=> ssList(app(sk5,sk6)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f512,plain,
( sQ8_spl
| ~ ssList(app(sk5,sk6)) ),
inference(component_clause,[status(thm)],[f510]) ).
fof(f513,definition,
( sQ9_spl
<=> ssList(sk1) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f516,plain,
( sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f505,f507,f510,f513]) ).
fof(f517,definition,
( sQ10_spl
<=> ssList(sk5) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f519,plain,
( sQ10_spl
| ~ ssList(sk5) ),
inference(component_clause,[status(thm)],[f517]) ).
fof(f520,plain,
( sQ2_spl
| ~ sQ10_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f506,f507,f517,f483]) ).
fof(f521,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f509,f439]) ).
fof(f522,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f521]) ).
fof(f523,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f519,f437]) ).
fof(f524,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f523]) ).
fof(f525,plain,
( sQ3_spl
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f488,f255]) ).
fof(f526,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f525,f430]) ).
fof(f527,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f526]) ).
fof(f528,plain,
! [X0] :
( ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f301,f436]) ).
fof(f531,definition,
! [X0] :
( sQ11_spl
<=> ( ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ ssList(X0)
| X0 = nil
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f532,plain,
! [X0] :
( ~ sQ11_spl
| ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ ssList(X0)
| X0 = nil
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f531]) ).
fof(f534,plain,
( sQ11_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f528,f495,f531]) ).
fof(f535,plain,
! [X0] :
( ~ sQ11_spl
| ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| X0 = nil
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f532]) ).
fof(f536,plain,
( sQ8_spl
| ~ ssList(sk5)
| ~ ssList(sk6) ),
inference(resolution,[status(thm)],[f512,f284]) ).
fof(f537,definition,
( sQ12_spl
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f539,plain,
( sQ12_spl
| ~ ssList(sk6) ),
inference(component_clause,[status(thm)],[f537]) ).
fof(f540,plain,
( sQ8_spl
| ~ sQ10_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f536,f537,f517,f510]) ).
fof(f541,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f539,f438]) ).
fof(f542,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f541]) ).
fof(f579,definition,
( sQ19_spl
<=> nil = sk7 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f580,plain,
( ~ sQ19_spl
| nil = sk7 ),
inference(component_clause,[status(thm)],[f579]) ).
fof(f594,plain,
( ~ sQ19_spl
| app(app(sk5,sk6),nil) = sk1 ),
inference(backward_demodulation,[status(thm)],[f580,f481]) ).
fof(f595,plain,
( ~ sQ19_spl
| app(sk5,nil) = sk2 ),
inference(backward_demodulation,[status(thm)],[f580,f480]) ).
fof(f597,plain,
( ~ sQ19_spl
| sk1 = app(sk5,sk6)
| ~ ssList(app(sk5,sk6)) ),
inference(paramodulation,[status(thm)],[f594,f272]) ).
fof(f601,definition,
( sQ22_spl
<=> sk1 = app(sk5,sk6) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f602,plain,
( ~ sQ22_spl
| sk1 = app(sk5,sk6) ),
inference(component_clause,[status(thm)],[f601]) ).
fof(f604,plain,
( ~ sQ19_spl
| sQ22_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f597,f510,f601,f579]) ).
fof(f932,plain,
! [X0] :
( segmentP(app(sk2,X0),sk7)
| ~ ssList(app(app(sk5,sk7),X0))
| ~ ssList(sk7)
| ~ ssList(sk5)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f480,f467]) ).
fof(f933,plain,
! [X0] :
( segmentP(app(sk1,X0),sk7)
| ~ ssList(app(app(app(sk5,sk6),sk7),X0))
| ~ ssList(sk7)
| ~ ssList(app(sk5,sk6))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f481,f467]) ).
fof(f940,definition,
! [X0] :
( sQ63_spl
<=> ( segmentP(app(sk2,X0),sk7)
| ~ ssList(app(app(sk5,sk7),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f941,plain,
! [X0] :
( ~ sQ63_spl
| segmentP(app(sk2,X0),sk7)
| ~ ssList(app(app(sk5,sk7),X0))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f940]) ).
fof(f943,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f932,f940,f517,f507]) ).
fof(f944,definition,
! [X0] :
( sQ64_spl
<=> ( segmentP(app(sk1,X0),sk7)
| ~ ssList(app(app(app(sk5,sk6),sk7),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f945,plain,
! [X0] :
( ~ sQ64_spl
| segmentP(app(sk1,X0),sk7)
| ~ ssList(app(app(app(sk5,sk6),sk7),X0))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f944]) ).
fof(f947,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sQ64_spl ),
inference(split_clause,[status(thm)],[f933,f944,f510,f507]) ).
fof(f948,plain,
! [X0] :
( ~ sQ63_spl
| segmentP(app(sk2,X0),sk7)
| ~ ssList(app(sk2,X0))
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f480,f941]) ).
fof(f949,plain,
! [X0] :
( ~ sQ64_spl
| segmentP(app(sk1,X0),sk7)
| ~ ssList(app(sk1,X0))
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f481,f945]) ).
fof(f2325,definition,
! [X0] :
( sQ220_spl
<=> ( segmentP(app(sk2,X0),sk2)
| ~ ssList(app(app(nil,sk2),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition]) ).
fof(f2326,plain,
! [X0] :
( ~ sQ220_spl
| segmentP(app(sk2,X0),sk2)
| ~ ssList(app(app(nil,sk2),X0))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2325]) ).
fof(f3093,definition,
( sQ302_spl
<=> ssList(app(sk1,nil)) ),
introduced(definition,[new_symbols(definition,[sQ302_spl])],[split_symbol_definition]) ).
fof(f3095,plain,
( sQ302_spl
| ~ ssList(app(sk1,nil)) ),
inference(component_clause,[status(thm)],[f3093]) ).
fof(f3284,definition,
( sQ322_spl
<=> sk5 = sk2 ),
introduced(definition,[new_symbols(definition,[sQ322_spl])],[split_symbol_definition]) ).
fof(f3285,plain,
( ~ sQ322_spl
| sk5 = sk2 ),
inference(component_clause,[status(thm)],[f3284]) ).
fof(f3595,definition,
( sQ361_spl
<=> ssList(app(nil,sk2)) ),
introduced(definition,[new_symbols(definition,[sQ361_spl])],[split_symbol_definition]) ).
fof(f3597,plain,
( sQ361_spl
| ~ ssList(app(nil,sk2)) ),
inference(component_clause,[status(thm)],[f3595]) ).
fof(f4325,plain,
! [X0] :
( ~ sQ220_spl
| ~ ssList(app(nil,sk2))
| ~ ssList(X0)
| segmentP(app(sk2,X0),sk2)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2326,f284]) ).
fof(f4326,definition,
! [X0] :
( sQ448_spl
<=> ( ~ ssList(X0)
| segmentP(app(sk2,X0),sk2)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ448_spl])],[split_symbol_definition]) ).
fof(f4327,plain,
! [X0] :
( ~ sQ448_spl
| ~ ssList(X0)
| segmentP(app(sk2,X0),sk2)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f4326]) ).
fof(f4329,plain,
( ~ sQ220_spl
| ~ sQ361_spl
| sQ448_spl ),
inference(split_clause,[status(thm)],[f4325,f4326,f3595,f2325]) ).
fof(f4330,plain,
! [X0] :
( ~ sQ448_spl
| segmentP(app(sk2,X0),sk2)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f4327]) ).
fof(f6066,plain,
( ~ sQ19_spl
| sk2 = sk5
| ~ ssList(sk5) ),
inference(paramodulation,[status(thm)],[f595,f272]) ).
fof(f6089,plain,
( ~ sQ19_spl
| sQ322_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f6066,f517,f3284,f579]) ).
fof(f6339,definition,
( sQ607_spl
<=> app(sk2,nil) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ607_spl])],[split_symbol_definition]) ).
fof(f6340,plain,
( ~ sQ607_spl
| app(sk2,nil) = sk2 ),
inference(component_clause,[status(thm)],[f6339]) ).
fof(f6341,plain,
( sQ607_spl
| app(sk2,nil) != sk2 ),
inference(component_clause,[status(thm)],[f6339]) ).
fof(f6938,definition,
( sQ665_spl
<=> app(sk1,nil) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ665_spl])],[split_symbol_definition]) ).
fof(f6939,plain,
( ~ sQ665_spl
| app(sk1,nil) = sk1 ),
inference(component_clause,[status(thm)],[f6938]) ).
fof(f6940,plain,
( sQ665_spl
| app(sk1,nil) != sk1 ),
inference(component_clause,[status(thm)],[f6938]) ).
fof(f9370,definition,
( sQ885_spl
<=> app(nil,sk2) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ885_spl])],[split_symbol_definition]) ).
fof(f9371,plain,
( ~ sQ885_spl
| app(nil,sk2) = sk2 ),
inference(component_clause,[status(thm)],[f9370]) ).
fof(f9372,plain,
( sQ885_spl
| app(nil,sk2) != sk2 ),
inference(component_clause,[status(thm)],[f9370]) ).
fof(f9822,plain,
! [X0] :
( ~ sQ885_spl
| segmentP(app(sk2,X0),sk2)
| ~ ssList(app(app(nil,sk2),X0))
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f9371,f467]) ).
fof(f9850,plain,
( ~ sQ885_spl
| ~ sQ2_spl
| ~ sQ5_spl
| sQ220_spl ),
inference(split_clause,[status(thm)],[f9822,f2325,f495,f483,f9370]) ).
fof(f9859,plain,
( sQ885_spl
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f9372,f273]) ).
fof(f9860,plain,
( sQ885_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9859,f430]) ).
fof(f9861,plain,
sQ885_spl,
inference(contradiction_clause,[status(thm)],[f9860]) ).
fof(f12222,plain,
( sQ665_spl
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f6940,f272]) ).
fof(f12223,plain,
( sQ665_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12222,f429]) ).
fof(f12224,plain,
sQ665_spl,
inference(contradiction_clause,[status(thm)],[f12223]) ).
fof(f12299,plain,
( sQ607_spl
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f6341,f272]) ).
fof(f12300,plain,
( sQ607_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12299,f430]) ).
fof(f12301,plain,
sQ607_spl,
inference(contradiction_clause,[status(thm)],[f12300]) ).
fof(f12451,definition,
! [X2] :
( sQ1123_spl
<=> ( ~ ssItem(X2)
| ~ ssItem(X2)
| ~ ssItem(X2) ) ),
introduced(definition,[new_symbols(definition,[sQ1123_spl])],[split_symbol_definition]) ).
fof(f12452,plain,
! [X0] :
( ~ sQ1123_spl
| ~ ssItem(X0)
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f12451]) ).
fof(f12458,plain,
! [X0] :
( ~ sQ1123_spl
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f12452]) ).
fof(f12528,definition,
( sQ1128_spl
<=> ssList(skaf45(sk6,nil)) ),
introduced(definition,[new_symbols(definition,[sQ1128_spl])],[split_symbol_definition]) ).
fof(f12530,plain,
( sQ1128_spl
| ~ ssList(skaf45(sk6,nil)) ),
inference(component_clause,[status(thm)],[f12528]) ).
fof(f12562,plain,
( sQ1128_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12530,f249]) ).
fof(f12563,plain,
sQ1128_spl,
inference(contradiction_clause,[status(thm)],[f12562]) ).
fof(f12570,plain,
( ~ sQ1123_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f245,f12458]) ).
fof(f12590,plain,
~ sQ1123_spl,
inference(contradiction_clause,[status(thm)],[f12570]) ).
fof(f12625,definition,
( sQ1131_spl
<=> ssList(skaf45(sk1,sk5)) ),
introduced(definition,[new_symbols(definition,[sQ1131_spl])],[split_symbol_definition]) ).
fof(f12627,plain,
( sQ1131_spl
| ~ ssList(skaf45(sk1,sk5)) ),
inference(component_clause,[status(thm)],[f12625]) ).
fof(f12692,plain,
( sQ1131_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12627,f249]) ).
fof(f12693,plain,
sQ1131_spl,
inference(contradiction_clause,[status(thm)],[f12692]) ).
fof(f13070,definition,
( sQ1166_spl
<=> ssList(skaf45(nil,sk7)) ),
introduced(definition,[new_symbols(definition,[sQ1166_spl])],[split_symbol_definition]) ).
fof(f13072,plain,
( sQ1166_spl
| ~ ssList(skaf45(nil,sk7)) ),
inference(component_clause,[status(thm)],[f13070]) ).
fof(f13135,plain,
( sQ1166_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f13072,f249]) ).
fof(f13136,plain,
sQ1166_spl,
inference(contradiction_clause,[status(thm)],[f13135]) ).
fof(f13163,plain,
( sQ302_spl
| ~ ssList(sk1)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3095,f284]) ).
fof(f13164,plain,
( sQ302_spl
| ~ sQ9_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f13163,f495,f513,f3093]) ).
fof(f13211,definition,
( sQ1184_spl
<=> ssList(skaf45(nil,sk5)) ),
introduced(definition,[new_symbols(definition,[sQ1184_spl])],[split_symbol_definition]) ).
fof(f13213,plain,
( sQ1184_spl
| ~ ssList(skaf45(nil,sk5)) ),
inference(component_clause,[status(thm)],[f13211]) ).
fof(f13270,plain,
( sQ1184_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f13213,f249]) ).
fof(f13271,plain,
sQ1184_spl,
inference(contradiction_clause,[status(thm)],[f13270]) ).
fof(f13376,definition,
( sQ1196_spl
<=> ssList(app(sk2,nil)) ),
introduced(definition,[new_symbols(definition,[sQ1196_spl])],[split_symbol_definition]) ).
fof(f13378,plain,
( sQ1196_spl
| ~ ssList(app(sk2,nil)) ),
inference(component_clause,[status(thm)],[f13376]) ).
fof(f13385,definition,
( sQ1197_spl
<=> ssList(skaf45(sk2,sk2)) ),
introduced(definition,[new_symbols(definition,[sQ1197_spl])],[split_symbol_definition]) ).
fof(f13387,plain,
( sQ1197_spl
| ~ ssList(skaf45(sk2,sk2)) ),
inference(component_clause,[status(thm)],[f13385]) ).
fof(f13416,plain,
( sQ1197_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f13387,f249]) ).
fof(f13417,plain,
sQ1197_spl,
inference(contradiction_clause,[status(thm)],[f13416]) ).
fof(f13419,plain,
( sQ1196_spl
| ~ sQ607_spl
| ~ ssList(sk2) ),
inference(forward_demodulation,[status(thm)],[f6340,f13378]) ).
fof(f13420,plain,
( sQ1196_spl
| ~ sQ607_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f13419,f430]) ).
fof(f13421,plain,
( sQ1196_spl
| ~ sQ607_spl ),
inference(contradiction_clause,[status(thm)],[f13420]) ).
fof(f14016,plain,
( ~ sQ665_spl
| ~ sQ64_spl
| segmentP(sk1,sk7)
| ~ ssList(app(sk1,nil))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f6939,f949]) ).
fof(f14023,definition,
( sQ1251_spl
<=> segmentP(sk1,sk7) ),
introduced(definition,[new_symbols(definition,[sQ1251_spl])],[split_symbol_definition]) ).
fof(f14024,plain,
( ~ sQ1251_spl
| segmentP(sk1,sk7) ),
inference(component_clause,[status(thm)],[f14023]) ).
fof(f14026,plain,
( ~ sQ665_spl
| ~ sQ64_spl
| sQ1251_spl
| ~ sQ302_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f14016,f495,f3093,f14023,f944,f6938]) ).
fof(f14027,plain,
( ~ sQ11_spl
| ~ sQ1251_spl
| ~ segmentP(sk2,sk7)
| sk7 = nil
| ~ ssList(sk7) ),
inference(resolution,[status(thm)],[f14024,f535]) ).
fof(f14034,definition,
( sQ1252_spl
<=> segmentP(sk2,sk7) ),
introduced(definition,[new_symbols(definition,[sQ1252_spl])],[split_symbol_definition]) ).
fof(f14037,plain,
( ~ sQ11_spl
| ~ sQ1251_spl
| ~ sQ1252_spl
| sQ19_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f14027,f507,f579,f14034,f14023,f531]) ).
fof(f14177,definition,
( sQ1269_spl
<=> ssList(skaf46(sk2,sk1)) ),
introduced(definition,[new_symbols(definition,[sQ1269_spl])],[split_symbol_definition]) ).
fof(f14179,plain,
( sQ1269_spl
| ~ ssList(skaf46(sk2,sk1)) ),
inference(component_clause,[status(thm)],[f14177]) ).
fof(f14216,plain,
( sQ1269_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14179,f248]) ).
fof(f14217,plain,
sQ1269_spl,
inference(contradiction_clause,[status(thm)],[f14216]) ).
fof(f14520,plain,
( ~ sQ607_spl
| ~ sQ63_spl
| segmentP(sk2,sk7)
| ~ ssList(app(sk2,nil))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f6340,f948]) ).
fof(f14527,plain,
( ~ sQ607_spl
| ~ sQ63_spl
| sQ1252_spl
| ~ sQ1196_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f14520,f495,f13376,f14034,f940,f6339]) ).
fof(f14610,plain,
( sQ361_spl
| ~ sQ885_spl
| ~ ssList(sk2) ),
inference(forward_demodulation,[status(thm)],[f9371,f3597]) ).
fof(f14611,plain,
( sQ361_spl
| ~ sQ885_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14610,f430]) ).
fof(f14612,plain,
( sQ361_spl
| ~ sQ885_spl ),
inference(contradiction_clause,[status(thm)],[f14611]) ).
fof(f15385,definition,
( sQ1306_spl
<=> ssList(skaf45(sk1,app(sk2,sk6))) ),
introduced(definition,[new_symbols(definition,[sQ1306_spl])],[split_symbol_definition]) ).
fof(f15387,plain,
( sQ1306_spl
| ~ ssList(skaf45(sk1,app(sk2,sk6))) ),
inference(component_clause,[status(thm)],[f15385]) ).
fof(f15390,plain,
( sQ1306_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f15387,f249]) ).
fof(f15391,plain,
sQ1306_spl,
inference(contradiction_clause,[status(thm)],[f15390]) ).
fof(f15527,plain,
( ~ sQ22_spl
| ~ sQ322_spl
| sk1 = app(sk2,sk6) ),
inference(forward_demodulation,[status(thm)],[f3285,f602]) ).
fof(f16619,definition,
( sQ1369_spl
<=> ssList(skaf51(nil)) ),
introduced(definition,[new_symbols(definition,[sQ1369_spl])],[split_symbol_definition]) ).
fof(f16621,plain,
( sQ1369_spl
| ~ ssList(skaf51(nil)) ),
inference(component_clause,[status(thm)],[f16619]) ).
fof(f16623,plain,
( sQ1369_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f16621,f242]) ).
fof(f16624,plain,
sQ1369_spl,
inference(contradiction_clause,[status(thm)],[f16623]) ).
fof(f17702,definition,
( sQ1457_spl
<=> sk1 = app(nil,sk1) ),
introduced(definition,[new_symbols(definition,[sQ1457_spl])],[split_symbol_definition]) ).
fof(f17704,plain,
( sQ1457_spl
| sk1 != app(nil,sk1) ),
inference(component_clause,[status(thm)],[f17702]) ).
fof(f18074,definition,
( sQ1485_spl
<=> ssList(skaf45(sk1,app(nil,sk6))) ),
introduced(definition,[new_symbols(definition,[sQ1485_spl])],[split_symbol_definition]) ).
fof(f18076,plain,
( sQ1485_spl
| ~ ssList(skaf45(sk1,app(nil,sk6))) ),
inference(component_clause,[status(thm)],[f18074]) ).
fof(f18081,plain,
( sQ1485_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f18076,f249]) ).
fof(f18082,plain,
sQ1485_spl,
inference(contradiction_clause,[status(thm)],[f18081]) ).
fof(f18479,plain,
( sQ1457_spl
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f17704,f273]) ).
fof(f18480,plain,
( sQ1457_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f18479,f429]) ).
fof(f18481,plain,
sQ1457_spl,
inference(contradiction_clause,[status(thm)],[f18480]) ).
fof(f19715,definition,
( sQ1664_spl
<=> ssItem(skaf50(nil)) ),
introduced(definition,[new_symbols(definition,[sQ1664_spl])],[split_symbol_definition]) ).
fof(f19717,plain,
( sQ1664_spl
| ~ ssItem(skaf50(nil)) ),
inference(component_clause,[status(thm)],[f19715]) ).
fof(f19718,definition,
( sQ1665_spl
<=> ssList(skaf53(nil)) ),
introduced(definition,[new_symbols(definition,[sQ1665_spl])],[split_symbol_definition]) ).
fof(f19720,plain,
( sQ1665_spl
| ~ ssList(skaf53(nil)) ),
inference(component_clause,[status(thm)],[f19718]) ).
fof(f19757,plain,
( sQ1665_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f19720,f240]) ).
fof(f19758,plain,
sQ1665_spl,
inference(contradiction_clause,[status(thm)],[f19757]) ).
fof(f19759,plain,
( sQ1664_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f19717,f243]) ).
fof(f19760,plain,
sQ1664_spl,
inference(contradiction_clause,[status(thm)],[f19759]) ).
fof(f20218,definition,
( sQ1724_spl
<=> ssList(skaf45(sk1,nil)) ),
introduced(definition,[new_symbols(definition,[sQ1724_spl])],[split_symbol_definition]) ).
fof(f20220,plain,
( sQ1724_spl
| ~ ssList(skaf45(sk1,nil)) ),
inference(component_clause,[status(thm)],[f20218]) ).
fof(f20230,plain,
( sQ1724_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f20220,f249]) ).
fof(f20231,plain,
sQ1724_spl,
inference(contradiction_clause,[status(thm)],[f20230]) ).
fof(f22396,plain,
( ~ sQ22_spl
| ~ sQ322_spl
| ~ sQ448_spl
| segmentP(sk1,sk2)
| ~ ssList(sk6) ),
inference(paramodulation,[status(thm)],[f15527,f4330]) ).
fof(f22403,plain,
( ~ sQ22_spl
| ~ sQ322_spl
| ~ sQ448_spl
| sQ4_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f22396,f537,f489,f4326,f3284,f601]) ).
fof(f22405,plain,
$false,
inference(sat_refutation,[status(thm)],[f492,f504,f516,f520,f522,f524,f527,f534,f540,f542,f604,f943,f947,f4329,f6089,f9850,f9861,f12224,f12301,f12563,f12590,f12693,f13136,f13164,f13271,f13417,f13421,f14026,f14037,f14217,f14527,f14612,f15391,f16624,f18082,f18481,f19758,f19760,f20231,f22403]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC083-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.49 % Computer : n005.cluster.edu
% 0.19/0.49 % Model : x86_64 x86_64
% 0.19/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.49 % Memory : 8046.5625MB
% 0.19/0.49 % OS : Linux 6.8.0-71-generic
% 0.19/0.49 % CPULimit : 300
% 0.19/0.49 % WCLimit : 300
% 0.19/0.49 % DateTime : Mon Sep 21 07:54:18 UTC 2026
% 0.19/0.49 % CPUTime :
% 0.23/0.52 % Drodi V4.1.1
% 216.37/28.08 % Refutation found
% 216.37/28.08 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 216.37/28.08 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 216.37/28.17 % Elapsed time: 27.660259 seconds
% 216.37/28.17 % CPU time: 218.601986 seconds
% 216.37/28.17 % Total memory used: 563.985 MB
% 216.37/28.17 % Net memory used: 519.002 MB
%------------------------------------------------------------------------------