%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC021-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 02:39:37 PM UTC 2026
% Result : Unsatisfiable 68.55s 9.25s
% Output : CNFRefutation 68.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 48
% Syntax : Number of formulae : 173 ( 29 unt; 20 def)
% Number of atoms : 576 ( 67 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 800 ( 397 ~; 383 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 29 ( 27 usr; 21 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 188 ( 188 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [U] : ssItem(skaf44(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [U,V] : ssList(skaf48(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(f56,axiom,
! [U] :
( segmentP(U,nil)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f60,axiom,
! [U] :
( frontsegP(U,nil)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f61,axiom,
! [U] :
( frontsegP(U,U)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [U] :
( strictorderedP(cons(U,nil))
| ~ ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f72,axiom,
! [U,V] :
( ssItem(V)
| duplicatefreeP(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(f75,axiom,
! [U] :
( nil = U
| ssList(tl(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(f86,axiom,
! [U,V] :
( ssList(cons(U,V))
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f98,axiom,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != nil ),
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(f104,axiom,
! [U] :
( nil = U
| cons(hd(U),tl(U)) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f144,axiom,
! [U,V,W] :
( frontsegP(W,U)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != W ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f154,axiom,
! [U,V,W] :
( frontsegP(U,W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ frontsegP(V,W)
| ~ frontsegP(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f178,axiom,
! [U,V,W,X] :
( frontsegP(cons(W,U),cons(X,V))
| ~ ssItem(W)
| ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(V)
| W != X
| ~ frontsegP(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f179,axiom,
! [U,V,W,X,Y] :
( ~ ssList(Y)
| ~ duplicatefreeP(Y)
| ~ ssItem(V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssList(X)
| app(app(U,cons(V,W)),cons(V,X)) != Y ),
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,
frontsegP(sk4,sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
! [A] :
( ~ frontsegP(sk1,A)
| ~ frontsegP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
! [A] :
( ~ strictorderedP(A)
| ~ segmentP(A,sk3)
| ~ frontsegP(sk4,A)
| ~ neq(sk3,A)
| ~ ssList(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
( nil != sk1
| nil != sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f204,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f243,plain,
! [X0] : ssItem(skaf44(X0)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f244,plain,
! [X0,X1] : ssList(skaf48(X0,X1)),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f247,plain,
! [X0,X1] : ssList(skaf45(X0,X1)),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f252,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f256,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f257,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f262,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f268,plain,
( ! [V] : ssItem(V)
| ! [U] :
( duplicatefreeP(U)
| ~ ssList(U) ) ),
inference(miniscoping,[status(thm)],[f72]) ).
fof(f269,plain,
! [X0,X1] :
( ssItem(X1)
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f268]) ).
fof(f270,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f272,plain,
! [X0] :
( nil = X0
| ssList(tl(X0))
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f282,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f283,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f295,plain,
! [V] :
( ~ ssList(V)
| ! [U] :
( ~ ssItem(U)
| cons(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f98]) ).
fof(f296,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f295]) ).
fof(f299,plain,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f303,plain,
! [X0] :
( nil = X0
| cons(hd(X0),tl(X0)) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f356,plain,
! [U,W] :
( frontsegP(W,U)
| ~ ssList(W)
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| app(U,V) != W ) ),
inference(miniscoping,[status(thm)],[f144]) ).
fof(f357,plain,
! [X0,X1,X2] :
( frontsegP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != X2 ),
inference(cnf_transformation,[status(thm)],[f356]) ).
fof(f374,plain,
! [U,W] :
( frontsegP(U,W)
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ~ ssList(W)
| ~ frontsegP(V,W)
| ~ frontsegP(U,V) ) ),
inference(miniscoping,[status(thm)],[f154]) ).
fof(f375,plain,
! [X0,X1,X2] :
( frontsegP(X0,X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f374]) ).
fof(f412,plain,
! [X0,X1,X2,X3] :
( frontsegP(cons(X2,X0),cons(X3,X1))
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ ssList(X0)
| ~ ssList(X1)
| X2 != X3
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f178]) ).
fof(f413,plain,
! [Y] :
( ~ ssList(Y)
| ~ duplicatefreeP(Y)
| ! [V] :
( ~ ssItem(V)
| ! [U] :
( ~ ssList(U)
| ! [W] :
( ~ ssList(W)
| ! [X] :
( ~ ssList(X)
| app(app(U,cons(V,W)),cons(V,X)) != Y ) ) ) ) ),
inference(miniscoping,[status(thm)],[f179]) ).
fof(f414,plain,
! [X0,X1,X2,X3,X4] :
( ~ ssList(X4)
| ~ duplicatefreeP(X4)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X0,cons(X1,X2)),cons(X1,X3)) != X4 ),
inference(cnf_transformation,[status(thm)],[f413]) ).
fof(f427,plain,
ssList(sk1),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f428,plain,
ssList(sk2),
inference(cnf_transformation,[status(thm)],[f187]) ).
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,
frontsegP(sk4,sk3),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f435,plain,
! [X0] :
( ~ frontsegP(sk1,X0)
| ~ frontsegP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f436,plain,
! [X0] :
( ~ strictorderedP(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0)
| ~ neq(sk3,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f437,plain,
( nil != sk1
| nil != sk2 ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f438,definition,
! [X0] :
( sQ0_spl
<=> ( duplicatefreeP(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f439,plain,
! [X0] :
( ~ sQ0_spl
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f441,definition,
! [X1] :
( sQ1_spl
<=> ssItem(X1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f442,plain,
! [X0] :
( ~ sQ1_spl
| ssItem(X0) ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f269,f438,f441]) ).
fof(f445,definition,
( sQ2_spl
<=> nil = sk2 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f448,definition,
( sQ3_spl
<=> nil = sk1 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f449,plain,
( ~ sQ3_spl
| nil = sk1 ),
inference(component_clause,[status(thm)],[f448]) ).
fof(f451,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f437,f445,f448]) ).
fof(f468,plain,
! [X1,X0] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f357]) ).
fof(f469,plain,
! [X0,X1] :
( frontsegP(app(X1,X0),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f468,f282]) ).
fof(f474,plain,
! [X0,X1,X3] :
( frontsegP(cons(X3,X0),cons(X3,X1))
| ~ ssItem(X3)
| ~ ssItem(X3)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f412]) ).
fof(f475,plain,
! [X0,X1,X2] :
( frontsegP(cons(X2,X0),cons(X2,X1))
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f474]) ).
fof(f476,plain,
! [X0,X1,X2,X3] :
( ~ ssList(app(app(X2,cons(X3,X1)),cons(X3,X0)))
| ~ duplicatefreeP(app(app(X2,cons(X3,X1)),cons(X3,X0)))
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f414]) ).
fof(f485,plain,
frontsegP(sk2,sk3),
inference(forward_demodulation,[status(thm)],[f431,f433]) ).
fof(f486,plain,
frontsegP(sk2,sk1),
inference(forward_demodulation,[status(thm)],[f432,f485]) ).
fof(f488,plain,
! [X0] :
( ~ strictorderedP(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0)
| ~ neq(sk1,X0)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f432,f436]) ).
fof(f489,plain,
! [X0] :
( ~ strictorderedP(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk2,X0)
| ~ neq(sk1,X0)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f431,f488]) ).
fof(f490,plain,
! [X0] :
( ~ strictorderedP(X0)
| ~ segmentP(X0,sk1)
| ~ frontsegP(sk2,X0)
| ~ neq(sk1,X0)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f432,f489]) ).
fof(f491,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| ~ ssList(app(app(X2,cons(X3,X1)),cons(X3,X0)))
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f476,f439]) ).
fof(f494,definition,
( sQ4_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f496,plain,
( sQ4_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f494]) ).
fof(f502,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f496,f204]) ).
fof(f503,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f502]) ).
fof(f533,plain,
! [X0] :
( sk1 = X0
| neq(sk1,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f299,f427]) ).
fof(f584,definition,
( sQ6_spl
<=> ssList(sk2) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f586,plain,
( sQ6_spl
| ~ ssList(sk2) ),
inference(component_clause,[status(thm)],[f584]) ).
fof(f587,definition,
( sQ7_spl
<=> frontsegP(sk2,sk2) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f598,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f586,f428]) ).
fof(f599,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f598]) ).
fof(f600,plain,
! [X0] :
( ~ strictorderedP(X0)
| ~ segmentP(X0,sk1)
| ~ frontsegP(sk2,X0)
| ~ ssList(X0)
| sk1 = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f533,f490]) ).
fof(f601,plain,
( ~ frontsegP(sk1,sk1)
| ~ frontsegP(sk2,sk1)
| ~ ssList(sk1)
| sk1 = nil
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f533,f435]) ).
fof(f603,plain,
! [X0] :
( ~ strictorderedP(X0)
| ~ segmentP(X0,sk1)
| ~ frontsegP(sk2,X0)
| sk1 = X0
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f600]) ).
fof(f604,definition,
( sQ10_spl
<=> ssList(sk1) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f606,plain,
( sQ10_spl
| ~ ssList(sk1) ),
inference(component_clause,[status(thm)],[f604]) ).
fof(f607,definition,
( sQ11_spl
<=> frontsegP(sk2,sk1) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f609,plain,
( sQ11_spl
| ~ frontsegP(sk2,sk1) ),
inference(component_clause,[status(thm)],[f607]) ).
fof(f610,definition,
( sQ12_spl
<=> frontsegP(sk1,sk1) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f612,plain,
( sQ12_spl
| ~ frontsegP(sk1,sk1) ),
inference(component_clause,[status(thm)],[f610]) ).
fof(f613,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sQ3_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f601,f494,f448,f604,f607,f610]) ).
fof(f618,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f606,f427]) ).
fof(f619,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f618]) ).
fof(f627,plain,
( sQ12_spl
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f612,f257]) ).
fof(f628,plain,
( sQ12_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f627,f604,f610]) ).
fof(f629,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f609,f486]) ).
fof(f630,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f629]) ).
fof(f631,plain,
! [X0] :
( ~ sQ3_spl
| ~ strictorderedP(X0)
| ~ segmentP(X0,nil)
| ~ frontsegP(sk2,X0)
| sk1 = X0
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f449,f603]) ).
fof(f642,plain,
! [X0] :
( ~ sQ3_spl
| ~ strictorderedP(X0)
| ~ segmentP(X0,nil)
| ~ frontsegP(sk2,X0)
| nil = X0
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f449,f631]) ).
fof(f643,plain,
! [X0] :
( ~ sQ3_spl
| ~ strictorderedP(X0)
| ~ frontsegP(sk2,X0)
| nil = X0
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f642,f252]) ).
fof(f694,plain,
! [X0] :
( ~ sQ3_spl
| ~ ssItem(X0)
| ~ frontsegP(sk2,cons(X0,nil))
| nil = cons(X0,nil)
| ~ ssList(cons(X0,nil)) ),
inference(resolution,[status(thm)],[f643,f262]) ).
fof(f763,plain,
app(sk2,nil) = sk2,
inference(resolution,[status(thm)],[f270,f428]) ).
fof(f824,plain,
( frontsegP(sk2,sk2)
| ~ ssList(sk2)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f763,f469]) ).
fof(f829,plain,
( sQ7_spl
| ~ sQ6_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f824,f494,f584,f587]) ).
fof(f1111,plain,
! [X0] :
( ~ sQ3_spl
| ~ ssItem(X0)
| ~ frontsegP(sk2,cons(X0,nil))
| nil = cons(X0,nil)
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f283,f694]) ).
fof(f1119,definition,
! [X0] :
( sQ59_spl
<=> ( ~ ssItem(X0)
| ~ frontsegP(sk2,cons(X0,nil))
| nil = cons(X0,nil)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f1120,plain,
! [X0] :
( ~ sQ59_spl
| ~ ssItem(X0)
| ~ frontsegP(sk2,cons(X0,nil))
| nil = cons(X0,nil)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1119]) ).
fof(f1122,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f1111,f1119,f494,f448]) ).
fof(f1123,plain,
! [X0] :
( ~ sQ59_spl
| ~ frontsegP(sk2,cons(X0,nil))
| nil = cons(X0,nil)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1120]) ).
fof(f1125,plain,
! [X0,X1] :
( ~ sQ59_spl
| ~ ssList(sk2)
| ~ ssList(X1)
| ~ ssList(cons(X0,nil))
| ~ frontsegP(X1,cons(X0,nil))
| ~ frontsegP(sk2,X1)
| nil = cons(X0,nil)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1123,f375]) ).
fof(f1126,definition,
! [X0,X1] :
( sQ60_spl
<=> ( ~ ssList(X1)
| ~ ssList(cons(X0,nil))
| ~ frontsegP(X1,cons(X0,nil))
| ~ frontsegP(sk2,X1)
| nil = cons(X0,nil)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f1127,plain,
! [X0,X1] :
( ~ sQ60_spl
| ~ ssList(X1)
| ~ ssList(cons(X0,nil))
| ~ frontsegP(X1,cons(X0,nil))
| ~ frontsegP(sk2,X1)
| nil = cons(X0,nil)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1126]) ).
fof(f1129,plain,
( ~ sQ59_spl
| ~ sQ6_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f1125,f1126,f584,f1119]) ).
fof(f1130,plain,
! [X0,X1] :
( ~ sQ60_spl
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(X1,cons(X0,nil))
| ~ frontsegP(sk2,X1)
| nil = cons(X0,nil)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1127,f283]) ).
fof(f1131,definition,
! [X0,X1] :
( sQ61_spl
<=> ( ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(X1,cons(X0,nil))
| ~ frontsegP(sk2,X1)
| nil = cons(X0,nil)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f1132,plain,
! [X0,X1] :
( ~ sQ61_spl
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(X1,cons(X0,nil))
| ~ frontsegP(sk2,X1)
| nil = cons(X0,nil)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1131]) ).
fof(f1134,plain,
( ~ sQ60_spl
| ~ sQ4_spl
| sQ61_spl ),
inference(split_clause,[status(thm)],[f1130,f1131,f494,f1126]) ).
fof(f1135,plain,
! [X0,X1] :
( ~ sQ61_spl
| ~ ssList(X1)
| ~ frontsegP(X1,cons(X0,nil))
| ~ frontsegP(sk2,X1)
| nil = cons(X0,nil)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1132]) ).
fof(f1199,plain,
! [X0,X1] :
( ~ sQ61_spl
| ~ ssList(cons(X1,X0))
| ~ frontsegP(sk2,cons(X1,X0))
| nil = cons(X1,nil)
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(X0,nil) ),
inference(resolution,[status(thm)],[f475,f1135]) ).
fof(f1215,definition,
! [X0,X1] :
( sQ69_spl
<=> ( ~ ssList(cons(X1,X0))
| ~ frontsegP(sk2,cons(X1,X0))
| nil = cons(X1,nil)
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f1216,plain,
! [X0,X1] :
( ~ sQ69_spl
| ~ ssList(cons(X1,X0))
| ~ frontsegP(sk2,cons(X1,X0))
| nil = cons(X1,nil)
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ),
inference(component_clause,[status(thm)],[f1215]) ).
fof(f1218,plain,
( ~ sQ61_spl
| ~ sQ4_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f1199,f1215,f494,f1131]) ).
fof(f1220,plain,
! [X0,X1] :
( ~ sQ69_spl
| ~ ssList(cons(X1,X0))
| ~ frontsegP(sk2,cons(X1,X0))
| nil = cons(X1,nil)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ),
inference(duplicate_literals_removal,[status(thm)],[f1216]) ).
fof(f1221,plain,
! [X0,X1] :
( ~ sQ69_spl
| ~ ssList(cons(X1,X0))
| ~ frontsegP(sk2,cons(X1,X0))
| nil = cons(X1,nil)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1220,f256]) ).
fof(f1374,plain,
! [X0,X1] :
( ~ sQ69_spl
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ frontsegP(sk2,cons(X1,X0))
| nil = cons(X1,nil)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1221,f283]) ).
fof(f1375,plain,
! [X0,X1] :
( ~ sQ69_spl
| ~ frontsegP(sk2,cons(X1,X0))
| nil = cons(X1,nil)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1374]) ).
fof(f2172,plain,
! [X0] :
( ssList(app(sk2,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f282,f428]) ).
fof(f2185,plain,
! [X0,X1] :
( ssList(app(app(sk2,X0),X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2172,f282]) ).
fof(f3494,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ ssList(cons(X2,X0))
| ~ ssList(cons(X2,X1))
| ~ ssItem(X2)
| ~ ssList(sk2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f491,f2185]) ).
fof(f3495,definition,
! [X0,X1,X2] :
( sQ194_spl
<=> ( ~ ssList(cons(X2,X0))
| ~ ssList(cons(X2,X1))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ194_spl])],[split_symbol_definition]) ).
fof(f3496,plain,
! [X0,X1,X2] :
( ~ sQ194_spl
| ~ ssList(cons(X2,X0))
| ~ ssList(cons(X2,X1))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3495]) ).
fof(f3498,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| sQ194_spl ),
inference(split_clause,[status(thm)],[f3494,f3495,f584,f438]) ).
fof(f3499,plain,
! [X0,X1,X2] :
( ~ sQ194_spl
| ~ ssList(cons(X2,X0))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3496,f283]) ).
fof(f3539,plain,
! [X0,X1] :
( ~ sQ69_spl
| ~ sQ1_spl
| ~ frontsegP(sk2,cons(X1,X0))
| nil = cons(X1,nil)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f1375,f442]) ).
fof(f3563,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ ssList(X1)
| cons(X0,X1) != nil ),
inference(backward_subsumption_resolution,[status(thm)],[f296,f442]) ).
fof(f3640,definition,
! [X0,X2] :
( sQ195_spl
<=> ( ~ ssList(cons(X2,X0))
| ~ ssItem(X2)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ195_spl])],[split_symbol_definition]) ).
fof(f3641,plain,
! [X0,X1] :
( ~ sQ195_spl
| ~ ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3640]) ).
fof(f3643,definition,
! [X1] :
( sQ196_spl
<=> ~ ssList(X1) ),
introduced(definition,[new_symbols(definition,[sQ196_spl])],[split_symbol_definition]) ).
fof(f3644,plain,
! [X0] :
( ~ sQ196_spl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3643]) ).
fof(f3646,plain,
( ~ sQ194_spl
| sQ196_spl
| sQ195_spl ),
inference(split_clause,[status(thm)],[f3499,f3640,f3643,f3495]) ).
fof(f3649,plain,
! [X0,X1] :
( ~ sQ195_spl
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3641,f283]) ).
fof(f3708,plain,
! [X0] :
( ~ sQ195_spl
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3649,f243]) ).
fof(f3709,plain,
( ~ sQ195_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f244,f3708]) ).
fof(f3738,plain,
~ sQ195_spl,
inference(contradiction_clause,[status(thm)],[f3709]) ).
fof(f3739,plain,
( ~ sQ196_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f244,f3644]) ).
fof(f3740,plain,
~ sQ196_spl,
inference(contradiction_clause,[status(thm)],[f3739]) ).
fof(f3914,definition,
( sQ208_spl
<=> ssList(skaf45(sk2,sk2)) ),
introduced(definition,[new_symbols(definition,[sQ208_spl])],[split_symbol_definition]) ).
fof(f3916,plain,
( sQ208_spl
| ~ ssList(skaf45(sk2,sk2)) ),
inference(component_clause,[status(thm)],[f3914]) ).
fof(f3922,plain,
( sQ208_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3916,f247]) ).
fof(f3923,plain,
sQ208_spl,
inference(contradiction_clause,[status(thm)],[f3922]) ).
fof(f3974,plain,
! [X0] :
( ~ sQ1_spl
| cons(X0,nil) != nil ),
inference(resolution,[status(thm)],[f3563,f204]) ).
fof(f3978,plain,
! [X0,X1] :
( ~ sQ69_spl
| ~ sQ1_spl
| ~ frontsegP(sk2,cons(X1,X0))
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f3539,f3974]) ).
fof(f4078,plain,
( nil = sk2
| cons(hd(sk2),tl(sk2)) = sk2 ),
inference(resolution,[status(thm)],[f303,f428]) ).
fof(f4083,definition,
( sQ211_spl
<=> cons(hd(sk2),tl(sk2)) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ211_spl])],[split_symbol_definition]) ).
fof(f4084,plain,
( ~ sQ211_spl
| cons(hd(sk2),tl(sk2)) = sk2 ),
inference(component_clause,[status(thm)],[f4083]) ).
fof(f4086,plain,
( sQ2_spl
| sQ211_spl ),
inference(split_clause,[status(thm)],[f4078,f4083,f445]) ).
fof(f5047,plain,
( ~ sQ211_spl
| ~ sQ69_spl
| ~ sQ1_spl
| ~ frontsegP(sk2,sk2)
| ~ ssList(tl(sk2)) ),
inference(paramodulation,[status(thm)],[f4084,f3978]) ).
fof(f5052,definition,
( sQ230_spl
<=> ssList(tl(sk2)) ),
introduced(definition,[new_symbols(definition,[sQ230_spl])],[split_symbol_definition]) ).
fof(f5054,plain,
( sQ230_spl
| ~ ssList(tl(sk2)) ),
inference(component_clause,[status(thm)],[f5052]) ).
fof(f5077,plain,
( ~ sQ211_spl
| ~ sQ69_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ230_spl ),
inference(split_clause,[status(thm)],[f5047,f5052,f587,f441,f1215,f4083]) ).
fof(f5112,plain,
( sQ230_spl
| nil = sk2
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f5054,f272]) ).
fof(f5113,plain,
( sQ230_spl
| sQ2_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f5112,f584,f445,f5052]) ).
fof(f5114,plain,
$false,
inference(sat_refutation,[status(thm)],[f444,f451,f503,f599,f613,f619,f628,f630,f829,f1122,f1129,f1134,f1218,f3498,f3646,f3738,f3740,f3923,f4086,f5077,f5113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC021-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.48 % Computer : n015.cluster.edu
% 0.18/0.48 % Model : x86_64 x86_64
% 0.18/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.48 % Memory : 8046.5625MB
% 0.18/0.48 % OS : Linux 6.8.0-71-generic
% 0.18/0.48 % CPULimit : 300
% 0.18/0.48 % WCLimit : 300
% 0.18/0.48 % DateTime : Mon Sep 21 07:52:52 UTC 2026
% 0.18/0.49 % CPUTime :
% 0.22/0.54 % Drodi V4.1.1
% 68.55/9.25 % Refutation found
% 68.55/9.25 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 68.55/9.25 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.94/9.31 % Elapsed time: 8.796232 seconds
% 7.94/9.31 % CPU time: 69.133037 seconds
% 7.94/9.31 % Total memory used: 389.669 MB
% 7.94/9.31 % Net memory used: 365.563 MB
%------------------------------------------------------------------------------