%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC079-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 02:39:52 PM UTC 2026
% Result : Unsatisfiable 129.11s 16.77s
% Output : CNFRefutation 48.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 64
% Syntax : Number of formulae : 258 ( 28 unt; 32 def)
% Number of atoms : 846 ( 121 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1152 ( 564 ~; 556 |; 0 &)
% ( 32 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 41 ( 39 usr; 33 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 225 ( 225 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [U] : ssItem(skaf83(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [U] : ssList(skaf82(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [U] : ssList(skaf58(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [U,V] : ssList(skaf45(U,V)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [U] :
( segmentP(U,U)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,axiom,
! [U] :
( frontsegP(U,nil)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f72,axiom,
! [U,V] :
( ssItem(V)
| duplicatefreeP(U)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f74,axiom,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f75,axiom,
! [U] :
( nil = U
| ssList(tl(U))
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f76,axiom,
! [U] :
( nil = U
| ssItem(hd(U))
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [U,V] :
( ssList(app(V,U))
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f86,axiom,
! [U,V] :
( ssList(cons(U,V))
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,axiom,
! [U,V] :
( tl(cons(U,V)) = V
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,axiom,
! [U,V] :
( hd(cons(U,V)) = U
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f99,axiom,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f100,axiom,
! [U,V] :
( V = U
| neq(V,U)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f101,axiom,
! [U] :
( cons(skaf44(U),nil) = U
| ~ ssList(U)
| ~ singletonP(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f109,axiom,
! [U] :
( nil = U
| cons(skaf83(U),skaf82(U)) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f115,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f116,axiom,
! [U,V] :
( singletonP(V)
| ~ ssList(V)
| ~ ssItem(U)
| cons(U,nil) != V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f132,axiom,
! [U,V] :
( app(V,skaf45(U,V)) = U
| ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f186,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f187,negated_conjecture,
ssList(sk2),
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,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
! [A] :
( ~ neq(sk4,nil)
| ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
! [A,B] :
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| hd(sk4) != B
| cons(B,nil) != A
| ~ ssItem(B)
| sk3 = A
| ~ ssList(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f205,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f209,plain,
! [X0] : ssItem(skaf83(X0)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f210,plain,
! [X0] : ssList(skaf82(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f234,plain,
! [X0] : ssList(skaf58(X0)),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f248,plain,
! [X0,X1] : ssList(skaf45(X0,X1)),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f254,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f257,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f269,plain,
( ! [V] : ssItem(V)
| ! [U] :
( duplicatefreeP(U)
| ~ ssList(U) ) ),
inference(miniscoping,[status(thm)],[f72]) ).
fof(f270,plain,
! [X0,X1] :
( ssItem(X1)
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f272,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f273,plain,
! [X0] :
( nil = X0
| ssList(tl(X0))
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f274,plain,
! [X0] :
( nil = X0
| ssItem(hd(X0))
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f283,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f284,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f294,plain,
! [X0,X1] :
( tl(cons(X0,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f295,plain,
! [X0,X1] :
( hd(cons(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f298,plain,
! [V] :
( ~ ssList(V)
| ! [U] :
( ~ ssItem(U)
| cons(U,V) != V ) ),
inference(miniscoping,[status(thm)],[f99]) ).
fof(f299,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != X1 ),
inference(cnf_transformation,[status(thm)],[f298]) ).
fof(f300,plain,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f301,plain,
! [X0] :
( cons(skaf44(X0),nil) = X0
| ~ ssList(X0)
| ~ singletonP(X0) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f309,plain,
! [X0] :
( nil = X0
| cons(skaf83(X0),skaf82(X0)) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f318,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ~ neq(U,V)
| U != V ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f319,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f318]) ).
fof(f320,plain,
! [V] :
( singletonP(V)
| ~ ssList(V)
| ! [U] :
( ~ ssItem(U)
| cons(U,nil) != V ) ),
inference(miniscoping,[status(thm)],[f116]) ).
fof(f321,plain,
! [X0,X1] :
( singletonP(X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,nil) != X1 ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f342,plain,
! [X0,X1] :
( app(X1,skaf45(X0,X1)) = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f402,plain,
! [X0,X1,X2,X3] :
( segmentP(app(app(X3,X0),X2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f413,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(f414,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(f415,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)],[f414]) ).
fof(f428,plain,
ssList(sk1),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f429,plain,
ssList(sk2),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f432,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f433,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f434,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f440,plain,
( ~ neq(sk4,nil)
| ! [A] :
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A) ) ),
inference(miniscoping,[status(thm)],[f196]) ).
fof(f441,plain,
! [X0] :
( ~ neq(sk4,nil)
| ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f440]) ).
fof(f442,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| ! [B] :
( hd(sk4) != B
| ! [A] :
( cons(B,nil) != A
| ~ ssItem(B)
| sk3 = A
| ~ ssList(A) ) ) ),
inference(miniscoping,[status(thm)],[f197]) ).
fof(f443,plain,
! [X0,X1] :
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| hd(sk4) != X1
| cons(X1,nil) != X0
| ~ ssItem(X1)
| sk3 = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f442]) ).
fof(f444,definition,
! [X0] :
( sQ0_spl
<=> ( duplicatefreeP(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f445,plain,
! [X0] :
( ~ sQ0_spl
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f444]) ).
fof(f447,definition,
! [X1] :
( sQ1_spl
<=> ssItem(X1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f448,plain,
! [X0] :
( ~ sQ1_spl
| ssItem(X0) ),
inference(component_clause,[status(thm)],[f447]) ).
fof(f450,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f270,f444,f447]) ).
fof(f451,definition,
( sQ2_spl
<=> neq(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f452,plain,
( ~ sQ2_spl
| neq(sk2,nil) ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f454,plain,
sQ2_spl,
inference(split_clause,[status(thm)],[f434,f451]) ).
fof(f455,definition,
( sQ3_spl
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( sQ3_spl
| ~ neq(sk4,nil) ),
inference(component_clause,[status(thm)],[f455]) ).
fof(f459,definition,
! [X0] :
( sQ4_spl
<=> ( ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f460,plain,
! [X0] :
( ~ sQ4_spl
| ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f459]) ).
fof(f463,definition,
! [X0,X1] :
( sQ5_spl
<=> ( hd(sk4) != X1
| cons(X1,nil) != X0
| ~ ssItem(X1)
| sk3 = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f464,plain,
! [X0,X1] :
( ~ sQ5_spl
| hd(sk4) != X1
| cons(X1,nil) != X0
| ~ ssItem(X1)
| sk3 = X0
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f463]) ).
fof(f466,definition,
( sQ6_spl
<=> neq(nil,sk4) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f468,plain,
( sQ6_spl
| ~ neq(nil,sk4) ),
inference(component_clause,[status(thm)],[f466]) ).
fof(f470,plain,
( ~ sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f441,f459,f455]) ).
fof(f471,plain,
( ~ sQ3_spl
| ~ sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f443,f463,f466,f455]) ).
fof(f479,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f319]) ).
fof(f480,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f479]) ).
fof(f481,plain,
! [X0] :
( singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil))
| ~ ssItem(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f321]) ).
fof(f494,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)],[f413]) ).
fof(f495,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)],[f494]) ).
fof(f496,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)],[f415]) ).
fof(f505,plain,
( sQ3_spl
| ~ neq(sk2,nil) ),
inference(forward_demodulation,[status(thm)],[f432,f457]) ).
fof(f506,plain,
( sQ3_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f505,f452]) ).
fof(f507,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f506]) ).
fof(f508,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)],[f496,f445]) ).
fof(f509,plain,
! [X0,X1] :
( ~ sQ5_spl
| hd(sk4) != X1
| cons(X1,nil) != X0
| ~ ssItem(X1)
| sk1 = X0
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f433,f464]) ).
fof(f510,plain,
! [X0,X1] :
( ~ sQ5_spl
| hd(sk2) != X1
| cons(X1,nil) != X0
| ~ ssItem(X1)
| sk1 = X0
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f432,f509]) ).
fof(f511,plain,
( ~ sQ5_spl
| ~ ssItem(hd(sk2))
| sk1 = cons(hd(sk2),nil)
| ~ ssList(cons(hd(sk2),nil)) ),
inference(destructive_equality_resolution,[status(thm)],[f510]) ).
fof(f514,definition,
( sQ7_spl
<=> ssList(sk2) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f516,plain,
( sQ7_spl
| ~ ssList(sk2) ),
inference(component_clause,[status(thm)],[f514]) ).
fof(f524,plain,
( sQ6_spl
| ~ neq(nil,sk2) ),
inference(forward_demodulation,[status(thm)],[f432,f468]) ).
fof(f527,definition,
( sQ10_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f529,plain,
( sQ10_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f527]) ).
fof(f535,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f529,f205]) ).
fof(f536,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f535]) ).
fof(f537,plain,
( ~ sQ5_spl
| ~ ssItem(hd(sk2))
| sk1 = cons(hd(sk2),nil)
| ~ ssList(nil)
| ~ ssItem(hd(sk2)) ),
inference(resolution,[status(thm)],[f284,f511]) ).
fof(f538,definition,
( sQ12_spl
<=> ssItem(hd(sk2)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f539,plain,
( ~ sQ12_spl
| ssItem(hd(sk2)) ),
inference(component_clause,[status(thm)],[f538]) ).
fof(f540,plain,
( sQ12_spl
| ~ ssItem(hd(sk2)) ),
inference(component_clause,[status(thm)],[f538]) ).
fof(f541,definition,
( sQ13_spl
<=> sk1 = cons(hd(sk2),nil) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f542,plain,
( ~ sQ13_spl
| sk1 = cons(hd(sk2),nil) ),
inference(component_clause,[status(thm)],[f541]) ).
fof(f544,plain,
( ~ sQ5_spl
| sQ13_spl
| ~ sQ10_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f537,f538,f527,f541,f463]) ).
fof(f551,plain,
( sQ12_spl
| nil = sk2
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f540,f274]) ).
fof(f552,definition,
( sQ14_spl
<=> nil = sk2 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f553,plain,
( ~ sQ14_spl
| nil = sk2 ),
inference(component_clause,[status(thm)],[f552]) ).
fof(f555,plain,
( sQ12_spl
| sQ14_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f551,f514,f552,f538]) ).
fof(f556,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f516,f429]) ).
fof(f557,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f556]) ).
fof(f560,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| neq(nil,nil) ),
inference(backward_demodulation,[status(thm)],[f553,f452]) ).
fof(f574,plain,
! [X0] :
( ~ sQ12_spl
| hd(cons(hd(sk2),X0)) = hd(sk2)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f539,f295]) ).
fof(f587,plain,
! [X0] :
( ~ sQ12_spl
| ~ ssList(X0)
| cons(hd(sk2),X0) != X0 ),
inference(resolution,[status(thm)],[f299,f539]) ).
fof(f616,plain,
( sQ6_spl
| nil = sk2
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f300,f524]) ).
fof(f617,plain,
! [X0] :
( ~ sQ4_spl
| ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f300,f460]) ).
fof(f620,plain,
( sQ6_spl
| sQ14_spl
| ~ sQ10_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f616,f514,f527,f552,f466]) ).
fof(f621,definition,
! [X0] :
( sQ16_spl
<=> ( ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ ssList(X0)
| X0 = nil
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f622,plain,
! [X0] :
( ~ sQ16_spl
| ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ ssList(X0)
| X0 = nil
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f621]) ).
fof(f624,plain,
( ~ sQ4_spl
| sQ16_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f617,f527,f621,f459]) ).
fof(f625,plain,
! [X0] :
( ~ sQ16_spl
| ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| X0 = nil
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f622]) ).
fof(f651,plain,
( ~ sQ13_spl
| ssList(sk1)
| ~ ssList(nil)
| ~ ssItem(hd(sk2)) ),
inference(paramodulation,[status(thm)],[f542,f284]) ).
fof(f652,definition,
( sQ19_spl
<=> ssList(sk1) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f655,plain,
( ~ sQ13_spl
| sQ19_spl
| ~ sQ10_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f651,f538,f527,f652,f541]) ).
fof(f671,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f560,f480]) ).
fof(f672,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f671,f527,f552,f451]) ).
fof(f705,definition,
( sQ23_spl
<=> nil = sk1 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f706,plain,
( ~ sQ23_spl
| nil = sk1 ),
inference(component_clause,[status(thm)],[f705]) ).
fof(f782,definition,
! [X1] :
( sQ31_spl
<=> ( ~ ssList(X1)
| ~ ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f783,plain,
! [X0] :
( ~ sQ31_spl
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f782]) ).
fof(f844,plain,
( ~ sQ12_spl
| cons(hd(sk2),nil) != nil ),
inference(resolution,[status(thm)],[f587,f205]) ).
fof(f846,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| sk1 != nil ),
inference(forward_demodulation,[status(thm)],[f542,f844]) ).
fof(f849,plain,
( ~ sQ16_spl
| ~ ssList(sk1)
| ~ segmentP(sk2,sk1)
| sk1 = nil
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f625,f254]) ).
fof(f858,definition,
( sQ35_spl
<=> segmentP(sk2,sk1) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f861,plain,
( ~ sQ16_spl
| ~ sQ35_spl
| sQ23_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f849,f652,f705,f858,f621]) ).
fof(f862,plain,
( ~ sQ23_spl
| ~ sQ12_spl
| ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f706,f846]) ).
fof(f863,plain,
( ~ sQ23_spl
| ~ sQ12_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f862]) ).
fof(f1141,plain,
! [X0,X1] : app(nil,skaf45(X0,X1)) = skaf45(X0,X1),
inference(resolution,[status(thm)],[f272,f248]) ).
fof(f1168,plain,
app(nil,sk1) = sk1,
inference(resolution,[status(thm)],[f272,f428]) ).
fof(f1233,plain,
( ~ sQ12_spl
| hd(cons(hd(sk2),nil)) = hd(sk2) ),
inference(resolution,[status(thm)],[f574,f205]) ).
fof(f1239,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| sk1 = cons(hd(sk1),nil) ),
inference(backward_demodulation,[status(thm)],[f1334,f542]) ).
fof(f1334,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| hd(sk1) = hd(sk2) ),
inference(forward_demodulation,[status(thm)],[f542,f1233]) ).
fof(f2013,plain,
( nil = sk2
| cons(skaf83(sk2),skaf82(sk2)) = sk2 ),
inference(resolution,[status(thm)],[f309,f429]) ).
fof(f2030,plain,
( nil = sk1
| cons(skaf83(sk1),skaf82(sk1)) = sk1 ),
inference(resolution,[status(thm)],[f309,f428]) ).
fof(f2032,definition,
( sQ66_spl
<=> cons(skaf83(sk2),skaf82(sk2)) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f2033,plain,
( ~ sQ66_spl
| cons(skaf83(sk2),skaf82(sk2)) = sk2 ),
inference(component_clause,[status(thm)],[f2032]) ).
fof(f2035,plain,
( sQ14_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f2013,f2032,f552]) ).
fof(f2040,definition,
( sQ68_spl
<=> cons(skaf83(sk1),skaf82(sk1)) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f2041,plain,
( ~ sQ68_spl
| cons(skaf83(sk1),skaf82(sk1)) = sk1 ),
inference(component_clause,[status(thm)],[f2040]) ).
fof(f2043,plain,
( sQ23_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f2030,f2040,f705]) ).
fof(f2121,definition,
( sQ73_spl
<=> ssList(tl(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f2122,plain,
( ~ sQ73_spl
| ssList(tl(sk1)) ),
inference(component_clause,[status(thm)],[f2121]) ).
fof(f2123,plain,
( sQ73_spl
| ~ ssList(tl(sk1)) ),
inference(component_clause,[status(thm)],[f2121]) ).
fof(f2318,definition,
( sQ80_spl
<=> ssList(tl(sk2)) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f2319,plain,
( ~ sQ80_spl
| ssList(tl(sk2)) ),
inference(component_clause,[status(thm)],[f2318]) ).
fof(f2320,plain,
( sQ80_spl
| ~ ssList(tl(sk2)) ),
inference(component_clause,[status(thm)],[f2318]) ).
fof(f2399,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,skaf45(X0,nil)) = X0
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f342,f257]) ).
fof(f2401,definition,
! [X0] :
( sQ82_spl
<=> ( ~ ssList(X0)
| app(nil,skaf45(X0,nil)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f2402,plain,
! [X0] :
( ~ sQ82_spl
| ~ ssList(X0)
| app(nil,skaf45(X0,nil)) = X0
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2401]) ).
fof(f2404,plain,
( sQ82_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2399,f527,f2401]) ).
fof(f2406,plain,
! [X0] :
( ~ sQ82_spl
| ~ ssList(X0)
| skaf45(X0,nil) = X0
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f1141,f2402]) ).
fof(f2407,plain,
! [X0] :
( ~ sQ82_spl
| skaf45(X0,nil) = X0
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2406]) ).
fof(f2793,definition,
( sQ113_spl
<=> ssList(skaf82(sk2)) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f2795,plain,
( sQ113_spl
| ~ ssList(skaf82(sk2)) ),
inference(component_clause,[status(thm)],[f2793]) ).
fof(f2904,plain,
( ~ sQ82_spl
| skaf45(nil,nil) = nil ),
inference(resolution,[status(thm)],[f2407,f205]) ).
fof(f3374,definition,
! [X1] :
( sQ154_spl
<=> ~ ssList(X1) ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f3375,plain,
! [X0] :
( ~ sQ154_spl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3374]) ).
fof(f4146,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| ~ ssList(app(X2,cons(X3,X1)))
| ~ ssList(cons(X3,X0))
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f508,f283]) ).
fof(f4157,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| ~ ssList(app(X2,cons(X3,X1)))
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f4146,f284]) ).
fof(f4203,plain,
! [X0,X1] :
( ~ sQ1_spl
| hd(cons(X1,X0)) = X1
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f295,f448]) ).
fof(f4303,plain,
! [X0,X1] :
( ~ sQ1_spl
| tl(cons(X1,X0)) = X0
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f294,f448]) ).
fof(f4311,plain,
! [X0] :
( ~ sQ1_spl
| singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil)) ),
inference(backward_subsumption_resolution,[status(thm)],[f481,f448]) ).
fof(f4338,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| frontsegP(cons(X2,X0),cons(X2,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f495,f448]) ).
fof(f4643,plain,
( sQ113_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2795,f210]) ).
fof(f4644,plain,
sQ113_spl,
inference(contradiction_clause,[status(thm)],[f4643]) ).
fof(f4647,definition,
! [X1,X2,X3] :
( sQ246_spl
<=> ( ~ ssList(app(X2,cons(X3,X1)))
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ246_spl])],[split_symbol_definition]) ).
fof(f4648,plain,
! [X0,X1,X2] :
( ~ sQ246_spl
| ~ ssList(app(X1,cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f4647]) ).
fof(f4650,plain,
( ~ sQ0_spl
| sQ246_spl
| sQ154_spl ),
inference(split_clause,[status(thm)],[f4157,f3374,f4647,f444]) ).
fof(f4737,plain,
( sQ80_spl
| nil = sk2
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f2320,f273]) ).
fof(f4738,plain,
( sQ80_spl
| sQ14_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4737,f514,f552,f2318]) ).
fof(f4741,plain,
( sQ73_spl
| nil = sk1
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f2123,f273]) ).
fof(f4742,plain,
( sQ73_spl
| sQ23_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f4741,f652,f705,f2121]) ).
fof(f4778,plain,
! [X0,X1] :
( ~ sQ1_spl
| hd(cons(X0,skaf82(X1))) = X0 ),
inference(resolution,[status(thm)],[f4203,f210]) ).
fof(f4779,plain,
! [X0] :
( ~ sQ1_spl
| hd(cons(X0,nil)) = X0 ),
inference(resolution,[status(thm)],[f4203,f205]) ).
fof(f5880,plain,
( ~ sQ31_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f429,f5914]) ).
fof(f5914,plain,
! [X0] :
( ~ sQ31_spl
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f783]) ).
fof(f5915,plain,
~ sQ31_spl,
inference(contradiction_clause,[status(thm)],[f5880]) ).
fof(f6035,definition,
( sQ270_spl
<=> nil = tl(sk1) ),
introduced(definition,[new_symbols(definition,[sQ270_spl])],[split_symbol_definition]) ).
fof(f6036,plain,
( ~ sQ270_spl
| nil = tl(sk1) ),
inference(component_clause,[status(thm)],[f6035]) ).
fof(f7942,plain,
( ~ sQ80_spl
| ~ sQ154_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f2319,f3375]) ).
fof(f8013,plain,
( ~ sQ80_spl
| ~ sQ154_spl ),
inference(contradiction_clause,[status(thm)],[f7942]) ).
fof(f8070,plain,
( ~ sQ73_spl
| ~ sQ270_spl
| ssList(nil) ),
inference(forward_demodulation,[status(thm)],[f6036,f2122]) ).
fof(f8152,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| segmentP(app(app(X1,X2),X0),X2)
| ~ ssList(X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f402,f254]) ).
fof(f8155,plain,
! [X0,X1,X2] :
( segmentP(app(app(X1,X2),X0),X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f8152]) ).
fof(f8170,plain,
! [X0] :
( ~ sQ73_spl
| ~ sQ270_spl
| ssList(cons(X0,nil))
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f284,f8070]) ).
fof(f8421,plain,
! [X0,X1] :
( ssList(cons(X0,skaf58(X1)))
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f234,f284]) ).
fof(f8426,plain,
! [X0,X1,X2] :
( ~ sQ246_spl
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(cons(X0,X1)) ),
inference(resolution,[status(thm)],[f283,f4648]) ).
fof(f8442,definition,
! [X0,X1] :
( sQ310_spl
<=> ( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(cons(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ310_spl])],[split_symbol_definition]) ).
fof(f8443,plain,
! [X0,X1] :
( ~ sQ310_spl
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(cons(X0,X1)) ),
inference(component_clause,[status(thm)],[f8442]) ).
fof(f8445,plain,
( ~ sQ246_spl
| sQ31_spl
| sQ310_spl ),
inference(split_clause,[status(thm)],[f8426,f8442,f782,f4647]) ).
fof(f8451,plain,
! [X0] :
( ~ sQ310_spl
| ~ ssItem(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f8421,f8474]) ).
fof(f8474,plain,
! [X0,X1] :
( ~ sQ310_spl
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f8443,f284]) ).
fof(f8475,plain,
( ~ sQ310_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f209,f8451]) ).
fof(f8493,plain,
~ sQ310_spl,
inference(contradiction_clause,[status(thm)],[f8475]) ).
fof(f8539,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ73_spl
| ~ sQ270_spl
| singletonP(cons(X0,nil)) ),
inference(backward_subsumption_resolution,[status(thm)],[f4311,f8540]) ).
fof(f8540,plain,
! [X0] :
( ~ sQ73_spl
| ~ sQ270_spl
| ~ sQ1_spl
| ssList(cons(X0,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[f8170,f448]) ).
fof(f8834,plain,
( ~ sQ82_spl
| ssList(nil) ),
inference(paramodulation,[status(thm)],[f2904,f248]) ).
fof(f8947,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ73_spl
| ~ sQ270_spl
| cons(skaf44(cons(X0,nil)),nil) = cons(X0,nil)
| ~ ssList(cons(X0,nil)) ),
inference(resolution,[status(thm)],[f301,f8539]) ).
fof(f8952,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ73_spl
| ~ sQ270_spl
| cons(skaf44(cons(X0,nil)),nil) = cons(X0,nil) ),
inference(forward_subsumption_resolution,[status(thm)],[f8947,f8540]) ).
fof(f11716,plain,
( ~ sQ66_spl
| ~ sQ1_spl
| hd(sk2) = skaf83(sk2) ),
inference(paramodulation,[status(thm)],[f2033,f4778]) ).
fof(f11717,plain,
( ~ sQ68_spl
| ~ sQ1_spl
| hd(sk1) = skaf83(sk1) ),
inference(paramodulation,[status(thm)],[f2041,f4778]) ).
fof(f11721,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ66_spl
| ~ sQ1_spl
| sk1 = cons(skaf83(sk2),nil) ),
inference(backward_demodulation,[status(thm)],[f11725,f1239]) ).
fof(f11725,plain,
( ~ sQ66_spl
| ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ13_spl
| hd(sk1) = skaf83(sk2) ),
inference(forward_demodulation,[status(thm)],[f1334,f11716]) ).
fof(f11726,plain,
( ~ sQ66_spl
| ~ sQ68_spl
| ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ13_spl
| cons(skaf83(sk1),skaf82(sk2)) = sk2 ),
inference(backward_demodulation,[status(thm)],[f11728,f2033]) ).
fof(f11728,plain,
( ~ sQ68_spl
| ~ sQ1_spl
| ~ sQ66_spl
| ~ sQ12_spl
| ~ sQ13_spl
| skaf83(sk2) = skaf83(sk1) ),
inference(forward_demodulation,[status(thm)],[f11725,f11717]) ).
fof(f11734,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ66_spl
| ~ sQ1_spl
| ~ sQ68_spl
| sk1 = cons(skaf83(sk1),nil) ),
inference(forward_demodulation,[status(thm)],[f11728,f11721]) ).
fof(f14279,plain,
! [X0] :
( ~ sQ82_spl
| ~ sQ1_spl
| tl(cons(X0,nil)) = nil ),
inference(resolution,[status(thm)],[f4303,f8834]) ).
fof(f14471,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ66_spl
| ~ sQ1_spl
| ~ sQ68_spl
| ~ sQ82_spl
| tl(sk1) = nil ),
inference(paramodulation,[status(thm)],[f11734,f14279]) ).
fof(f14472,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ66_spl
| ~ sQ1_spl
| ~ sQ68_spl
| ~ sQ82_spl
| sQ270_spl ),
inference(split_clause,[status(thm)],[f14471,f6035,f2401,f2040,f447,f2032,f538,f541]) ).
fof(f14629,plain,
! [X0] :
( segmentP(app(sk1,X0),sk1)
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1168,f8155]) ).
fof(f14666,definition,
! [X0] :
( sQ555_spl
<=> ( segmentP(app(sk1,X0),sk1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ555_spl])],[split_symbol_definition]) ).
fof(f14667,plain,
! [X0] :
( ~ sQ555_spl
| segmentP(app(sk1,X0),sk1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f14666]) ).
fof(f14669,plain,
( ~ sQ19_spl
| ~ sQ10_spl
| sQ555_spl ),
inference(split_clause,[status(thm)],[f14629,f14666,f527,f652]) ).
fof(f17648,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ73_spl
| ~ sQ270_spl
| hd(cons(X0,nil)) = skaf44(cons(X0,nil)) ),
inference(paramodulation,[status(thm)],[f8952,f4779]) ).
fof(f17667,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ73_spl
| ~ sQ270_spl
| frontsegP(cons(skaf44(cons(X1,nil)),X0),cons(X1,nil))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(X0,nil) ),
inference(paramodulation,[status(thm)],[f8952,f4338]) ).
fof(f17688,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ73_spl
| ~ sQ270_spl
| X0 = skaf44(cons(X0,nil)) ),
inference(forward_demodulation,[status(thm)],[f4779,f17648]) ).
fof(f17757,definition,
! [X0,X1] :
( sQ820_spl
<=> ( frontsegP(cons(skaf44(cons(X1,nil)),X0),cons(X1,nil))
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ820_spl])],[split_symbol_definition]) ).
fof(f17758,plain,
! [X0,X1] :
( ~ sQ820_spl
| frontsegP(cons(skaf44(cons(X1,nil)),X0),cons(X1,nil))
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ),
inference(component_clause,[status(thm)],[f17757]) ).
fof(f17760,plain,
( ~ sQ1_spl
| ~ sQ73_spl
| ~ sQ270_spl
| ~ sQ10_spl
| sQ820_spl ),
inference(split_clause,[status(thm)],[f17667,f17757,f527,f6035,f2121,f447]) ).
fof(f17844,plain,
! [X0,X1] :
( ~ sQ820_spl
| ~ sQ1_spl
| ~ sQ73_spl
| ~ sQ270_spl
| frontsegP(cons(X1,X0),cons(X1,nil))
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ),
inference(forward_demodulation,[status(thm)],[f17688,f17758]) ).
fof(f17846,plain,
! [X0,X1] :
( ~ sQ820_spl
| ~ sQ1_spl
| ~ sQ73_spl
| ~ sQ270_spl
| frontsegP(cons(X1,X0),cons(X1,nil))
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f17844,f257]) ).
fof(f19743,plain,
( ~ sQ66_spl
| ~ sQ68_spl
| ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ820_spl
| ~ sQ73_spl
| ~ sQ270_spl
| frontsegP(sk2,cons(skaf83(sk1),nil))
| ~ ssList(skaf82(sk2)) ),
inference(paramodulation,[status(thm)],[f11726,f17846]) ).
fof(f19760,definition,
( sQ912_spl
<=> frontsegP(sk2,cons(skaf83(sk1),nil)) ),
introduced(definition,[new_symbols(definition,[sQ912_spl])],[split_symbol_definition]) ).
fof(f19761,plain,
( ~ sQ912_spl
| frontsegP(sk2,cons(skaf83(sk1),nil)) ),
inference(component_clause,[status(thm)],[f19760]) ).
fof(f19763,plain,
( ~ sQ66_spl
| ~ sQ68_spl
| ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ820_spl
| ~ sQ73_spl
| ~ sQ270_spl
| sQ912_spl
| ~ sQ113_spl ),
inference(split_clause,[status(thm)],[f19743,f2793,f19760,f6035,f2121,f17757,f541,f538,f447,f2040,f2032]) ).
fof(f19771,plain,
( ~ sQ912_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ66_spl
| ~ sQ1_spl
| ~ sQ68_spl
| frontsegP(sk2,sk1) ),
inference(forward_demodulation,[status(thm)],[f11734,f19761]) ).
fof(f19774,plain,
( ~ sQ912_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ66_spl
| ~ sQ1_spl
| ~ sQ68_spl
| app(sk1,skaf45(sk2,sk1)) = sk2
| ~ ssList(sk2)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f19771,f342]) ).
fof(f19780,definition,
( sQ915_spl
<=> app(sk1,skaf45(sk2,sk1)) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ915_spl])],[split_symbol_definition]) ).
fof(f19781,plain,
( ~ sQ915_spl
| app(sk1,skaf45(sk2,sk1)) = sk2 ),
inference(component_clause,[status(thm)],[f19780]) ).
fof(f19783,plain,
( ~ sQ912_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ66_spl
| ~ sQ1_spl
| ~ sQ68_spl
| sQ915_spl
| ~ sQ7_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f19774,f652,f514,f19780,f2040,f447,f2032,f538,f541,f19760]) ).
fof(f19799,plain,
( ~ sQ915_spl
| ~ sQ555_spl
| segmentP(sk2,sk1)
| ~ ssList(skaf45(sk2,sk1)) ),
inference(paramodulation,[status(thm)],[f19781,f14667]) ).
fof(f19809,definition,
( sQ918_spl
<=> ssList(skaf45(sk2,sk1)) ),
introduced(definition,[new_symbols(definition,[sQ918_spl])],[split_symbol_definition]) ).
fof(f19811,plain,
( sQ918_spl
| ~ ssList(skaf45(sk2,sk1)) ),
inference(component_clause,[status(thm)],[f19809]) ).
fof(f19812,plain,
( ~ sQ915_spl
| ~ sQ555_spl
| sQ35_spl
| ~ sQ918_spl ),
inference(split_clause,[status(thm)],[f19799,f19809,f858,f14666,f19780]) ).
fof(f19839,plain,
( sQ918_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f19811,f248]) ).
fof(f19840,plain,
sQ918_spl,
inference(contradiction_clause,[status(thm)],[f19839]) ).
fof(f19841,plain,
$false,
inference(sat_refutation,[status(thm)],[f450,f454,f470,f471,f507,f536,f544,f555,f557,f620,f624,f655,f672,f861,f863,f2035,f2043,f2404,f4644,f4650,f4738,f4742,f5915,f8013,f8445,f8493,f14472,f14669,f17760,f19763,f19783,f19812,f19840]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC079-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n006.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Mon Sep 21 07:53:42 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 129.11/16.77 % Refutation found
% 129.11/16.77 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 129.11/16.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 48.58/16.87 % Elapsed time: 16.494695 seconds
% 48.58/16.87 % CPU time: 130.400004 seconds
% 48.58/16.87 % Total memory used: 583.440 MB
% 48.58/16.87 % Net memory used: 547.215 MB
%------------------------------------------------------------------------------