%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC413-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 02:41:08 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.42s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 72
% Syntax : Number of formulae : 208 ( 18 unt; 30 def)
% Number of atoms : 610 ( 139 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 737 ( 335 ~; 372 |; 0 &)
% ( 30 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 34 ( 32 usr; 31 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 14 con; 0-2 aty)
% Number of variables : 169 ( 169 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [U] : ssList(skaf71(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [U] : ssList(skaf68(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [U] : ssItem(skaf65(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f73,axiom,
! [U] :
( app(U,nil) = 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(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(f118,axiom,
! [U,V] :
( nil = U
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f119,axiom,
! [U,V] :
( nil = V
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f145,axiom,
! [U,V] :
( app(U,V) = nil
| ~ ssList(U)
| ~ ssList(V)
| nil != V
| nil != U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f150,axiom,
! [U,V,W] :
( V = W
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != app(U,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f151,axiom,
! [U,V,W] :
( U = W
| ~ ssList(W)
| ~ ssList(V)
| ~ ssList(U)
| app(U,V) != app(W,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f170,axiom,
! [U,V,W,X] :
( U = W
| ~ ssList(V)
| ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| cons(U,V) != cons(W,X) ),
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,
! [A,B,C,D,E,F] :
( app(app(cons(D,nil),cons(E,nil)),F) != sk4
| ~ ssList(F)
| ~ ssItem(E)
| ~ ssItem(D)
| app(app(cons(B,nil),cons(A,nil)),C) != sk1
| app(app(cons(A,nil),cons(B,nil)),C) != sk2
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
! [A,B,C] :
( ssItem(sk11)
| app(app(cons(B,nil),cons(A,nil)),C) != sk1
| app(app(cons(A,nil),cons(B,nil)),C) != sk2
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
! [A,B,C] :
( ssItem(sk12)
| app(app(cons(B,nil),cons(A,nil)),C) != sk1
| app(app(cons(A,nil),cons(B,nil)),C) != sk2
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f201,negated_conjecture,
! [A,B,C] :
( app(app(cons(A,nil),cons(B,nil)),C) != sk4
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A)
| ssItem(sk8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f202,negated_conjecture,
! [A,B,C] :
( app(app(cons(A,nil),cons(B,nil)),C) != sk4
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A)
| ssItem(sk9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f203,negated_conjecture,
! [A,B,C] :
( app(app(cons(A,nil),cons(B,nil)),C) != sk4
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A)
| ssList(sk10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f204,negated_conjecture,
! [A,B,C] :
( app(app(cons(A,nil),cons(B,nil)),C) != sk4
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A)
| app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f205,negated_conjecture,
! [A,B,C] :
( app(app(cons(A,nil),cons(B,nil)),C) != sk4
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A)
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f206,negated_conjecture,
( ssItem(sk11)
| ssItem(sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f207,negated_conjecture,
( ssItem(sk11)
| ssItem(sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f208,negated_conjecture,
( ssItem(sk11)
| ssList(sk7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f209,negated_conjecture,
( ssItem(sk11)
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f210,negated_conjecture,
( ssItem(sk12)
| ssItem(sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f211,negated_conjecture,
( ssList(sk13)
| ssItem(sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f212,negated_conjecture,
( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2
| ssItem(sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f213,negated_conjecture,
( ssItem(sk12)
| ssItem(sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f214,negated_conjecture,
( ssItem(sk12)
| ssList(sk7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f215,negated_conjecture,
( ssItem(sk12)
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f216,negated_conjecture,
( ssList(sk13)
| ssItem(sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f217,negated_conjecture,
( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2
| ssItem(sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f218,negated_conjecture,
( ssList(sk13)
| ssList(sk7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f219,negated_conjecture,
( ssList(sk13)
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f220,negated_conjecture,
( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2
| ssList(sk7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f221,negated_conjecture,
( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f226,negated_conjecture,
( ssItem(sk11)
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f233,negated_conjecture,
( ssItem(sk12)
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f249,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f265,plain,
! [X0] : ssList(skaf71(X0)),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f268,plain,
! [X0] : ssList(skaf68(X0)),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f271,plain,
! [X0] : ssItem(skaf65(X0)),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f315,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f316,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f327,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f328,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f368,plain,
! [U] :
( nil = U
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f118]) ).
fof(f369,plain,
! [X0,X1] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f368]) ).
fof(f370,plain,
! [V] :
( nil = V
| ! [U] :
( ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f119]) ).
fof(f371,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f370]) ).
fof(f403,plain,
! [X0,X1] :
( app(X0,X1) = nil
| ~ ssList(X0)
| ~ ssList(X1)
| nil != X1
| nil != X0 ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f411,plain,
! [V,W] :
( V = W
| ~ ssList(W)
| ! [U] :
( ~ ssList(U)
| ~ ssList(V)
| app(U,V) != app(U,W) ) ),
inference(miniscoping,[status(thm)],[f150]) ).
fof(f412,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != app(X0,X2) ),
inference(cnf_transformation,[status(thm)],[f411]) ).
fof(f413,plain,
! [U,W] :
( U = W
| ~ ssList(W)
| ! [V] :
( ~ ssList(V)
| ~ ssList(U)
| app(U,V) != app(W,V) ) ),
inference(miniscoping,[status(thm)],[f151]) ).
fof(f414,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) != app(X2,X1) ),
inference(cnf_transformation,[status(thm)],[f413]) ).
fof(f442,plain,
! [U,W] :
( U = W
| ! [V] :
( ~ ssList(V)
| ! [X] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| cons(U,V) != cons(W,X) ) ) ),
inference(miniscoping,[status(thm)],[f170]) ).
fof(f443,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X0)
| ~ ssItem(X2)
| cons(X0,X1) != cons(X2,X3) ),
inference(cnf_transformation,[status(thm)],[f442]) ).
fof(f476,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f477,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f478,plain,
! [D,E,F] :
( app(app(cons(D,nil),cons(E,nil)),F) != sk4
| ~ ssList(F)
| ~ ssItem(E)
| ~ ssItem(D)
| ! [A,B,C] :
( app(app(cons(B,nil),cons(A,nil)),C) != sk1
| app(app(cons(A,nil),cons(B,nil)),C) != sk2
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ) ),
inference(miniscoping,[status(thm)],[f192]) ).
fof(f479,plain,
! [X0,X1,X2,X3,X4,X5] :
( app(app(cons(X3,nil),cons(X4,nil)),X5) != sk4
| ~ ssList(X5)
| ~ ssItem(X4)
| ~ ssItem(X3)
| app(app(cons(X1,nil),cons(X0,nil)),X2) != sk1
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk2
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f478]) ).
fof(f480,plain,
( ssItem(sk11)
| ! [A,B,C] :
( app(app(cons(B,nil),cons(A,nil)),C) != sk1
| app(app(cons(A,nil),cons(B,nil)),C) != sk2
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ) ),
inference(miniscoping,[status(thm)],[f193]) ).
fof(f481,plain,
! [X0,X1,X2] :
( ssItem(sk11)
| app(app(cons(X1,nil),cons(X0,nil)),X2) != sk1
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk2
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f480]) ).
fof(f482,plain,
( ssItem(sk12)
| ! [A,B,C] :
( app(app(cons(B,nil),cons(A,nil)),C) != sk1
| app(app(cons(A,nil),cons(B,nil)),C) != sk2
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ) ),
inference(miniscoping,[status(thm)],[f194]) ).
fof(f483,plain,
! [X0,X1,X2] :
( ssItem(sk12)
| app(app(cons(X1,nil),cons(X0,nil)),X2) != sk1
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk2
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f482]) ).
fof(f492,plain,
! [X0,X1,X2] :
( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ssItem(sk8) ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f493,plain,
! [X0,X1,X2] :
( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ssItem(sk9) ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f494,plain,
! [X0,X1,X2] :
( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ssList(sk10) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f495,plain,
! [X0,X1,X2] :
( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f496,plain,
! [X0,X1,X2] :
( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ),
inference(cnf_transformation,[status(thm)],[f205]) ).
fof(f497,plain,
( ssItem(sk11)
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f206]) ).
fof(f498,plain,
( ssItem(sk11)
| ssItem(sk6) ),
inference(cnf_transformation,[status(thm)],[f207]) ).
fof(f499,plain,
( ssItem(sk11)
| ssList(sk7) ),
inference(cnf_transformation,[status(thm)],[f208]) ).
fof(f500,plain,
( ssItem(sk11)
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
inference(cnf_transformation,[status(thm)],[f209]) ).
fof(f501,plain,
( ssItem(sk12)
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f502,plain,
( ssList(sk13)
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f503,plain,
( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f212]) ).
fof(f504,plain,
( ssItem(sk12)
| ssItem(sk6) ),
inference(cnf_transformation,[status(thm)],[f213]) ).
fof(f505,plain,
( ssItem(sk12)
| ssList(sk7) ),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f506,plain,
( ssItem(sk12)
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
inference(cnf_transformation,[status(thm)],[f215]) ).
fof(f507,plain,
( ssList(sk13)
| ssItem(sk6) ),
inference(cnf_transformation,[status(thm)],[f216]) ).
fof(f508,plain,
( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2
| ssItem(sk6) ),
inference(cnf_transformation,[status(thm)],[f217]) ).
fof(f509,plain,
( ssList(sk13)
| ssList(sk7) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f510,plain,
( ssList(sk13)
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
inference(cnf_transformation,[status(thm)],[f219]) ).
fof(f511,plain,
( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2
| ssList(sk7) ),
inference(cnf_transformation,[status(thm)],[f220]) ).
fof(f512,plain,
( app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f517,plain,
( ssItem(sk11)
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f524,plain,
( ssItem(sk12)
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ),
inference(cnf_transformation,[status(thm)],[f233]) ).
fof(f540,definition,
! [X0,X1,X2] :
( sQ2_spl
<=> ( app(app(cons(X1,nil),cons(X0,nil)),X2) != sk1
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk2
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f541,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| app(app(cons(X1,nil),cons(X0,nil)),X2) != sk1
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk2
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f540]) ).
fof(f543,definition,
! [X3,X4,X5] :
( sQ3_spl
<=> ( app(app(cons(X3,nil),cons(X4,nil)),X5) != sk4
| ~ ssList(X5)
| ~ ssItem(X4)
| ~ ssItem(X3) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f544,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f543]) ).
fof(f546,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f479,f540,f543]) ).
fof(f547,definition,
( sQ4_spl
<=> ssItem(sk11) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f550,plain,
( sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f481,f540,f547]) ).
fof(f551,definition,
( sQ5_spl
<=> ssItem(sk12) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f554,plain,
( sQ5_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f483,f540,f551]) ).
fof(f555,definition,
( sQ6_spl
<=> ssList(sk13) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f559,definition,
( sQ7_spl
<=> app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f560,plain,
( ~ sQ7_spl
| app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2 ),
inference(component_clause,[status(thm)],[f559]) ).
fof(f563,definition,
( sQ8_spl
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f567,definition,
( sQ9_spl
<=> ssItem(sk6) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f571,definition,
( sQ10_spl
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f575,definition,
( sQ11_spl
<=> app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f576,plain,
( ~ sQ11_spl
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
inference(component_clause,[status(thm)],[f575]) ).
fof(f579,definition,
( sQ12_spl
<=> ssItem(sk8) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f582,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f492,f579,f543]) ).
fof(f583,definition,
( sQ13_spl
<=> ssItem(sk9) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f586,plain,
( sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f493,f583,f543]) ).
fof(f587,definition,
( sQ14_spl
<=> ssList(sk10) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f590,plain,
( sQ3_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f494,f587,f543]) ).
fof(f591,definition,
( sQ15_spl
<=> app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f592,plain,
( ~ sQ15_spl
| app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4 ),
inference(component_clause,[status(thm)],[f591]) ).
fof(f594,plain,
( sQ3_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f495,f591,f543]) ).
fof(f595,definition,
( sQ16_spl
<=> app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f596,plain,
( ~ sQ16_spl
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3 ),
inference(component_clause,[status(thm)],[f595]) ).
fof(f598,plain,
( sQ3_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f496,f595,f543]) ).
fof(f599,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f497,f563,f547]) ).
fof(f600,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f498,f567,f547]) ).
fof(f601,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f499,f571,f547]) ).
fof(f602,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f500,f575,f547]) ).
fof(f603,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f501,f563,f551]) ).
fof(f604,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f502,f563,f555]) ).
fof(f605,plain,
( sQ7_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f503,f563,f559]) ).
fof(f606,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f504,f567,f551]) ).
fof(f607,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f505,f571,f551]) ).
fof(f608,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f506,f575,f551]) ).
fof(f609,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f507,f567,f555]) ).
fof(f610,plain,
( sQ7_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f508,f567,f559]) ).
fof(f611,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f509,f571,f555]) ).
fof(f612,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f510,f575,f555]) ).
fof(f613,plain,
( sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f511,f571,f559]) ).
fof(f614,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f512,f575,f559]) ).
fof(f619,plain,
( sQ4_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f517,f595,f547]) ).
fof(f626,plain,
( sQ5_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f524,f595,f551]) ).
fof(f648,definition,
( sQ17_spl
<=> ssList(app(cons(sk11,nil),cons(sk12,nil))) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f650,plain,
( sQ17_spl
| ~ ssList(app(cons(sk11,nil),cons(sk12,nil))) ),
inference(component_clause,[status(thm)],[f648]) ).
fof(f655,plain,
( ~ ssList(nil)
| nil = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f369,f316]) ).
fof(f658,definition,
( sQ19_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f660,plain,
( sQ19_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f658]) ).
fof(f661,definition,
( sQ20_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f664,plain,
( sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f655,f658,f661]) ).
fof(f673,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f660,f249]) ).
fof(f674,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f673]) ).
fof(f675,plain,
( sQ17_spl
| ~ ssList(cons(sk11,nil))
| ~ ssList(cons(sk12,nil)) ),
inference(resolution,[status(thm)],[f650,f327]) ).
fof(f676,definition,
( sQ23_spl
<=> ssList(cons(sk12,nil)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f678,plain,
( sQ23_spl
| ~ ssList(cons(sk12,nil)) ),
inference(component_clause,[status(thm)],[f676]) ).
fof(f679,definition,
( sQ24_spl
<=> ssList(cons(sk11,nil)) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f681,plain,
( sQ24_spl
| ~ ssList(cons(sk11,nil)) ),
inference(component_clause,[status(thm)],[f679]) ).
fof(f682,plain,
( sQ17_spl
| ~ sQ24_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f675,f676,f679,f648]) ).
fof(f683,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk2
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f476,f544]) ).
fof(f684,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ ssList(sk13)
| ~ ssItem(sk12)
| ~ ssItem(sk11) ),
inference(resolution,[status(thm)],[f683,f560]) ).
fof(f686,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f684,f547,f551,f555,f543,f559]) ).
fof(f691,plain,
( ~ sQ15_spl
| app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk2 ),
inference(forward_demodulation,[status(thm)],[f476,f592]) ).
fof(f692,plain,
( ~ sQ16_spl
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk1 ),
inference(forward_demodulation,[status(thm)],[f477,f596]) ).
fof(f709,plain,
( sQ23_spl
| ~ ssList(nil)
| ~ ssItem(sk12) ),
inference(resolution,[status(thm)],[f678,f328]) ).
fof(f710,plain,
( sQ23_spl
| ~ sQ19_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f709,f551,f658,f676]) ).
fof(f711,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| nil != X1
| nil != X0 ),
inference(resolution,[status(thm)],[f403,f371]) ).
fof(f713,definition,
! [X0] :
( sQ28_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0)
| nil != X0 ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f714,plain,
! [X0] :
( ~ sQ28_spl
| ~ ssList(X0)
| ~ ssList(X0)
| nil != X0 ),
inference(component_clause,[status(thm)],[f713]) ).
fof(f716,definition,
! [X1] :
( sQ29_spl
<=> ( nil = X1
| ~ ssList(X1)
| ~ ssList(X1)
| nil != X1 ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f719,plain,
( sQ29_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f711,f713,f716]) ).
fof(f721,plain,
! [X0] :
( ~ sQ28_spl
| ~ ssList(X0)
| nil != X0 ),
inference(duplicate_literals_removal,[status(thm)],[f714]) ).
fof(f722,plain,
( sQ24_spl
| ~ ssList(nil)
| ~ ssItem(sk11) ),
inference(resolution,[status(thm)],[f681,f328]) ).
fof(f723,plain,
( sQ24_spl
| ~ sQ19_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f722,f547,f658,f679]) ).
fof(f781,plain,
( ~ sQ28_spl
| nil != nil ),
inference(resolution,[status(thm)],[f721,f249]) ).
fof(f784,plain,
( ~ sQ28_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f781]) ).
fof(f785,plain,
~ sQ28_spl,
inference(contradiction_clause,[status(thm)],[f784]) ).
fof(f786,plain,
! [X0] :
( ~ ssList(app(nil,X0))
| app(nil,X0) = X0
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(app(nil,X0)) ),
inference(resolution,[status(thm)],[f412,f316]) ).
fof(f790,plain,
! [X0,X1] :
( X0 = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[f412]) ).
fof(f791,definition,
! [X0] :
( sQ38_spl
<=> ( ~ ssList(app(nil,X0))
| app(nil,X0) = X0
| ~ ssList(X0)
| ~ ssList(app(nil,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f794,plain,
( ~ sQ19_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f786,f791,f658]) ).
fof(f801,definition,
! [X0] :
( sQ40_spl
<=> ( X0 = X0
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f804,definition,
! [X1] :
( sQ41_spl
<=> ~ ssList(X1) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f805,plain,
! [X0] :
( ~ sQ41_spl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f804]) ).
fof(f807,plain,
( sQ41_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f790,f801,f804]) ).
fof(f809,plain,
! [X0] :
( ~ ssList(app(X0,nil))
| app(X0,nil) = X0
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(app(X0,nil)) ),
inference(resolution,[status(thm)],[f414,f315]) ).
fof(f814,definition,
! [X0] :
( sQ42_spl
<=> ( ~ ssList(app(X0,nil))
| app(X0,nil) = X0
| ~ ssList(X0)
| ~ ssList(app(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f817,plain,
( ~ sQ19_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f809,f814,f658]) ).
fof(f835,plain,
( ~ sQ41_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f265,f805]) ).
fof(f849,plain,
~ sQ41_spl,
inference(contradiction_clause,[status(thm)],[f835]) ).
fof(f850,plain,
! [X0,X1] :
( X0 = X0
| ~ ssList(X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(equality_resolution,[status(thm)],[f443]) ).
fof(f851,definition,
! [X0] :
( sQ44_spl
<=> ( X0 = X0
| ~ ssItem(X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f854,definition,
! [X1] :
( sQ45_spl
<=> ( ~ ssList(X1)
| ~ ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f855,plain,
! [X0] :
( ~ sQ45_spl
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f854]) ).
fof(f857,plain,
( sQ45_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f850,f851,f854]) ).
fof(f858,plain,
! [X0] :
( ~ sQ45_spl
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f855]) ).
fof(f859,plain,
( ~ sQ45_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f268,f858]) ).
fof(f860,plain,
~ sQ45_spl,
inference(contradiction_clause,[status(thm)],[f859]) ).
fof(f862,definition,
! [X0] :
( sQ46_spl
<=> ( ~ ssItem(X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f863,plain,
! [X0] :
( ~ sQ46_spl
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f862]) ).
fof(f866,plain,
! [X0] :
( ~ sQ46_spl
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f863]) ).
fof(f868,plain,
( ~ sQ11_spl
| ~ sQ3_spl
| ~ ssList(sk7)
| ~ ssItem(sk6)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f683,f576]) ).
fof(f873,plain,
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f868,f563,f567,f571,f543,f575]) ).
fof(f880,plain,
( ~ sQ46_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f271,f866]) ).
fof(f889,plain,
~ sQ46_spl,
inference(contradiction_clause,[status(thm)],[f880]) ).
fof(f924,plain,
( ~ sQ15_spl
| ~ sQ2_spl
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) != sk1
| ~ ssList(sk10)
| ~ ssItem(sk9)
| ~ ssItem(sk8) ),
inference(resolution,[status(thm)],[f541,f691]) ).
fof(f929,definition,
( sQ54_spl
<=> app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f931,plain,
( sQ54_spl
| app(app(cons(sk9,nil),cons(sk8,nil)),sk10) != sk1 ),
inference(component_clause,[status(thm)],[f929]) ).
fof(f932,plain,
( ~ sQ15_spl
| ~ sQ2_spl
| ~ sQ54_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f924,f579,f583,f587,f929,f540,f591]) ).
fof(f940,plain,
( sQ54_spl
| ~ sQ16_spl
| sk1 != sk1 ),
inference(forward_demodulation,[status(thm)],[f692,f931]) ).
fof(f941,plain,
( sQ54_spl
| ~ sQ16_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f940]) ).
fof(f942,plain,
( sQ54_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f941]) ).
fof(f943,plain,
$false,
inference(sat_refutation,[status(thm)],[f546,f550,f554,f582,f586,f590,f594,f598,f599,f600,f601,f602,f603,f604,f605,f606,f607,f608,f609,f610,f611,f612,f613,f614,f619,f626,f664,f674,f682,f686,f710,f719,f723,f785,f794,f807,f817,f849,f857,f860,f873,f889,f932,f942]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC413-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 08:17:57 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.42 % Refutation found
% 0.12/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.43 % Elapsed time: 0.073284 seconds
% 0.12/0.43 % CPU time: 0.272793 seconds
% 0.12/0.43 % Total memory used: 113.534 MB
% 0.12/0.43 % Net memory used: 113.272 MB
%------------------------------------------------------------------------------