%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC315-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:40:45 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 68
% Syntax : Number of formulae : 211 ( 18 unt; 35 def)
% Number of atoms : 599 ( 158 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 742 ( 354 ~; 353 |; 0 &)
% ( 35 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 40 ( 38 usr; 36 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 127 ( 127 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [U] : ssList(skaf61(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [U] : ssItem(skaf55(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f73,axiom,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f74,axiom,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [U,V] :
( ssList(app(V,U))
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(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(f118,axiom,
! [U,V] :
( nil = U
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f119,axiom,
! [U,V] :
( nil = V
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f120,axiom,
! [U,V] :
( app(cons(U,nil),V) = cons(U,V)
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f145,axiom,
! [U,V] :
( app(U,V) = nil
| ~ ssList(U)
| ~ ssList(V)
| nil != V
| nil != U ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f157,axiom,
! [U,V,W] :
( cons(U,app(V,W)) = app(cons(U,V),W)
| ~ ssList(W)
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f171,axiom,
! [U,V,W,X] :
( X = V
| ~ ssList(V)
| ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| cons(U,V) != cons(W,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f186,negated_conjecture,
ssList(sk1),
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,
( nil != sk4
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
( nil = sk2
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
( nil != sk1
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
( nil = sk2
| ssList(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
( nil = sk2
| app(cons(sk5,nil),sk6) = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( nil = sk2
| app(sk6,cons(sk5,nil)) != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
( nil != sk1
| ssList(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f199,negated_conjecture,
( nil != sk1
| app(cons(sk5,nil),sk6) = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f201,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f202,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f203,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk7,nil),sk8) = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f204,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk8,cons(sk7,nil)) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f212,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f238,plain,
! [X0] : ssList(skaf61(X0)),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f244,plain,
! [X0] : ssItem(skaf55(X0)),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f278,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f279,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f290,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f291,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f303,plain,
! [V] :
( ~ ssList(V)
| ! [U] :
( ~ ssItem(U)
| cons(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f98]) ).
fof(f304,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f303]) ).
fof(f307,plain,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f331,plain,
! [U] :
( nil = U
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f118]) ).
fof(f332,plain,
! [X0,X1] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f331]) ).
fof(f333,plain,
! [V] :
( nil = V
| ! [U] :
( ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f119]) ).
fof(f334,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f333]) ).
fof(f335,plain,
! [X0,X1] :
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f366,plain,
! [X0,X1] :
( app(X0,X1) = nil
| ~ ssList(X0)
| ~ ssList(X1)
| nil != X1
| nil != X0 ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f374,plain,
! [V,W] :
( V = W
| ~ ssList(W)
| ! [U] :
( ~ ssList(U)
| ~ ssList(V)
| app(U,V) != app(U,W) ) ),
inference(miniscoping,[status(thm)],[f150]) ).
fof(f375,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != app(X0,X2) ),
inference(cnf_transformation,[status(thm)],[f374]) ).
fof(f376,plain,
! [U,W] :
( U = W
| ~ ssList(W)
| ! [V] :
( ~ ssList(V)
| ~ ssList(U)
| app(U,V) != app(W,V) ) ),
inference(miniscoping,[status(thm)],[f151]) ).
fof(f377,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) != app(X2,X1) ),
inference(cnf_transformation,[status(thm)],[f376]) ).
fof(f388,plain,
! [X0,X1,X2] :
( cons(X0,app(X1,X2)) = app(cons(X0,X1),X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f405,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(f406,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)],[f405]) ).
fof(f407,plain,
! [V,X] :
( X = V
| ~ ssList(V)
| ~ ssList(X)
| ! [U] :
( ~ ssItem(U)
| ! [W] :
( ~ ssItem(W)
| cons(U,V) != cons(W,X) ) ) ),
inference(miniscoping,[status(thm)],[f171]) ).
fof(f408,plain,
! [X0,X1,X2,X3] :
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X0)
| ~ ssItem(X2)
| cons(X0,X1) != cons(X2,X3) ),
inference(cnf_transformation,[status(thm)],[f407]) ).
fof(f435,plain,
ssList(sk1),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f439,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f440,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f441,plain,
( nil != sk4
| nil = sk3 ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f442,plain,
( nil = sk2
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f443,plain,
( nil != sk1
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f444,plain,
( nil = sk2
| ssList(sk6) ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f445,plain,
( nil = sk2
| app(cons(sk5,nil),sk6) = sk2 ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f446,plain,
( nil = sk2
| app(sk6,cons(sk5,nil)) != sk1 ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f447,plain,
( nil != sk1
| ssList(sk6) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f448,plain,
( nil != sk1
| app(cons(sk5,nil),sk6) = sk2 ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f450,plain,
( ~ neq(sk4,nil)
| ssItem(sk7) ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f451,plain,
( ~ neq(sk4,nil)
| ssList(sk8) ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f452,plain,
( ~ neq(sk4,nil)
| app(cons(sk7,nil),sk8) = sk4 ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f453,plain,
( ~ neq(sk4,nil)
| app(sk8,cons(sk7,nil)) = sk3 ),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f461,definition,
( sQ2_spl
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f462,plain,
( ~ sQ2_spl
| nil = sk3 ),
inference(component_clause,[status(thm)],[f461]) ).
fof(f464,definition,
( sQ3_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f466,plain,
( sQ3_spl
| nil != sk4 ),
inference(component_clause,[status(thm)],[f464]) ).
fof(f467,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f441,f461,f464]) ).
fof(f468,definition,
( sQ4_spl
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f471,definition,
( sQ5_spl
<=> nil = sk2 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f472,plain,
( ~ sQ5_spl
| nil = sk2 ),
inference(component_clause,[status(thm)],[f471]) ).
fof(f474,plain,
( sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f442,f468,f471]) ).
fof(f475,definition,
( sQ6_spl
<=> nil = sk1 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f477,plain,
( sQ6_spl
| nil != sk1 ),
inference(component_clause,[status(thm)],[f475]) ).
fof(f478,plain,
( ~ sQ6_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f443,f468,f475]) ).
fof(f479,definition,
( sQ7_spl
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f482,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f444,f479,f471]) ).
fof(f483,definition,
( sQ8_spl
<=> app(cons(sk5,nil),sk6) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f484,plain,
( ~ sQ8_spl
| app(cons(sk5,nil),sk6) = sk2 ),
inference(component_clause,[status(thm)],[f483]) ).
fof(f486,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f445,f483,f471]) ).
fof(f487,definition,
( sQ9_spl
<=> app(sk6,cons(sk5,nil)) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f489,plain,
( sQ9_spl
| app(sk6,cons(sk5,nil)) != sk1 ),
inference(component_clause,[status(thm)],[f487]) ).
fof(f490,plain,
( sQ5_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f446,f487,f471]) ).
fof(f491,plain,
( ~ sQ6_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f447,f479,f475]) ).
fof(f492,plain,
( ~ sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f448,f483,f475]) ).
fof(f494,definition,
( sQ10_spl
<=> ssItem(sk7) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f497,definition,
( sQ11_spl
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f499,plain,
( sQ11_spl
| ~ neq(sk4,nil) ),
inference(component_clause,[status(thm)],[f497]) ).
fof(f500,plain,
( ~ sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f450,f494,f497]) ).
fof(f501,definition,
( sQ12_spl
<=> ssList(sk8) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f504,plain,
( ~ sQ11_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f451,f501,f497]) ).
fof(f505,definition,
( sQ13_spl
<=> app(cons(sk7,nil),sk8) = sk4 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f506,plain,
( ~ sQ13_spl
| app(cons(sk7,nil),sk8) = sk4 ),
inference(component_clause,[status(thm)],[f505]) ).
fof(f508,plain,
( ~ sQ11_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f452,f505,f497]) ).
fof(f509,definition,
( sQ14_spl
<=> app(sk8,cons(sk7,nil)) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f510,plain,
( ~ sQ14_spl
| app(sk8,cons(sk7,nil)) = sk3 ),
inference(component_clause,[status(thm)],[f509]) ).
fof(f512,plain,
( ~ sQ11_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f453,f509,f497]) ).
fof(f527,plain,
( ~ sQ2_spl
| sk1 = nil ),
inference(backward_demodulation,[status(thm)],[f462,f440]) ).
fof(f528,plain,
( ~ sQ2_spl
| sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f527,f477]) ).
fof(f529,plain,
( ~ sQ2_spl
| sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f528]) ).
fof(f530,plain,
( sQ11_spl
| ~ neq(sk2,nil) ),
inference(backward_demodulation,[status(thm)],[f439,f499]) ).
fof(f532,definition,
( sQ15_spl
<=> ssList(cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f534,plain,
( sQ15_spl
| ~ ssList(cons(sk5,nil)) ),
inference(component_clause,[status(thm)],[f532]) ).
fof(f535,definition,
( sQ16_spl
<=> ssList(sk2) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f539,plain,
( sQ3_spl
| nil != sk2 ),
inference(forward_demodulation,[status(thm)],[f439,f466]) ).
fof(f540,plain,
( ~ sQ5_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f472,f539]) ).
fof(f541,plain,
( ~ sQ5_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f540]) ).
fof(f550,plain,
( sQ11_spl
| sk2 = nil
| ~ ssList(sk2)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f530,f307]) ).
fof(f558,definition,
( sQ19_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f560,plain,
( sQ19_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f558]) ).
fof(f561,plain,
( sQ11_spl
| sQ5_spl
| ~ sQ16_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f550,f558,f535,f471,f497]) ).
fof(f568,plain,
( ~ ssList(nil)
| nil = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f332,f279]) ).
fof(f570,definition,
( sQ20_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f573,plain,
( sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f568,f558,f570]) ).
fof(f575,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f560,f212]) ).
fof(f576,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f575]) ).
fof(f604,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| nil != X1
| nil != X0 ),
inference(resolution,[status(thm)],[f366,f334]) ).
fof(f607,definition,
! [X0] :
( sQ23_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0)
| nil != X0 ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f608,plain,
! [X0] :
( ~ sQ23_spl
| ~ ssList(X0)
| ~ ssList(X0)
| nil != X0 ),
inference(component_clause,[status(thm)],[f607]) ).
fof(f610,definition,
! [X1] :
( sQ24_spl
<=> ( nil = X1
| ~ ssList(X1)
| ~ ssList(X1)
| nil != X1 ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f613,plain,
( sQ24_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f604,f607,f610]) ).
fof(f615,plain,
! [X0] :
( ~ sQ23_spl
| ~ ssList(X0)
| nil != X0 ),
inference(duplicate_literals_removal,[status(thm)],[f608]) ).
fof(f623,definition,
( sQ25_spl
<=> ssList(cons(sk7,nil)) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f625,plain,
( sQ25_spl
| ~ ssList(cons(sk7,nil)) ),
inference(component_clause,[status(thm)],[f623]) ).
fof(f657,plain,
( ~ sQ23_spl
| nil != nil ),
inference(resolution,[status(thm)],[f615,f212]) ).
fof(f658,plain,
( ~ sQ23_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f657]) ).
fof(f659,plain,
~ sQ23_spl,
inference(contradiction_clause,[status(thm)],[f658]) ).
fof(f660,plain,
( sQ15_spl
| ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f534,f291]) ).
fof(f661,plain,
( sQ15_spl
| ~ sQ19_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f660,f468,f558,f532]) ).
fof(f667,plain,
! [X0] :
( ~ ssList(app(nil,X0))
| app(nil,X0) = X0
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(app(nil,X0)) ),
inference(resolution,[status(thm)],[f375,f279]) ).
fof(f671,plain,
! [X0,X1] :
( X0 = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[f375]) ).
fof(f672,definition,
! [X0] :
( sQ29_spl
<=> ( ~ ssList(app(nil,X0))
| app(nil,X0) = X0
| ~ ssList(X0)
| ~ ssList(app(nil,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f675,plain,
( ~ sQ19_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f667,f672,f558]) ).
fof(f682,definition,
! [X0] :
( sQ31_spl
<=> ( X0 = X0
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f685,definition,
! [X1] :
( sQ32_spl
<=> ~ ssList(X1) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f686,plain,
! [X0] :
( ~ sQ32_spl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f685]) ).
fof(f688,plain,
( sQ32_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f671,f682,f685]) ).
fof(f690,plain,
( sQ25_spl
| ~ ssList(nil)
| ~ ssItem(sk7) ),
inference(resolution,[status(thm)],[f625,f291]) ).
fof(f691,plain,
( sQ25_spl
| ~ sQ19_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f690,f494,f558,f623]) ).
fof(f692,plain,
( ~ sQ13_spl
| app(cons(sk7,nil),sk8) = sk2 ),
inference(forward_demodulation,[status(thm)],[f439,f506]) ).
fof(f693,plain,
( ~ sQ13_spl
| sk2 = cons(sk7,sk8)
| ~ ssList(sk8)
| ~ ssItem(sk7) ),
inference(paramodulation,[status(thm)],[f692,f335]) ).
fof(f698,definition,
( sQ33_spl
<=> sk2 = cons(sk7,sk8) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f699,plain,
( ~ sQ33_spl
| sk2 = cons(sk7,sk8) ),
inference(component_clause,[status(thm)],[f698]) ).
fof(f701,plain,
( ~ sQ13_spl
| sQ33_spl
| ~ sQ12_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f693,f494,f501,f698,f505]) ).
fof(f712,plain,
( ~ sQ32_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f238,f686]) ).
fof(f731,plain,
~ sQ32_spl,
inference(contradiction_clause,[status(thm)],[f712]) ).
fof(f753,plain,
! [X0] :
( ~ sQ8_spl
| X0 = cons(sk5,nil)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6)
| ~ ssList(X0)
| app(X0,sk6) != sk2 ),
inference(paramodulation,[status(thm)],[f484,f377]) ).
fof(f755,definition,
! [X0] :
( sQ38_spl
<=> ( X0 = cons(sk5,nil)
| ~ ssList(X0)
| app(X0,sk6) != sk2 ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f756,plain,
! [X0] :
( ~ sQ38_spl
| X0 = cons(sk5,nil)
| ~ ssList(X0)
| app(X0,sk6) != sk2 ),
inference(component_clause,[status(thm)],[f755]) ).
fof(f758,plain,
( ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ7_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f753,f755,f479,f532,f483]) ).
fof(f760,plain,
! [X0,X1] :
( X0 = X0
| ~ ssList(X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(equality_resolution,[status(thm)],[f406]) ).
fof(f761,definition,
! [X0] :
( sQ39_spl
<=> ( X0 = X0
| ~ ssItem(X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f764,definition,
! [X1] :
( sQ40_spl
<=> ( ~ ssList(X1)
| ~ ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f765,plain,
! [X0] :
( ~ sQ40_spl
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f764]) ).
fof(f767,plain,
( sQ40_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f760,f761,f764]) ).
fof(f768,plain,
! [X0] :
( ~ sQ40_spl
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f765]) ).
fof(f770,definition,
! [X0] :
( sQ41_spl
<=> ( ~ ssItem(X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f771,plain,
! [X0] :
( ~ sQ41_spl
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f770]) ).
fof(f774,plain,
! [X0] :
( ~ sQ41_spl
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f771]) ).
fof(f775,plain,
( ~ sQ40_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f435,f768]) ).
fof(f779,plain,
~ sQ40_spl,
inference(contradiction_clause,[status(thm)],[f775]) ).
fof(f780,plain,
( ~ sQ41_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f244,f774]) ).
fof(f781,plain,
~ sQ41_spl,
inference(contradiction_clause,[status(thm)],[f780]) ).
fof(f782,plain,
( ~ sQ14_spl
| app(sk8,cons(sk7,nil)) = sk1 ),
inference(forward_demodulation,[status(thm)],[f440,f510]) ).
fof(f837,plain,
( ~ sQ8_spl
| sk2 = cons(sk5,sk6)
| ~ ssList(sk6)
| ~ ssItem(sk5) ),
inference(paramodulation,[status(thm)],[f484,f335]) ).
fof(f839,definition,
( sQ46_spl
<=> sk2 = cons(sk5,sk6) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f840,plain,
( ~ sQ46_spl
| sk2 = cons(sk5,sk6) ),
inference(component_clause,[status(thm)],[f839]) ).
fof(f842,plain,
( ~ sQ8_spl
| sQ46_spl
| ~ sQ7_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f837,f468,f479,f839,f483]) ).
fof(f921,plain,
( ~ sQ8_spl
| cons(sk5,app(nil,sk6)) = sk2
| ~ ssList(sk6)
| ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(paramodulation,[status(thm)],[f484,f388]) ).
fof(f926,definition,
( sQ56_spl
<=> cons(sk5,app(nil,sk6)) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f927,plain,
( ~ sQ56_spl
| cons(sk5,app(nil,sk6)) = sk2 ),
inference(component_clause,[status(thm)],[f926]) ).
fof(f929,plain,
( ~ sQ8_spl
| sQ56_spl
| ~ sQ7_spl
| ~ sQ19_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f921,f468,f558,f479,f926,f483]) ).
fof(f953,plain,
( ~ sQ56_spl
| ssList(sk2)
| ~ ssList(app(nil,sk6))
| ~ ssItem(sk5) ),
inference(paramodulation,[status(thm)],[f927,f291]) ).
fof(f954,plain,
( ~ sQ56_spl
| ~ ssList(app(nil,sk6))
| ~ ssItem(sk5)
| sk2 != nil ),
inference(paramodulation,[status(thm)],[f927,f304]) ).
fof(f956,definition,
( sQ61_spl
<=> ssList(app(nil,sk6)) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f958,plain,
( sQ61_spl
| ~ ssList(app(nil,sk6)) ),
inference(component_clause,[status(thm)],[f956]) ).
fof(f963,plain,
( ~ sQ56_spl
| sQ16_spl
| ~ sQ61_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f953,f468,f956,f535,f926]) ).
fof(f964,plain,
( ~ sQ56_spl
| ~ sQ61_spl
| ~ sQ4_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f954,f471,f468,f956,f926]) ).
fof(f970,plain,
! [X0,X1] :
( ~ sQ46_spl
| X1 = sk6
| ~ ssList(sk6)
| ~ ssList(X1)
| ~ ssItem(sk5)
| ~ ssItem(X0)
| sk2 != cons(X0,X1) ),
inference(paramodulation,[status(thm)],[f840,f408]) ).
fof(f982,definition,
! [X0,X1] :
( sQ65_spl
<=> ( X1 = sk6
| ~ ssList(X1)
| ~ ssItem(X0)
| sk2 != cons(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f983,plain,
! [X0,X1] :
( ~ sQ65_spl
| X1 = sk6
| ~ ssList(X1)
| ~ ssItem(X0)
| sk2 != cons(X0,X1) ),
inference(component_clause,[status(thm)],[f982]) ).
fof(f985,plain,
( ~ sQ46_spl
| ~ sQ7_spl
| ~ sQ4_spl
| sQ65_spl ),
inference(split_clause,[status(thm)],[f970,f982,f468,f479,f839]) ).
fof(f1023,plain,
( sQ61_spl
| ~ ssList(nil)
| ~ ssList(sk6) ),
inference(resolution,[status(thm)],[f958,f290]) ).
fof(f1024,plain,
( sQ61_spl
| ~ sQ19_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1023,f479,f558,f956]) ).
fof(f1032,plain,
! [X0] :
( ~ ssList(app(X0,nil))
| app(X0,nil) = X0
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(app(X0,nil)) ),
inference(resolution,[status(thm)],[f377,f278]) ).
fof(f1041,definition,
! [X0] :
( sQ71_spl
<=> ( ~ ssList(app(X0,nil))
| app(X0,nil) = X0
| ~ ssList(X0)
| ~ ssList(app(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f1044,plain,
( ~ sQ19_spl
| sQ71_spl ),
inference(split_clause,[status(thm)],[f1032,f1041,f558]) ).
fof(f1065,plain,
( ~ sQ33_spl
| ~ sQ65_spl
| sk8 = sk6
| ~ ssList(sk8)
| ~ ssItem(sk7) ),
inference(resolution,[status(thm)],[f983,f699]) ).
fof(f1073,definition,
( sQ74_spl
<=> sk8 = sk6 ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f1074,plain,
( ~ sQ74_spl
| sk8 = sk6 ),
inference(component_clause,[status(thm)],[f1073]) ).
fof(f1076,plain,
( ~ sQ33_spl
| ~ sQ65_spl
| sQ74_spl
| ~ sQ12_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f1065,f494,f501,f1073,f982,f698]) ).
fof(f1099,plain,
( ~ sQ14_spl
| ~ sQ74_spl
| app(sk6,cons(sk7,nil)) = sk1 ),
inference(backward_demodulation,[status(thm)],[f1074,f782]) ).
fof(f1101,plain,
( ~ sQ13_spl
| ~ sQ74_spl
| app(cons(sk7,nil),sk6) = sk2 ),
inference(backward_demodulation,[status(thm)],[f1074,f692]) ).
fof(f1134,plain,
( ~ sQ38_spl
| ~ sQ13_spl
| ~ sQ74_spl
| cons(sk7,nil) = cons(sk5,nil)
| ~ ssList(cons(sk7,nil)) ),
inference(resolution,[status(thm)],[f1101,f756]) ).
fof(f1147,definition,
( sQ81_spl
<=> cons(sk7,nil) = cons(sk5,nil) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f1148,plain,
( ~ sQ81_spl
| cons(sk7,nil) = cons(sk5,nil) ),
inference(component_clause,[status(thm)],[f1147]) ).
fof(f1150,plain,
( ~ sQ38_spl
| ~ sQ13_spl
| ~ sQ74_spl
| sQ81_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f1134,f623,f1147,f1073,f505,f755]) ).
fof(f1271,plain,
( ~ sQ14_spl
| ~ sQ74_spl
| ~ sQ81_spl
| app(sk6,cons(sk5,nil)) = sk1 ),
inference(backward_demodulation,[status(thm)],[f1148,f1099]) ).
fof(f1294,plain,
( ~ sQ14_spl
| ~ sQ74_spl
| ~ sQ81_spl
| sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1271,f489]) ).
fof(f1295,plain,
( ~ sQ14_spl
| ~ sQ74_spl
| ~ sQ81_spl
| sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f1294]) ).
fof(f1296,plain,
$false,
inference(sat_refutation,[status(thm)],[f467,f474,f478,f482,f486,f490,f491,f492,f500,f504,f508,f512,f529,f541,f561,f573,f576,f613,f659,f661,f675,f688,f691,f701,f731,f758,f767,f779,f781,f842,f929,f963,f964,f985,f1024,f1044,f1076,f1150,f1295]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC315-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 08:15:05 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.14/0.39 % Drodi V4.1.1
% 0.14/0.43 % Refutation found
% 0.14/0.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.45 % Elapsed time: 0.079098 seconds
% 0.14/0.45 % CPU time: 0.330602 seconds
% 0.14/0.45 % Total memory used: 113.692 MB
% 0.14/0.45 % Net memory used: 113.395 MB
%------------------------------------------------------------------------------