%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC377-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 02:41:00 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.52s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 57
% Syntax : Number of formulae : 193 ( 17 unt; 30 def)
% Number of atoms : 614 ( 60 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 806 ( 385 ~; 391 |; 0 &)
% ( 30 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 36 ( 34 usr; 31 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 119 ( 119 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [U,V] : ssList(skaf42(U,V)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f71,axiom,
! [U] :
( ~ ssItem(U)
| ~ memberP(nil,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(f100,axiom,
! [U,V] :
( V = U
| neq(V,U)
| ~ ssList(V)
| ~ 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(f118,axiom,
! [U,V] :
( nil = U
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f120,axiom,
! [U,V] :
( app(cons(U,nil),V) = cons(U,V)
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f138,axiom,
! [U,V,W] :
( memberP(cons(V,W),U)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ ssList(W)
| U != V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f139,axiom,
! [U,V,W] :
( memberP(cons(W,U),V)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ ssList(U)
| ~ memberP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f140,axiom,
! [U,V,W] :
( memberP(app(U,W),V)
| ~ ssItem(V)
| ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f141,axiom,
! [U,V,W] :
( memberP(app(W,U),V)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(U)
| ~ memberP(U,V) ),
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(f158,axiom,
! [U,V,W] :
( memberP(U,W)
| memberP(V,W)
| ~ ssItem(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ memberP(app(U,V),W) ),
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,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
( memberP(sk1,sk5)
| memberP(sk2,sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
( ~ memberP(sk1,sk5)
| ~ memberP(sk2,sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
( nil != sk4
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk6,nil),sk7) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f199,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk7,cons(sk6,nil)) = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f207,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f252,plain,
! [X0,X1] : ssList(skaf42(X0,X1)),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f270,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f274,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f285,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f286,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f302,plain,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f320,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ~ neq(U,V)
| U != V ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f321,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f326,plain,
! [U] :
( nil = U
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f118]) ).
fof(f327,plain,
! [X0,X1] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f326]) ).
fof(f330,plain,
! [X0,X1] :
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f352,plain,
! [X0,X1,X2] :
( memberP(cons(X1,X2),X0)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f353,plain,
! [X0,X1,X2] :
( memberP(cons(X2,X0),X1)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f354,plain,
! [X0,X1,X2] :
( memberP(app(X0,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f355,plain,
! [X0,X1,X2] :
( memberP(app(X2,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f369,plain,
! [V,W] :
( V = W
| ~ ssList(W)
| ! [U] :
( ~ ssList(U)
| ~ ssList(V)
| app(U,V) != app(U,W) ) ),
inference(miniscoping,[status(thm)],[f150]) ).
fof(f370,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != app(X0,X2) ),
inference(cnf_transformation,[status(thm)],[f369]) ).
fof(f384,plain,
! [U,W] :
( memberP(U,W)
| ! [V] :
( memberP(V,W)
| ~ ssItem(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ memberP(app(U,V),W) ) ),
inference(miniscoping,[status(thm)],[f158]) ).
fof(f385,plain,
! [X0,X1,X2] :
( memberP(X0,X2)
| memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ memberP(app(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f431,plain,
ssList(sk2),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f434,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f435,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f436,plain,
ssItem(sk5),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f437,plain,
( memberP(sk1,sk5)
| memberP(sk2,sk5) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f438,plain,
( ~ memberP(sk1,sk5)
| ~ memberP(sk2,sk5) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f439,plain,
( nil != sk4
| nil = sk3 ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f440,plain,
( ~ neq(sk4,nil)
| ssItem(sk6) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f441,plain,
( ~ neq(sk4,nil)
| ssList(sk7) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f442,plain,
( ~ neq(sk4,nil)
| app(cons(sk6,nil),sk7) = sk3 ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f443,plain,
( ~ neq(sk4,nil)
| app(sk7,cons(sk6,nil)) = sk4 ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f451,definition,
( sQ2_spl
<=> memberP(sk2,sk5) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f452,plain,
( ~ sQ2_spl
| memberP(sk2,sk5) ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f453,plain,
( sQ2_spl
| ~ memberP(sk2,sk5) ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f454,definition,
( sQ3_spl
<=> memberP(sk1,sk5) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f455,plain,
( ~ sQ3_spl
| memberP(sk1,sk5) ),
inference(component_clause,[status(thm)],[f454]) ).
fof(f457,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f437,f451,f454]) ).
fof(f458,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f438,f451,f454]) ).
fof(f459,definition,
( sQ4_spl
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f460,plain,
( ~ sQ4_spl
| nil = sk3 ),
inference(component_clause,[status(thm)],[f459]) ).
fof(f462,definition,
( sQ5_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f463,plain,
( ~ sQ5_spl
| nil = sk4 ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f464,plain,
( sQ5_spl
| nil != sk4 ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f465,plain,
( ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f439,f459,f462]) ).
fof(f466,definition,
( sQ6_spl
<=> ssItem(sk6) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f469,definition,
( sQ7_spl
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f470,plain,
( ~ sQ7_spl
| neq(sk4,nil) ),
inference(component_clause,[status(thm)],[f469]) ).
fof(f471,plain,
( sQ7_spl
| ~ neq(sk4,nil) ),
inference(component_clause,[status(thm)],[f469]) ).
fof(f472,plain,
( ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f440,f466,f469]) ).
fof(f473,definition,
( sQ8_spl
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f476,plain,
( ~ sQ7_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f441,f473,f469]) ).
fof(f477,definition,
( sQ9_spl
<=> app(cons(sk6,nil),sk7) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f478,plain,
( ~ sQ9_spl
| app(cons(sk6,nil),sk7) = sk3 ),
inference(component_clause,[status(thm)],[f477]) ).
fof(f480,plain,
( ~ sQ7_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f442,f477,f469]) ).
fof(f481,definition,
( sQ10_spl
<=> app(sk7,cons(sk6,nil)) = sk4 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f482,plain,
( ~ sQ10_spl
| app(sk7,cons(sk6,nil)) = sk4 ),
inference(component_clause,[status(thm)],[f481]) ).
fof(f484,plain,
( ~ sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f443,f481,f469]) ).
fof(f492,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f321]) ).
fof(f493,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f492]) ).
fof(f497,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(destructive_equality_resolution,[status(thm)],[f352]) ).
fof(f498,plain,
! [X0,X1] :
( memberP(cons(X1,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f497]) ).
fof(f515,plain,
( sQ7_spl
| ~ neq(sk2,nil) ),
inference(forward_demodulation,[status(thm)],[f434,f471]) ).
fof(f518,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| memberP(nil,sk5) ),
inference(backward_demodulation,[status(thm)],[f520,f455]) ).
fof(f520,plain,
( ~ sQ4_spl
| nil = sk1 ),
inference(forward_demodulation,[status(thm)],[f435,f460]) ).
fof(f521,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f518,f270]) ).
fof(f522,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f521,f436]) ).
fof(f523,plain,
( ~ sQ3_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f522]) ).
fof(f524,plain,
( sQ5_spl
| nil != sk2 ),
inference(forward_demodulation,[status(thm)],[f434,f464]) ).
fof(f525,plain,
( sQ7_spl
| sk2 = nil
| ~ ssList(sk2)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f302,f515]) ).
fof(f528,definition,
( sQ11_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f530,plain,
( sQ11_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f528]) ).
fof(f531,definition,
( sQ12_spl
<=> ssList(sk2) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f533,plain,
( sQ12_spl
| ~ ssList(sk2) ),
inference(component_clause,[status(thm)],[f531]) ).
fof(f534,definition,
( sQ13_spl
<=> sk2 = nil ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f535,plain,
( ~ sQ13_spl
| sk2 = nil ),
inference(component_clause,[status(thm)],[f534]) ).
fof(f537,plain,
( sQ7_spl
| sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f525,f528,f531,f534,f469]) ).
fof(f538,plain,
( ~ sQ13_spl
| sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f535,f524]) ).
fof(f539,plain,
( ~ sQ13_spl
| sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f538]) ).
fof(f540,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f533,f431]) ).
fof(f541,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f540]) ).
fof(f542,plain,
( ~ sQ5_spl
| nil = sk2 ),
inference(forward_demodulation,[status(thm)],[f434,f463]) ).
fof(f543,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f530,f207]) ).
fof(f544,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f543]) ).
fof(f545,plain,
( ~ sQ10_spl
| app(sk7,cons(sk6,nil)) = sk2 ),
inference(forward_demodulation,[status(thm)],[f434,f482]) ).
fof(f546,plain,
( ~ sQ7_spl
| neq(sk2,nil) ),
inference(forward_demodulation,[status(thm)],[f434,f470]) ).
fof(f549,plain,
( ~ ssList(nil)
| nil = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f327,f274]) ).
fof(f551,definition,
( sQ14_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f554,plain,
( sQ14_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f549,f528,f551]) ).
fof(f560,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| neq(nil,nil) ),
inference(backward_demodulation,[status(thm)],[f542,f546]) ).
fof(f561,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| memberP(nil,sk5) ),
inference(backward_demodulation,[status(thm)],[f542,f452]) ).
fof(f565,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f560,f493]) ).
fof(f566,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f565,f528,f462,f469]) ).
fof(f567,plain,
( ~ sQ9_spl
| app(cons(sk6,nil),sk7) = sk1 ),
inference(forward_demodulation,[status(thm)],[f435,f478]) ).
fof(f570,plain,
( ~ sQ9_spl
| ssList(sk1)
| ~ ssList(cons(sk6,nil))
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f567,f285]) ).
fof(f574,definition,
( sQ16_spl
<=> ssList(cons(sk6,nil)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f576,plain,
( sQ16_spl
| ~ ssList(cons(sk6,nil)) ),
inference(component_clause,[status(thm)],[f574]) ).
fof(f585,definition,
( sQ19_spl
<=> ssList(sk1) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f588,plain,
( ~ sQ9_spl
| sQ19_spl
| ~ sQ16_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f570,f473,f574,f585,f477]) ).
fof(f590,plain,
( sQ16_spl
| ~ ssList(nil)
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f576,f286]) ).
fof(f591,plain,
( sQ16_spl
| ~ sQ11_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f590,f466,f528,f574]) ).
fof(f592,plain,
! [X0] :
( ~ sQ9_spl
| memberP(sk1,X0)
| ~ ssItem(X0)
| ~ ssList(cons(sk6,nil))
| ~ ssList(sk7)
| ~ memberP(cons(sk6,nil),X0) ),
inference(paramodulation,[status(thm)],[f567,f354]) ).
fof(f593,definition,
! [X0] :
( sQ20_spl
<=> ( memberP(sk1,X0)
| ~ ssItem(X0)
| ~ memberP(cons(sk6,nil),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f594,plain,
! [X0] :
( ~ sQ20_spl
| memberP(sk1,X0)
| ~ ssItem(X0)
| ~ memberP(cons(sk6,nil),X0) ),
inference(component_clause,[status(thm)],[f593]) ).
fof(f596,plain,
( ~ sQ9_spl
| ~ sQ16_spl
| ~ sQ8_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f592,f593,f473,f574,f477]) ).
fof(f597,plain,
! [X0] :
( ~ sQ20_spl
| ~ ssItem(X0)
| ~ ssItem(sk6)
| ~ ssList(nil)
| ~ memberP(nil,X0)
| memberP(sk1,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f594,f353]) ).
fof(f598,plain,
( ~ sQ20_spl
| ~ ssItem(sk6)
| ~ ssList(nil)
| memberP(sk1,sk6)
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f594,f498]) ).
fof(f599,definition,
! [X0] :
( sQ21_spl
<=> ( ~ ssItem(X0)
| ~ memberP(nil,X0)
| memberP(sk1,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f602,plain,
( ~ sQ20_spl
| ~ sQ6_spl
| ~ sQ11_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f597,f599,f528,f466,f593]) ).
fof(f603,definition,
( sQ22_spl
<=> memberP(sk1,sk6) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f606,plain,
( ~ sQ20_spl
| ~ sQ11_spl
| sQ22_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f598,f466,f603,f528,f593]) ).
fof(f608,plain,
! [X0] :
( ~ sQ9_spl
| memberP(sk1,X0)
| ~ ssItem(X0)
| ~ ssList(cons(sk6,nil))
| ~ ssList(sk7)
| ~ memberP(sk7,X0) ),
inference(paramodulation,[status(thm)],[f567,f355]) ).
fof(f609,definition,
! [X0] :
( sQ23_spl
<=> ( memberP(sk1,X0)
| ~ ssItem(X0)
| ~ memberP(sk7,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f610,plain,
! [X0] :
( ~ sQ23_spl
| memberP(sk1,X0)
| ~ ssItem(X0)
| ~ memberP(sk7,X0) ),
inference(component_clause,[status(thm)],[f609]) ).
fof(f612,plain,
( ~ sQ9_spl
| ~ sQ16_spl
| ~ sQ8_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f608,f609,f473,f574,f477]) ).
fof(f613,plain,
( ~ sQ9_spl
| sk1 = cons(sk6,sk7)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(paramodulation,[status(thm)],[f567,f330]) ).
fof(f614,definition,
( sQ24_spl
<=> sk1 = cons(sk6,sk7) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f617,plain,
( ~ sQ9_spl
| sQ24_spl
| ~ sQ8_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f613,f466,f473,f614,f477]) ).
fof(f652,plain,
! [X0] :
( ~ sQ10_spl
| memberP(sk2,X0)
| ~ ssItem(X0)
| ~ ssList(sk7)
| ~ ssList(cons(sk6,nil))
| ~ memberP(cons(sk6,nil),X0) ),
inference(paramodulation,[status(thm)],[f545,f355]) ).
fof(f653,plain,
! [X0] :
( ~ sQ10_spl
| memberP(sk2,X0)
| ~ ssItem(X0)
| ~ ssList(sk7)
| ~ ssList(cons(sk6,nil))
| ~ memberP(sk7,X0) ),
inference(paramodulation,[status(thm)],[f545,f354]) ).
fof(f657,definition,
! [X0] :
( sQ25_spl
<=> ( memberP(sk2,X0)
| ~ ssItem(X0)
| ~ memberP(cons(sk6,nil),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f658,plain,
! [X0] :
( ~ sQ25_spl
| memberP(sk2,X0)
| ~ ssItem(X0)
| ~ memberP(cons(sk6,nil),X0) ),
inference(component_clause,[status(thm)],[f657]) ).
fof(f660,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ16_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f652,f657,f574,f473,f481]) ).
fof(f661,definition,
! [X0] :
( sQ26_spl
<=> ( memberP(sk2,X0)
| ~ ssItem(X0)
| ~ memberP(sk7,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f662,plain,
! [X0] :
( ~ sQ26_spl
| memberP(sk2,X0)
| ~ ssItem(X0)
| ~ memberP(sk7,X0) ),
inference(component_clause,[status(thm)],[f661]) ).
fof(f664,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ16_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f653,f661,f574,f473,f481]) ).
fof(f668,plain,
! [X0] :
( ~ sQ25_spl
| ~ ssItem(X0)
| ~ ssItem(sk6)
| ~ ssList(nil)
| ~ memberP(nil,X0)
| memberP(sk2,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f658,f353]) ).
fof(f669,plain,
( ~ sQ25_spl
| ~ ssItem(sk6)
| ~ ssList(nil)
| memberP(sk2,sk6)
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f658,f498]) ).
fof(f670,definition,
! [X0] :
( sQ27_spl
<=> ( ~ ssItem(X0)
| ~ memberP(nil,X0)
| memberP(sk2,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f673,plain,
( ~ sQ25_spl
| ~ sQ6_spl
| ~ sQ11_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f668,f670,f528,f466,f657]) ).
fof(f674,definition,
( sQ28_spl
<=> memberP(sk2,sk6) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f677,plain,
( ~ sQ25_spl
| ~ sQ11_spl
| sQ28_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f669,f466,f674,f528,f657]) ).
fof(f681,plain,
! [X0] :
( ~ sQ10_spl
| memberP(sk7,X0)
| memberP(cons(sk6,nil),X0)
| ~ ssItem(X0)
| ~ ssList(sk7)
| ~ ssList(cons(sk6,nil))
| ~ memberP(sk2,X0) ),
inference(paramodulation,[status(thm)],[f545,f385]) ).
fof(f682,plain,
! [X0] :
( ~ sQ9_spl
| memberP(cons(sk6,nil),X0)
| memberP(sk7,X0)
| ~ ssItem(X0)
| ~ ssList(cons(sk6,nil))
| ~ ssList(sk7)
| ~ memberP(sk1,X0) ),
inference(paramodulation,[status(thm)],[f567,f385]) ).
fof(f683,definition,
! [X0] :
( sQ29_spl
<=> ( memberP(sk7,X0)
| memberP(cons(sk6,nil),X0)
| ~ ssItem(X0)
| ~ memberP(sk2,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f684,plain,
! [X0] :
( ~ sQ29_spl
| memberP(sk7,X0)
| memberP(cons(sk6,nil),X0)
| ~ ssItem(X0)
| ~ memberP(sk2,X0) ),
inference(component_clause,[status(thm)],[f683]) ).
fof(f686,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ16_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f681,f683,f574,f473,f481]) ).
fof(f687,definition,
! [X0] :
( sQ30_spl
<=> ( memberP(cons(sk6,nil),X0)
| memberP(sk7,X0)
| ~ ssItem(X0)
| ~ memberP(sk1,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f688,plain,
! [X0] :
( ~ sQ30_spl
| memberP(cons(sk6,nil),X0)
| memberP(sk7,X0)
| ~ ssItem(X0)
| ~ memberP(sk1,X0) ),
inference(component_clause,[status(thm)],[f687]) ).
fof(f690,plain,
( ~ sQ9_spl
| ~ sQ16_spl
| ~ sQ8_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f682,f687,f473,f574,f477]) ).
fof(f691,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ30_spl
| memberP(sk2,X0)
| ~ ssItem(X0)
| memberP(sk7,X0)
| ~ ssItem(X0)
| ~ memberP(sk1,X0) ),
inference(resolution,[status(thm)],[f688,f658]) ).
fof(f693,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ30_spl
| memberP(sk2,X0)
| memberP(sk7,X0)
| ~ ssItem(X0)
| ~ memberP(sk1,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f691]) ).
fof(f694,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ30_spl
| ~ sQ26_spl
| memberP(sk2,X0)
| ~ ssItem(X0)
| ~ memberP(sk1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f693,f662]) ).
fof(f695,plain,
( sQ2_spl
| ~ sQ25_spl
| ~ sQ30_spl
| ~ sQ26_spl
| ~ ssItem(sk5)
| ~ memberP(sk1,sk5) ),
inference(resolution,[status(thm)],[f694,f453]) ).
fof(f696,definition,
( sQ31_spl
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f698,plain,
( sQ31_spl
| ~ ssItem(sk5) ),
inference(component_clause,[status(thm)],[f696]) ).
fof(f699,plain,
( sQ2_spl
| ~ sQ25_spl
| ~ sQ30_spl
| ~ sQ26_spl
| ~ sQ31_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f695,f454,f696,f661,f687,f657,f451]) ).
fof(f700,plain,
( sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f698,f436]) ).
fof(f701,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f700]) ).
fof(f703,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ29_spl
| memberP(sk1,X0)
| ~ ssItem(X0)
| memberP(sk7,X0)
| ~ ssItem(X0)
| ~ memberP(sk2,X0) ),
inference(resolution,[status(thm)],[f684,f594]) ).
fof(f704,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ29_spl
| memberP(sk1,X0)
| memberP(sk7,X0)
| ~ ssItem(X0)
| ~ memberP(sk2,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f703]) ).
fof(f705,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ29_spl
| ~ sQ23_spl
| memberP(sk1,X0)
| ~ ssItem(X0)
| ~ memberP(sk2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f704,f610]) ).
fof(f706,plain,
( ~ sQ2_spl
| ~ sQ20_spl
| ~ sQ29_spl
| ~ sQ23_spl
| memberP(sk1,sk5)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f705,f452]) ).
fof(f709,plain,
( ~ sQ2_spl
| ~ sQ20_spl
| ~ sQ29_spl
| ~ sQ23_spl
| sQ3_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f706,f696,f454,f609,f683,f593,f451]) ).
fof(f715,plain,
! [X0] :
( ~ ssList(app(nil,X0))
| app(nil,X0) = X0
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(app(nil,X0)) ),
inference(resolution,[status(thm)],[f370,f274]) ).
fof(f717,plain,
! [X0,X1] :
( X0 = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[f370]) ).
fof(f718,definition,
! [X0] :
( sQ32_spl
<=> ( ~ ssList(app(nil,X0))
| app(nil,X0) = X0
| ~ ssList(X0)
| ~ ssList(app(nil,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f721,plain,
( ~ sQ11_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f715,f718,f528]) ).
fof(f723,definition,
! [X0] :
( sQ33_spl
<=> ( X0 = X0
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f726,definition,
! [X1] :
( sQ34_spl
<=> ~ ssList(X1) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f727,plain,
! [X0] :
( ~ sQ34_spl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f726]) ).
fof(f729,plain,
( sQ34_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f717,f723,f726]) ).
fof(f745,plain,
( ~ sQ34_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f252,f727]) ).
fof(f776,plain,
~ sQ34_spl,
inference(contradiction_clause,[status(thm)],[f745]) ).
fof(f784,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f270,f561]) ).
fof(f785,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f784,f696,f462,f451]) ).
fof(f786,plain,
$false,
inference(sat_refutation,[status(thm)],[f457,f458,f465,f472,f476,f480,f484,f523,f537,f539,f541,f544,f554,f566,f588,f591,f596,f602,f606,f612,f617,f660,f664,f673,f677,f686,f690,f699,f701,f709,f721,f729,f776,f785]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC377-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 08:22:16 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.52 % Refutation found
% 0.10/0.52 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.53 % Elapsed time: 0.167235 seconds
% 0.10/0.53 % CPU time: 1.021733 seconds
% 0.10/0.53 % Total memory used: 129.939 MB
% 0.10/0.53 % Net memory used: 128.810 MB
%------------------------------------------------------------------------------