%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC378-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 66
% Syntax : Number of formulae : 216 ( 18 unt; 49 def)
% Number of atoms : 777 ( 94 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 1050 ( 489 ~; 512 |; 0 &)
% ( 49 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 54 ( 52 usr; 50 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 135 ( 135 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f85,axiom,
! [U,V] :
( ssList(app(V,U))
| ~ ssList(V)
| ~ ssList(U) ),
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(f149,axiom,
! [U,V,W] :
( app(app(W,V),U) = app(W,app(V,U))
| ~ ssList(W)
| ~ ssList(V)
| ~ ssList(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(f157,axiom,
! [U,V,W] :
( cons(U,app(V,W)) = app(cons(U,V),W)
| ~ ssList(W)
| ~ ssList(V)
| ~ ssItem(U) ),
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(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,
ssList(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
app(sk5,sk6) = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
app(sk6,sk5) = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
ssItem(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( memberP(sk1,sk7)
| memberP(sk2,sk7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
( ~ memberP(sk1,sk7)
| ~ memberP(sk2,sk7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f284,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f353,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(f354,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(f367,plain,
! [X0,X1,X2] :
( app(app(X2,X1),X0) = app(X2,app(X1,X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f368,plain,
! [V,W] :
( V = W
| ~ ssList(W)
| ! [U] :
( ~ ssList(U)
| ~ ssList(V)
| app(U,V) != app(U,W) ) ),
inference(miniscoping,[status(thm)],[f150]) ).
fof(f369,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != app(X0,X2) ),
inference(cnf_transformation,[status(thm)],[f368]) ).
fof(f370,plain,
! [U,W] :
( U = W
| ~ ssList(W)
| ! [V] :
( ~ ssList(V)
| ~ ssList(U)
| app(U,V) != app(W,V) ) ),
inference(miniscoping,[status(thm)],[f151]) ).
fof(f371,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) != app(X2,X1) ),
inference(cnf_transformation,[status(thm)],[f370]) ).
fof(f382,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(f383,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(f384,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)],[f383]) ).
fof(f433,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f434,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f435,plain,
ssList(sk5),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f436,plain,
ssList(sk6),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f437,plain,
app(sk5,sk6) = sk4,
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f438,plain,
app(sk6,sk5) = sk3,
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f439,plain,
ssItem(sk7),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f440,plain,
( memberP(sk1,sk7)
| memberP(sk2,sk7) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f441,plain,
( ~ memberP(sk1,sk7)
| ~ memberP(sk2,sk7) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f449,definition,
( sQ2_spl
<=> memberP(sk2,sk7) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f450,plain,
( ~ sQ2_spl
| memberP(sk2,sk7) ),
inference(component_clause,[status(thm)],[f449]) ).
fof(f451,plain,
( sQ2_spl
| ~ memberP(sk2,sk7) ),
inference(component_clause,[status(thm)],[f449]) ).
fof(f452,definition,
( sQ3_spl
<=> memberP(sk1,sk7) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f453,plain,
( ~ sQ3_spl
| memberP(sk1,sk7) ),
inference(component_clause,[status(thm)],[f452]) ).
fof(f454,plain,
( sQ3_spl
| ~ memberP(sk1,sk7) ),
inference(component_clause,[status(thm)],[f452]) ).
fof(f455,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f440,f449,f452]) ).
fof(f456,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f441,f449,f452]) ).
fof(f488,plain,
( sQ2_spl
| ~ memberP(sk4,sk7) ),
inference(forward_demodulation,[status(thm)],[f433,f451]) ).
fof(f489,plain,
( ~ sQ3_spl
| memberP(sk3,sk7) ),
inference(forward_demodulation,[status(thm)],[f434,f453]) ).
fof(f490,plain,
( ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(sk5) ),
inference(paramodulation,[status(thm)],[f438,f284]) ).
fof(f491,plain,
( ssList(sk4)
| ~ ssList(sk5)
| ~ ssList(sk6) ),
inference(paramodulation,[status(thm)],[f437,f284]) ).
fof(f492,definition,
( sQ4_spl
<=> ssList(sk5) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f494,plain,
( sQ4_spl
| ~ ssList(sk5) ),
inference(component_clause,[status(thm)],[f492]) ).
fof(f495,definition,
( sQ5_spl
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f497,plain,
( sQ5_spl
| ~ ssList(sk6) ),
inference(component_clause,[status(thm)],[f495]) ).
fof(f498,definition,
( sQ6_spl
<=> ssList(sk3) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f501,plain,
( sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f490,f492,f495,f498]) ).
fof(f502,definition,
( sQ7_spl
<=> ssList(sk4) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f505,plain,
( sQ7_spl
| ~ sQ4_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f491,f495,f492,f502]) ).
fof(f506,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f494,f435]) ).
fof(f507,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f506]) ).
fof(f508,plain,
( ~ sQ2_spl
| memberP(sk4,sk7) ),
inference(forward_demodulation,[status(thm)],[f433,f450]) ).
fof(f509,plain,
( sQ3_spl
| ~ memberP(sk3,sk7) ),
inference(forward_demodulation,[status(thm)],[f434,f454]) ).
fof(f510,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f497,f436]) ).
fof(f511,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f510]) ).
fof(f512,plain,
! [X0] :
( sk5 = X0
| ~ ssList(X0)
| ~ ssList(sk6)
| ~ ssList(sk5)
| sk3 != app(sk6,X0) ),
inference(paramodulation,[status(thm)],[f438,f369]) ).
fof(f513,plain,
! [X0] :
( sk6 = X0
| ~ ssList(X0)
| ~ ssList(sk5)
| ~ ssList(sk6)
| sk4 != app(sk5,X0) ),
inference(paramodulation,[status(thm)],[f437,f369]) ).
fof(f517,definition,
! [X0] :
( sQ8_spl
<=> ( sk5 = X0
| ~ ssList(X0)
| sk3 != app(sk6,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f518,plain,
! [X0] :
( ~ sQ8_spl
| sk5 = X0
| ~ ssList(X0)
| sk3 != app(sk6,X0) ),
inference(component_clause,[status(thm)],[f517]) ).
fof(f520,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f512,f517,f492,f495]) ).
fof(f521,definition,
! [X0] :
( sQ9_spl
<=> ( sk6 = X0
| ~ ssList(X0)
| sk4 != app(sk5,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f522,plain,
! [X0] :
( ~ sQ9_spl
| sk6 = X0
| ~ ssList(X0)
| sk4 != app(sk5,X0) ),
inference(component_clause,[status(thm)],[f521]) ).
fof(f524,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f513,f521,f495,f492]) ).
fof(f534,plain,
( ~ sQ8_spl
| sk5 = sk5
| ~ ssList(sk5) ),
inference(resolution,[status(thm)],[f518,f438]) ).
fof(f536,definition,
( sQ12_spl
<=> sk5 = sk5 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f539,plain,
( ~ sQ8_spl
| sQ12_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f534,f492,f536,f517]) ).
fof(f544,plain,
( ~ sQ9_spl
| sk6 = sk6
| ~ ssList(sk6) ),
inference(resolution,[status(thm)],[f522,f437]) ).
fof(f546,definition,
( sQ14_spl
<=> sk6 = sk6 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f549,plain,
( ~ sQ9_spl
| sQ14_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f544,f495,f546,f521]) ).
fof(f554,plain,
! [X0] :
( sk6 = X0
| ~ ssList(X0)
| ~ ssList(sk5)
| ~ ssList(sk6)
| sk3 != app(X0,sk5) ),
inference(paramodulation,[status(thm)],[f438,f371]) ).
fof(f555,plain,
! [X0] :
( sk5 = X0
| ~ ssList(X0)
| ~ ssList(sk6)
| ~ ssList(sk5)
| sk4 != app(X0,sk6) ),
inference(paramodulation,[status(thm)],[f437,f371]) ).
fof(f559,definition,
! [X0] :
( sQ16_spl
<=> ( sk6 = X0
| ~ ssList(X0)
| sk3 != app(X0,sk5) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f560,plain,
! [X0] :
( ~ sQ16_spl
| sk6 = X0
| ~ ssList(X0)
| sk3 != app(X0,sk5) ),
inference(component_clause,[status(thm)],[f559]) ).
fof(f562,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f554,f559,f495,f492]) ).
fof(f563,definition,
! [X0] :
( sQ17_spl
<=> ( sk5 = X0
| ~ ssList(X0)
| sk4 != app(X0,sk6) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f566,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f555,f563,f492,f495]) ).
fof(f578,plain,
! [X0] :
( memberP(sk3,X0)
| ~ ssItem(X0)
| ~ ssList(sk6)
| ~ ssList(sk5)
| ~ memberP(sk6,X0) ),
inference(paramodulation,[status(thm)],[f438,f353]) ).
fof(f579,plain,
! [X0] :
( memberP(sk4,X0)
| ~ ssItem(X0)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ memberP(sk5,X0) ),
inference(paramodulation,[status(thm)],[f437,f353]) ).
fof(f580,definition,
! [X0] :
( sQ18_spl
<=> ( memberP(sk3,X0)
| ~ ssItem(X0)
| ~ memberP(sk6,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f581,plain,
! [X0] :
( ~ sQ18_spl
| memberP(sk3,X0)
| ~ ssItem(X0)
| ~ memberP(sk6,X0) ),
inference(component_clause,[status(thm)],[f580]) ).
fof(f583,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f578,f580,f492,f495]) ).
fof(f584,definition,
! [X0] :
( sQ19_spl
<=> ( memberP(sk4,X0)
| ~ ssItem(X0)
| ~ memberP(sk5,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f587,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f579,f584,f495,f492]) ).
fof(f588,plain,
! [X0] :
( memberP(sk3,X0)
| ~ ssItem(X0)
| ~ ssList(sk6)
| ~ ssList(sk5)
| ~ memberP(sk5,X0) ),
inference(paramodulation,[status(thm)],[f438,f354]) ).
fof(f589,plain,
! [X0] :
( memberP(sk4,X0)
| ~ ssItem(X0)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ memberP(sk6,X0) ),
inference(paramodulation,[status(thm)],[f437,f354]) ).
fof(f590,definition,
! [X0] :
( sQ20_spl
<=> ( memberP(sk3,X0)
| ~ ssItem(X0)
| ~ memberP(sk5,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f593,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f588,f590,f492,f495]) ).
fof(f594,definition,
! [X0] :
( sQ21_spl
<=> ( memberP(sk4,X0)
| ~ ssItem(X0)
| ~ memberP(sk6,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f595,plain,
! [X0] :
( ~ sQ21_spl
| memberP(sk4,X0)
| ~ ssItem(X0)
| ~ memberP(sk6,X0) ),
inference(component_clause,[status(thm)],[f594]) ).
fof(f597,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f589,f594,f495,f492]) ).
fof(f600,plain,
! [X0] :
( app(sk3,X0) = app(sk6,app(sk5,X0))
| ~ ssList(sk6)
| ~ ssList(sk5)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f438,f367]) ).
fof(f601,plain,
! [X0] :
( app(sk4,X0) = app(sk5,app(sk6,X0))
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f437,f367]) ).
fof(f602,definition,
! [X0] :
( sQ22_spl
<=> ( app(sk3,X0) = app(sk6,app(sk5,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f603,plain,
! [X0] :
( ~ sQ22_spl
| app(sk3,X0) = app(sk6,app(sk5,X0))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f602]) ).
fof(f605,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f600,f602,f492,f495]) ).
fof(f606,definition,
! [X0] :
( sQ23_spl
<=> ( app(sk4,X0) = app(sk5,app(sk6,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f607,plain,
! [X0] :
( ~ sQ23_spl
| app(sk4,X0) = app(sk5,app(sk6,X0))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f606]) ).
fof(f609,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f601,f606,f495,f492]) ).
fof(f610,plain,
( ~ sQ22_spl
| app(sk3,sk6) = app(sk6,sk4)
| ~ ssList(sk6) ),
inference(paramodulation,[status(thm)],[f437,f603]) ).
fof(f611,definition,
( sQ24_spl
<=> app(sk3,sk6) = app(sk6,sk4) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f612,plain,
( ~ sQ24_spl
| app(sk3,sk6) = app(sk6,sk4) ),
inference(component_clause,[status(thm)],[f611]) ).
fof(f614,plain,
( ~ sQ22_spl
| sQ24_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f610,f495,f611,f602]) ).
fof(f615,plain,
! [X0] :
( cons(X0,sk3) = app(cons(X0,sk6),sk5)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f438,f382]) ).
fof(f616,plain,
! [X0] :
( cons(X0,sk4) = app(cons(X0,sk5),sk6)
| ~ ssList(sk6)
| ~ ssList(sk5)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f437,f382]) ).
fof(f617,definition,
! [X0] :
( sQ25_spl
<=> ( cons(X0,sk3) = app(cons(X0,sk6),sk5)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f620,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f615,f617,f495,f492]) ).
fof(f621,definition,
! [X0] :
( sQ26_spl
<=> ( cons(X0,sk4) = app(cons(X0,sk5),sk6)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f624,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f616,f621,f492,f495]) ).
fof(f627,plain,
! [X0] :
( memberP(sk6,X0)
| memberP(sk5,X0)
| ~ ssItem(X0)
| ~ ssList(sk6)
| ~ ssList(sk5)
| ~ memberP(sk3,X0) ),
inference(paramodulation,[status(thm)],[f438,f384]) ).
fof(f628,plain,
! [X0] :
( memberP(sk5,X0)
| memberP(sk6,X0)
| ~ ssItem(X0)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ memberP(sk4,X0) ),
inference(paramodulation,[status(thm)],[f437,f384]) ).
fof(f629,definition,
! [X0] :
( sQ27_spl
<=> ( memberP(sk6,X0)
| memberP(sk5,X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f632,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f627,f629,f492,f495]) ).
fof(f633,definition,
! [X0] :
( sQ28_spl
<=> ( memberP(sk5,X0)
| memberP(sk6,X0)
| ~ ssItem(X0)
| ~ memberP(sk4,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f636,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f628,f633,f495,f492]) ).
fof(f638,plain,
! [X0] :
( ~ sQ24_spl
| memberP(sk3,X0)
| memberP(sk6,X0)
| ~ ssItem(X0)
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ memberP(app(sk6,sk4),X0) ),
inference(paramodulation,[status(thm)],[f612,f384]) ).
fof(f639,plain,
! [X0] :
( ~ sQ24_spl
| cons(X0,app(sk6,sk4)) = app(cons(X0,sk3),sk6)
| ~ ssList(sk6)
| ~ ssList(sk3)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f612,f382]) ).
fof(f640,plain,
! [X0] :
( ~ sQ24_spl
| app(app(sk6,sk4),X0) = app(sk3,app(sk6,X0))
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f612,f367]) ).
fof(f641,plain,
! [X0] :
( ~ sQ24_spl
| memberP(app(sk6,sk4),X0)
| ~ ssItem(X0)
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ memberP(sk6,X0) ),
inference(paramodulation,[status(thm)],[f612,f354]) ).
fof(f642,plain,
! [X0] :
( ~ sQ24_spl
| memberP(app(sk6,sk4),X0)
| ~ ssItem(X0)
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ memberP(sk3,X0) ),
inference(paramodulation,[status(thm)],[f612,f353]) ).
fof(f643,plain,
! [X0] :
( ~ sQ24_spl
| X0 = sk3
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(X0)
| app(X0,sk6) != app(sk6,sk4) ),
inference(paramodulation,[status(thm)],[f612,f371]) ).
fof(f645,plain,
! [X0] :
( ~ sQ24_spl
| X0 = sk6
| ~ ssList(sk6)
| ~ ssList(sk3)
| ~ ssList(X0)
| app(sk3,X0) != app(sk6,sk4) ),
inference(paramodulation,[status(thm)],[f612,f369]) ).
fof(f647,plain,
( ~ sQ24_spl
| ssList(app(sk6,sk4))
| ~ ssList(sk3)
| ~ ssList(sk6) ),
inference(paramodulation,[status(thm)],[f612,f284]) ).
fof(f655,definition,
! [X0] :
( sQ31_spl
<=> ( memberP(sk3,X0)
| memberP(sk6,X0)
| ~ ssItem(X0)
| ~ memberP(app(sk6,sk4),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f656,plain,
! [X0] :
( ~ sQ31_spl
| memberP(sk3,X0)
| memberP(sk6,X0)
| ~ ssItem(X0)
| ~ memberP(app(sk6,sk4),X0) ),
inference(component_clause,[status(thm)],[f655]) ).
fof(f658,plain,
( ~ sQ24_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f638,f655,f495,f498,f611]) ).
fof(f659,definition,
! [X0] :
( sQ32_spl
<=> ( cons(X0,app(sk6,sk4)) = app(cons(X0,sk3),sk6)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f662,plain,
( ~ sQ24_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f639,f659,f498,f495,f611]) ).
fof(f663,definition,
! [X0] :
( sQ33_spl
<=> ( app(app(sk6,sk4),X0) = app(sk3,app(sk6,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f666,plain,
( ~ sQ24_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f640,f663,f495,f498,f611]) ).
fof(f667,definition,
! [X0] :
( sQ34_spl
<=> ( memberP(app(sk6,sk4),X0)
| ~ ssItem(X0)
| ~ memberP(sk6,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f668,plain,
! [X0] :
( ~ sQ34_spl
| memberP(app(sk6,sk4),X0)
| ~ ssItem(X0)
| ~ memberP(sk6,X0) ),
inference(component_clause,[status(thm)],[f667]) ).
fof(f670,plain,
( ~ sQ24_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f641,f667,f495,f498,f611]) ).
fof(f671,definition,
! [X0] :
( sQ35_spl
<=> ( memberP(app(sk6,sk4),X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f672,plain,
! [X0] :
( ~ sQ35_spl
| memberP(app(sk6,sk4),X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ),
inference(component_clause,[status(thm)],[f671]) ).
fof(f674,plain,
( ~ sQ24_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f642,f671,f495,f498,f611]) ).
fof(f675,definition,
! [X0] :
( sQ36_spl
<=> ( X0 = sk3
| ~ ssList(X0)
| app(X0,sk6) != app(sk6,sk4) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f678,plain,
( ~ sQ24_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f643,f675,f495,f498,f611]) ).
fof(f680,definition,
! [X0] :
( sQ37_spl
<=> ( X0 = sk6
| ~ ssList(X0)
| app(sk3,X0) != app(sk6,sk4) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f683,plain,
( ~ sQ24_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f645,f680,f498,f495,f611]) ).
fof(f685,definition,
( sQ38_spl
<=> ssList(app(sk6,sk4)) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f688,plain,
( ~ sQ24_spl
| sQ38_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f647,f495,f498,f685,f611]) ).
fof(f689,plain,
! [X0] :
( ~ sQ31_spl
| ~ sQ18_spl
| memberP(sk3,X0)
| ~ ssItem(X0)
| ~ memberP(app(sk6,sk4),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f656,f581]) ).
fof(f690,plain,
( ~ sQ23_spl
| app(sk4,sk5) = app(sk5,sk3)
| ~ ssList(sk5) ),
inference(paramodulation,[status(thm)],[f438,f607]) ).
fof(f691,definition,
( sQ39_spl
<=> app(sk4,sk5) = app(sk5,sk3) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f692,plain,
( ~ sQ39_spl
| app(sk4,sk5) = app(sk5,sk3) ),
inference(component_clause,[status(thm)],[f691]) ).
fof(f694,plain,
( ~ sQ23_spl
| sQ39_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f690,f492,f691,f606]) ).
fof(f695,plain,
( ~ sQ39_spl
| ~ sQ16_spl
| sk6 = sk4
| ~ ssList(sk4)
| sk3 != app(sk5,sk3) ),
inference(paramodulation,[status(thm)],[f692,f560]) ).
fof(f696,plain,
! [X0] :
( ~ sQ39_spl
| memberP(sk4,X0)
| memberP(sk5,X0)
| ~ ssItem(X0)
| ~ ssList(sk4)
| ~ ssList(sk5)
| ~ memberP(app(sk5,sk3),X0) ),
inference(paramodulation,[status(thm)],[f692,f384]) ).
fof(f697,plain,
! [X0] :
( ~ sQ39_spl
| cons(X0,app(sk5,sk3)) = app(cons(X0,sk4),sk5)
| ~ ssList(sk5)
| ~ ssList(sk4)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f692,f382]) ).
fof(f698,plain,
! [X0] :
( ~ sQ39_spl
| app(app(sk5,sk3),X0) = app(sk4,app(sk5,X0))
| ~ ssList(sk4)
| ~ ssList(sk5)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f692,f367]) ).
fof(f699,plain,
! [X0] :
( ~ sQ39_spl
| memberP(app(sk5,sk3),X0)
| ~ ssItem(X0)
| ~ ssList(sk4)
| ~ ssList(sk5)
| ~ memberP(sk5,X0) ),
inference(paramodulation,[status(thm)],[f692,f354]) ).
fof(f700,plain,
! [X0] :
( ~ sQ39_spl
| memberP(app(sk5,sk3),X0)
| ~ ssItem(X0)
| ~ ssList(sk4)
| ~ ssList(sk5)
| ~ memberP(sk4,X0) ),
inference(paramodulation,[status(thm)],[f692,f353]) ).
fof(f701,plain,
! [X0] :
( ~ sQ39_spl
| X0 = sk4
| ~ ssList(sk4)
| ~ ssList(sk5)
| ~ ssList(X0)
| app(X0,sk5) != app(sk5,sk3) ),
inference(paramodulation,[status(thm)],[f692,f371]) ).
fof(f703,plain,
! [X0] :
( ~ sQ39_spl
| X0 = sk5
| ~ ssList(sk5)
| ~ ssList(sk4)
| ~ ssList(X0)
| app(sk4,X0) != app(sk5,sk3) ),
inference(paramodulation,[status(thm)],[f692,f369]) ).
fof(f705,plain,
( ~ sQ39_spl
| ssList(app(sk5,sk3))
| ~ ssList(sk4)
| ~ ssList(sk5) ),
inference(paramodulation,[status(thm)],[f692,f284]) ).
fof(f706,definition,
( sQ40_spl
<=> sk3 = app(sk5,sk3) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f709,definition,
( sQ41_spl
<=> sk6 = sk4 ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f712,plain,
( ~ sQ39_spl
| ~ sQ16_spl
| sQ41_spl
| ~ sQ7_spl
| ~ sQ40_spl ),
inference(split_clause,[status(thm)],[f695,f706,f502,f709,f559,f691]) ).
fof(f713,definition,
! [X0] :
( sQ42_spl
<=> ( memberP(sk4,X0)
| memberP(sk5,X0)
| ~ ssItem(X0)
| ~ memberP(app(sk5,sk3),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f716,plain,
( ~ sQ39_spl
| ~ sQ7_spl
| ~ sQ4_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f696,f713,f492,f502,f691]) ).
fof(f717,definition,
! [X0] :
( sQ43_spl
<=> ( cons(X0,app(sk5,sk3)) = app(cons(X0,sk4),sk5)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f720,plain,
( ~ sQ39_spl
| ~ sQ4_spl
| ~ sQ7_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f697,f717,f502,f492,f691]) ).
fof(f721,definition,
! [X0] :
( sQ44_spl
<=> ( app(app(sk5,sk3),X0) = app(sk4,app(sk5,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f724,plain,
( ~ sQ39_spl
| ~ sQ7_spl
| ~ sQ4_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f698,f721,f492,f502,f691]) ).
fof(f725,definition,
! [X0] :
( sQ45_spl
<=> ( memberP(app(sk5,sk3),X0)
| ~ ssItem(X0)
| ~ memberP(sk5,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f728,plain,
( ~ sQ39_spl
| ~ sQ7_spl
| ~ sQ4_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f699,f725,f492,f502,f691]) ).
fof(f729,definition,
! [X0] :
( sQ46_spl
<=> ( memberP(app(sk5,sk3),X0)
| ~ ssItem(X0)
| ~ memberP(sk4,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f732,plain,
( ~ sQ39_spl
| ~ sQ7_spl
| ~ sQ4_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f700,f729,f492,f502,f691]) ).
fof(f733,definition,
! [X0] :
( sQ47_spl
<=> ( X0 = sk4
| ~ ssList(X0)
| app(X0,sk5) != app(sk5,sk3) ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f736,plain,
( ~ sQ39_spl
| ~ sQ7_spl
| ~ sQ4_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f701,f733,f492,f502,f691]) ).
fof(f738,definition,
! [X0] :
( sQ48_spl
<=> ( X0 = sk5
| ~ ssList(X0)
| app(sk4,X0) != app(sk5,sk3) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f741,plain,
( ~ sQ39_spl
| ~ sQ4_spl
| ~ sQ7_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f703,f738,f502,f492,f691]) ).
fof(f743,definition,
( sQ49_spl
<=> ssList(app(sk5,sk3)) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f746,plain,
( ~ sQ39_spl
| sQ49_spl
| ~ sQ7_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f705,f492,f502,f743,f691]) ).
fof(f748,plain,
! [X0] :
( ~ sQ31_spl
| ~ sQ18_spl
| ~ ssItem(X0)
| ~ ssList(sk6)
| ~ ssList(sk4)
| ~ memberP(sk4,X0)
| memberP(sk3,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f689,f354]) ).
fof(f749,plain,
! [X0] :
( ~ sQ31_spl
| ~ sQ18_spl
| ~ ssItem(X0)
| ~ ssList(sk6)
| ~ ssList(sk4)
| ~ memberP(sk6,X0)
| memberP(sk3,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f689,f353]) ).
fof(f750,definition,
! [X0] :
( sQ50_spl
<=> ( ~ ssItem(X0)
| ~ memberP(sk4,X0)
| memberP(sk3,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f751,plain,
! [X0] :
( ~ sQ50_spl
| ~ ssItem(X0)
| ~ memberP(sk4,X0)
| memberP(sk3,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f750]) ).
fof(f753,plain,
( ~ sQ31_spl
| ~ sQ18_spl
| ~ sQ5_spl
| ~ sQ7_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f748,f750,f502,f495,f580,f655]) ).
fof(f754,definition,
! [X0] :
( sQ51_spl
<=> ( ~ ssItem(X0)
| ~ memberP(sk6,X0)
| memberP(sk3,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f757,plain,
( ~ sQ31_spl
| ~ sQ18_spl
| ~ sQ5_spl
| ~ sQ7_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f749,f754,f502,f495,f580,f655]) ).
fof(f758,plain,
! [X0] :
( ~ sQ50_spl
| ~ memberP(sk4,X0)
| memberP(sk3,X0)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f751]) ).
fof(f760,plain,
( ~ sQ2_spl
| ~ sQ50_spl
| memberP(sk3,sk7)
| ~ ssItem(sk7) ),
inference(resolution,[status(thm)],[f758,f508]) ).
fof(f761,definition,
( sQ52_spl
<=> ssItem(sk7) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f763,plain,
( sQ52_spl
| ~ ssItem(sk7) ),
inference(component_clause,[status(thm)],[f761]) ).
fof(f764,definition,
( sQ53_spl
<=> memberP(sk3,sk7) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f765,plain,
( ~ sQ53_spl
| memberP(sk3,sk7) ),
inference(component_clause,[status(thm)],[f764]) ).
fof(f767,plain,
( ~ sQ2_spl
| ~ sQ50_spl
| sQ53_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f760,f761,f764,f750,f449]) ).
fof(f768,plain,
( sQ52_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f763,f439]) ).
fof(f769,plain,
sQ52_spl,
inference(contradiction_clause,[status(thm)],[f768]) ).
fof(f770,plain,
( ~ sQ53_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f765,f509]) ).
fof(f771,plain,
( ~ sQ53_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f770]) ).
fof(f773,plain,
! [X0] :
( ~ sQ34_spl
| memberP(sk6,X0)
| memberP(sk4,X0)
| ~ ssItem(X0)
| ~ ssList(sk6)
| ~ ssList(sk4)
| ~ ssItem(X0)
| ~ memberP(sk6,X0) ),
inference(resolution,[status(thm)],[f668,f384]) ).
fof(f775,definition,
! [X0] :
( sQ54_spl
<=> ( memberP(sk6,X0)
| memberP(sk4,X0)
| ~ ssItem(X0)
| ~ ssItem(X0)
| ~ memberP(sk6,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f778,plain,
( ~ sQ34_spl
| ~ sQ5_spl
| ~ sQ7_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f773,f775,f502,f495,f667]) ).
fof(f780,plain,
! [X0] :
( ~ sQ35_spl
| memberP(sk6,X0)
| memberP(sk4,X0)
| ~ ssItem(X0)
| ~ ssList(sk6)
| ~ ssList(sk4)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ),
inference(resolution,[status(thm)],[f672,f384]) ).
fof(f781,definition,
! [X0] :
( sQ55_spl
<=> ( memberP(sk6,X0)
| memberP(sk4,X0)
| ~ ssItem(X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f782,plain,
! [X0] :
( ~ sQ55_spl
| memberP(sk6,X0)
| memberP(sk4,X0)
| ~ ssItem(X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ),
inference(component_clause,[status(thm)],[f781]) ).
fof(f784,plain,
( ~ sQ35_spl
| ~ sQ5_spl
| ~ sQ7_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f780,f781,f502,f495,f671]) ).
fof(f785,plain,
! [X0] :
( ~ sQ55_spl
| memberP(sk6,X0)
| memberP(sk4,X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f782]) ).
fof(f786,plain,
! [X0] :
( ~ sQ55_spl
| ~ sQ21_spl
| memberP(sk4,X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f785,f595]) ).
fof(f787,plain,
( ~ sQ3_spl
| ~ sQ55_spl
| ~ sQ21_spl
| memberP(sk4,sk7)
| ~ ssItem(sk7) ),
inference(resolution,[status(thm)],[f786,f489]) ).
fof(f788,definition,
( sQ56_spl
<=> memberP(sk4,sk7) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f789,plain,
( ~ sQ56_spl
| memberP(sk4,sk7) ),
inference(component_clause,[status(thm)],[f788]) ).
fof(f791,plain,
( ~ sQ3_spl
| ~ sQ55_spl
| ~ sQ21_spl
| sQ56_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f787,f761,f788,f594,f781,f452]) ).
fof(f792,plain,
( ~ sQ56_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f789,f488]) ).
fof(f793,plain,
( ~ sQ56_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f792]) ).
fof(f794,plain,
$false,
inference(sat_refutation,[status(thm)],[f455,f456,f501,f505,f507,f511,f520,f524,f539,f549,f562,f566,f583,f587,f593,f597,f605,f609,f614,f620,f624,f632,f636,f658,f662,f666,f670,f674,f678,f683,f688,f694,f712,f716,f720,f724,f728,f732,f736,f741,f746,f753,f757,f767,f769,f771,f778,f784,f791,f793]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC378-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.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 08:19:34 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.060352 seconds
% 0.12/0.42 % CPU time: 0.182131 seconds
% 0.12/0.42 % Total memory used: 109.705 MB
% 0.12/0.42 % Net memory used: 109.524 MB
%------------------------------------------------------------------------------