%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC075-1 : 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 02:39:52 PM UTC 2026
% Result : Unsatisfiable 159.44s 20.67s
% Output : CNFRefutation 41.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 40
% Syntax : Number of formulae : 158 ( 31 unt; 22 def)
% Number of atoms : 396 ( 82 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 456 ( 218 ~; 216 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 23 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 58 ( 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [U] :
( segmentP(U,U)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f73,axiom,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f74,axiom,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f100,axiom,
! [U,V] :
( V = U
| neq(V,U)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f119,axiom,
! [U,V] :
( nil = V
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(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(f173,axiom,
! [U,V,W,X] :
( segmentP(X,V)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| app(app(U,V),W) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f188,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f189,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f190,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
! [A] :
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
ssList(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
app(sk5,sk6) = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
app(sk6,sk5) = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( nil != sk1
| nil != sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f205,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f254,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f271,plain,
! [X0] :
( X0 = app(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f272,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f300,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| X1 = X0
| neq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f326,plain,
! [V] :
( nil = V
| ! [U] :
( ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f119]) ).
fof(f327,plain,
! [X0,X1] :
( nil != app(X0,X1)
| X1 = nil
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f326]) ).
fof(f367,plain,
! [V,W] :
( V = W
| ~ ssList(W)
| ! [U] :
( ~ ssList(U)
| ~ ssList(V)
| app(U,V) != app(U,W) ) ),
inference(miniscoping,[status(thm)],[f150]) ).
fof(f368,plain,
! [X0,X1,X2] :
( app(X2,X0) != app(X2,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f367]) ).
fof(f403,plain,
! [V,X] :
( segmentP(X,V)
| ~ ssList(X)
| ~ ssList(V)
| ! [U] :
( ~ ssList(U)
| ! [W] :
( ~ ssList(W)
| app(app(U,V),W) != X ) ) ),
inference(miniscoping,[status(thm)],[f173]) ).
fof(f404,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| app(app(X0,X1),X2) != X3 ),
inference(cnf_transformation,[status(thm)],[f403]) ).
fof(f430,plain,
ssList(sk3),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f431,plain,
ssList(sk4),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f432,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f433,plain,
sk3 = sk1,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f434,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f435,plain,
ssList(sk5),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f436,plain,
ssList(sk6),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f437,plain,
sk4 = app(sk5,sk6),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f438,plain,
app(sk6,sk5) = sk3,
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f439,plain,
( nil != sk1
| nil != sk2 ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f447,definition,
( sQ2_spl
<=> nil = sk2 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f449,plain,
( sQ2_spl
| sk2 != nil ),
inference(component_clause,[status(thm)],[f447]) ).
fof(f450,definition,
( sQ3_spl
<=> nil = sk1 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f452,plain,
( sQ3_spl
| nil != sk1 ),
inference(component_clause,[status(thm)],[f450]) ).
fof(f453,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f439,f447,f450]) ).
fof(f476,plain,
! [X0,X1,X2] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f404]) ).
fof(f538,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(sk2,X0)
| ~ segmentP(sk3,X0) ),
inference(backward_demodulation,[status(thm)],[f433,f434]) ).
fof(f549,plain,
( sQ2_spl
| sk4 != nil ),
inference(backward_demodulation,[status(thm)],[f432,f449]) ).
fof(f566,definition,
( sQ20_spl
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f568,plain,
( sQ20_spl
| ~ ssList(sk6) ),
inference(component_clause,[status(thm)],[f566]) ).
fof(f569,definition,
( sQ21_spl
<=> ssList(sk5) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f571,plain,
( sQ21_spl
| ~ ssList(sk5) ),
inference(component_clause,[status(thm)],[f569]) ).
fof(f572,definition,
! [X0] :
( sQ22_spl
<=> ( ~ ssList(X0)
| X0 = sk6
| app(sk5,X0) != sk4 ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f573,plain,
! [X0] :
( ~ sQ22_spl
| sk6 = X0
| app(sk5,X0) != sk4
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f572]) ).
fof(f586,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f571,f435]) ).
fof(f587,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f586]) ).
fof(f588,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f568,f436]) ).
fof(f589,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f588]) ).
fof(f593,plain,
app(sk4,nil) = sk4,
inference(resolution,[status(thm)],[f271,f431]) ).
fof(f594,plain,
sk6 = app(sk6,nil),
inference(resolution,[status(thm)],[f271,f436]) ).
fof(f595,plain,
sk3 = app(sk3,nil),
inference(resolution,[status(thm)],[f271,f430]) ).
fof(f604,plain,
! [X0] :
( ~ neq(X0,nil)
| ~ segmentP(sk3,X0)
| ~ ssList(X0)
| ~ segmentP(sk4,X0) ),
inference(forward_demodulation,[status(thm)],[f432,f538]) ).
fof(f610,definition,
( sQ25_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f612,plain,
( sQ25_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f610]) ).
fof(f620,definition,
( sQ27_spl
<=> ssList(sk3) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f622,plain,
( sQ27_spl
| ~ ssList(sk3) ),
inference(component_clause,[status(thm)],[f620]) ).
fof(f625,plain,
( sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f612,f205]) ).
fof(f626,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f625]) ).
fof(f636,definition,
( sQ29_spl
<=> ssList(sk4) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f638,plain,
( sQ29_spl
| ~ ssList(sk4) ),
inference(component_clause,[status(thm)],[f636]) ).
fof(f644,plain,
( sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f638,f431]) ).
fof(f645,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f644]) ).
fof(f650,plain,
( ~ sQ22_spl
| sk6 = sk4
| sk4 != app(sk5,sk4) ),
inference(resolution,[status(thm)],[f573,f431]) ).
fof(f669,definition,
( sQ35_spl
<=> sk4 = app(sk5,sk4) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f671,plain,
( sQ35_spl
| sk4 != app(sk5,sk4) ),
inference(component_clause,[status(thm)],[f669]) ).
fof(f672,definition,
( sQ36_spl
<=> sk6 = sk4 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f673,plain,
( ~ sQ36_spl
| sk4 = sk6 ),
inference(component_clause,[status(thm)],[f672]) ).
fof(f675,plain,
( ~ sQ22_spl
| sQ36_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f650,f669,f672,f572]) ).
fof(f686,definition,
( sQ40_spl
<=> sk6 = nil ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f711,plain,
sk4 = app(nil,sk4),
inference(resolution,[status(thm)],[f272,f431]) ).
fof(f713,plain,
app(nil,sk3) = sk3,
inference(resolution,[status(thm)],[f272,f430]) ).
fof(f715,plain,
sk5 = app(nil,sk5),
inference(resolution,[status(thm)],[f272,f435]) ).
fof(f737,plain,
( sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f622,f430]) ).
fof(f738,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f737]) ).
fof(f792,plain,
! [X0] :
( ~ ssList(X0)
| sk3 = nil
| app(X0,sk3) != nil ),
inference(resolution,[status(thm)],[f327,f430]) ).
fof(f809,definition,
( sQ52_spl
<=> sk5 = nil ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f810,plain,
( ~ sQ52_spl
| sk5 = nil ),
inference(component_clause,[status(thm)],[f809]) ).
fof(f820,definition,
! [X0] :
( sQ55_spl
<=> ( ~ ssList(X0)
| app(X0,sk3) != nil ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f821,plain,
! [X0] :
( ~ sQ55_spl
| nil != app(X0,sk3)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f820]) ).
fof(f823,definition,
( sQ56_spl
<=> sk3 = nil ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f826,plain,
( sQ56_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f792,f820,f823]) ).
fof(f1137,plain,
( ~ sQ55_spl
| nil != app(nil,sk3) ),
inference(resolution,[status(thm)],[f821,f205]) ).
fof(f1146,plain,
( ~ sQ55_spl
| nil != sk3 ),
inference(forward_demodulation,[status(thm)],[f713,f1137]) ).
fof(f1721,plain,
( ~ sQ52_spl
| app(sk4,sk5) = sk4 ),
inference(backward_demodulation,[status(thm)],[f810,f593]) ).
fof(f1727,plain,
( ~ sQ52_spl
| sk6 = app(sk6,sk5) ),
inference(backward_demodulation,[status(thm)],[f810,f594]) ).
fof(f1732,plain,
( ~ sQ52_spl
| sk4 = app(sk5,sk4) ),
inference(backward_demodulation,[status(thm)],[f810,f711]) ).
fof(f1747,plain,
( ~ sQ52_spl
| sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1732,f671]) ).
fof(f1748,plain,
( ~ sQ52_spl
| sQ35_spl ),
inference(contradiction_clause,[status(thm)],[f1747]) ).
fof(f1750,plain,
( ~ ssList(sk4)
| ~ ssList(sk4)
| ~ segmentP(sk3,sk4)
| ~ neq(sk4,nil) ),
inference(resolution,[status(thm)],[f604,f254]) ).
fof(f1751,definition,
( sQ109_spl
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f1753,plain,
( sQ109_spl
| ~ neq(sk4,nil) ),
inference(component_clause,[status(thm)],[f1751]) ).
fof(f1754,definition,
( sQ110_spl
<=> segmentP(sk3,sk4) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f1756,plain,
( sQ110_spl
| ~ segmentP(sk3,sk4) ),
inference(component_clause,[status(thm)],[f1754]) ).
fof(f1757,plain,
( ~ sQ29_spl
| ~ sQ110_spl
| ~ sQ109_spl ),
inference(split_clause,[status(thm)],[f1750,f1751,f1754,f636]) ).
fof(f1765,plain,
( sQ2_spl
| ~ sQ36_spl
| sk6 != nil ),
inference(backward_demodulation,[status(thm)],[f673,f549]) ).
fof(f1771,plain,
( ~ sQ36_spl
| sk6 = sk2 ),
inference(backward_demodulation,[status(thm)],[f673,f432]) ).
fof(f1800,definition,
( sQ115_spl
<=> neq(sk5,nil) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f1802,plain,
( sQ115_spl
| ~ neq(sk5,nil) ),
inference(component_clause,[status(thm)],[f1800]) ).
fof(f1867,plain,
( ~ sQ36_spl
| sk6 = sk4 ),
inference(forward_demodulation,[status(thm)],[f432,f1771]) ).
fof(f1888,plain,
! [X0] :
( segmentP(app(app(sk6,sk5),X0),sk5)
| ~ ssList(sk5)
| ~ ssList(X0)
| ~ ssList(sk6)
| ~ ssList(app(sk3,X0)) ),
inference(paramodulation,[status(thm)],[f438,f476]) ).
fof(f1894,definition,
! [X0] :
( sQ126_spl
<=> ( segmentP(app(app(sk6,sk5),X0),sk5)
| ~ ssList(X0)
| ~ ssList(app(sk3,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f1895,plain,
! [X0] :
( ~ sQ126_spl
| segmentP(app(app(sk6,sk5),X0),sk5)
| ~ ssList(X0)
| ~ ssList(app(sk3,X0)) ),
inference(component_clause,[status(thm)],[f1894]) ).
fof(f1897,plain,
( ~ sQ21_spl
| ~ sQ20_spl
| sQ126_spl ),
inference(split_clause,[status(thm)],[f1888,f1894,f566,f569]) ).
fof(f1905,plain,
( ~ sQ52_spl
| ~ sQ36_spl
| app(sk6,sk5) = sk4 ),
inference(forward_demodulation,[status(thm)],[f1867,f1721]) ).
fof(f1906,plain,
( ~ sQ52_spl
| ~ sQ36_spl
| sk3 = sk4 ),
inference(forward_demodulation,[status(thm)],[f438,f1905]) ).
fof(f1907,plain,
( ~ sQ52_spl
| ~ sQ36_spl
| sk3 = sk6 ),
inference(forward_demodulation,[status(thm)],[f1867,f1906]) ).
fof(f1914,plain,
! [X0] :
( ~ sQ126_spl
| ~ ssList(X0)
| ~ ssList(app(sk3,X0))
| segmentP(app(sk3,X0),sk5) ),
inference(forward_demodulation,[status(thm)],[f438,f1895]) ).
fof(f1922,plain,
( ~ sQ52_spl
| sk6 = sk3 ),
inference(forward_demodulation,[status(thm)],[f438,f1727]) ).
fof(f1968,plain,
( ~ sQ55_spl
| ~ sQ52_spl
| ~ sQ36_spl
| nil != sk6 ),
inference(backward_demodulation,[status(thm)],[f1907,f1146]) ).
fof(f2041,plain,
( sQ109_spl
| ~ sQ36_spl
| ~ neq(sk6,nil) ),
inference(forward_demodulation,[status(thm)],[f1867,f1753]) ).
fof(f2042,plain,
( sQ109_spl
| ~ sQ36_spl
| ~ ssList(nil)
| ~ ssList(sk6)
| nil = sk6 ),
inference(resolution,[status(thm)],[f2041,f300]) ).
fof(f2043,plain,
( sQ109_spl
| ~ sQ36_spl
| ~ sQ25_spl
| ~ sQ20_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f2042,f686,f566,f610,f672,f1751]) ).
fof(f2044,plain,
( sQ110_spl
| ~ sQ36_spl
| ~ segmentP(sk3,sk6) ),
inference(forward_demodulation,[status(thm)],[f1867,f1756]) ).
fof(f2049,plain,
( sQ2_spl
| ~ sQ36_spl
| ~ sQ40_spl ),
inference(split_clause,[status(thm)],[f1765,f686,f672,f447]) ).
fof(f2059,plain,
( sQ3_spl
| nil != sk3 ),
inference(forward_demodulation,[status(thm)],[f433,f452]) ).
fof(f2104,plain,
( ~ sQ55_spl
| ~ sQ52_spl
| ~ sQ36_spl
| ~ sQ40_spl ),
inference(split_clause,[status(thm)],[f1968,f686,f672,f809,f820]) ).
fof(f2724,plain,
( sQ3_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f2059,f823,f450]) ).
fof(f3783,plain,
( sQ110_spl
| ~ sQ36_spl
| ~ sQ52_spl
| ~ segmentP(sk6,sk6) ),
inference(forward_demodulation,[status(thm)],[f1922,f2044]) ).
fof(f3785,plain,
( sQ110_spl
| ~ sQ36_spl
| ~ sQ52_spl
| ~ ssList(sk6) ),
inference(resolution,[status(thm)],[f3783,f254]) ).
fof(f3786,plain,
( sQ110_spl
| ~ sQ36_spl
| ~ sQ52_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f3785,f566,f809,f672,f1754]) ).
fof(f8448,plain,
( ~ sQ126_spl
| segmentP(app(sk3,nil),sk5)
| ~ ssList(nil)
| ~ ssList(sk3) ),
inference(paramodulation,[status(thm)],[f595,f1914]) ).
fof(f8453,definition,
( sQ602_spl
<=> segmentP(app(sk3,nil),sk5) ),
introduced(definition,[new_symbols(definition,[sQ602_spl])],[split_symbol_definition]) ).
fof(f8454,plain,
( ~ sQ602_spl
| segmentP(app(sk3,nil),sk5) ),
inference(component_clause,[status(thm)],[f8453]) ).
fof(f8456,plain,
( ~ sQ126_spl
| sQ602_spl
| ~ sQ25_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f8448,f620,f610,f8453,f1894]) ).
fof(f8457,plain,
( ~ sQ602_spl
| segmentP(sk3,sk5) ),
inference(forward_demodulation,[status(thm)],[f595,f8454]) ).
fof(f9313,plain,
! [X0,X1] :
( ~ ssList(X1)
| X1 = X0
| ~ ssList(X0)
| app(sk5,X0) != app(sk5,X1) ),
inference(resolution,[status(thm)],[f368,f435]) ).
fof(f10722,plain,
! [X0,X1] :
( segmentP(app(app(X0,X1),sk6),X1)
| ~ ssList(X1)
| ~ ssList(app(app(X0,X1),sk6))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f476,f436]) ).
fof(f18179,plain,
( ~ sQ602_spl
| ~ segmentP(sk4,sk5)
| ~ ssList(sk5)
| ~ neq(sk5,nil) ),
inference(resolution,[status(thm)],[f8457,f604]) ).
fof(f18185,definition,
( sQ819_spl
<=> segmentP(sk4,sk5) ),
introduced(definition,[new_symbols(definition,[sQ819_spl])],[split_symbol_definition]) ).
fof(f18187,plain,
( sQ819_spl
| ~ segmentP(sk4,sk5) ),
inference(component_clause,[status(thm)],[f18185]) ).
fof(f18188,plain,
( ~ sQ602_spl
| ~ sQ819_spl
| ~ sQ21_spl
| ~ sQ115_spl ),
inference(split_clause,[status(thm)],[f18179,f1800,f569,f18185,f8453]) ).
fof(f18349,plain,
( sQ115_spl
| ~ ssList(sk5)
| ~ ssList(nil)
| sk5 = nil ),
inference(resolution,[status(thm)],[f1802,f300]) ).
fof(f18350,plain,
( sQ115_spl
| ~ sQ21_spl
| ~ sQ25_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f18349,f809,f610,f569,f1800]) ).
fof(f28896,plain,
! [X0] :
( X0 = sk6
| ~ ssList(X0)
| app(sk5,X0) != sk4
| ~ ssList(sk6) ),
inference(paramodulation,[status(thm)],[f437,f9313]) ).
fof(f28898,plain,
( sQ22_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f28896,f566,f572]) ).
fof(f38886,plain,
( segmentP(app(app(nil,sk5),sk6),sk5)
| ~ ssList(sk5)
| ~ ssList(app(sk5,sk6))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f715,f10722]) ).
fof(f38930,definition,
( sQ1766_spl
<=> ssList(app(sk5,sk6)) ),
introduced(definition,[new_symbols(definition,[sQ1766_spl])],[split_symbol_definition]) ).
fof(f38932,plain,
( sQ1766_spl
| ~ ssList(app(sk5,sk6)) ),
inference(component_clause,[status(thm)],[f38930]) ).
fof(f38961,definition,
( sQ1774_spl
<=> segmentP(app(app(nil,sk5),sk6),sk5) ),
introduced(definition,[new_symbols(definition,[sQ1774_spl])],[split_symbol_definition]) ).
fof(f38962,plain,
( ~ sQ1774_spl
| segmentP(app(app(nil,sk5),sk6),sk5) ),
inference(component_clause,[status(thm)],[f38961]) ).
fof(f38964,plain,
( sQ1774_spl
| ~ sQ21_spl
| ~ sQ1766_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f38886,f610,f38930,f569,f38961]) ).
fof(f38968,plain,
( ~ sQ1774_spl
| segmentP(app(sk5,sk6),sk5) ),
inference(forward_demodulation,[status(thm)],[f715,f38962]) ).
fof(f38969,plain,
( ~ sQ1774_spl
| segmentP(sk4,sk5) ),
inference(forward_demodulation,[status(thm)],[f437,f38968]) ).
fof(f38970,plain,
( ~ sQ1774_spl
| sQ819_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f38969,f18187]) ).
fof(f38971,plain,
( ~ sQ1774_spl
| sQ819_spl ),
inference(contradiction_clause,[status(thm)],[f38970]) ).
fof(f38972,plain,
( sQ1766_spl
| ~ ssList(sk4) ),
inference(forward_demodulation,[status(thm)],[f437,f38932]) ).
fof(f38973,plain,
( sQ1766_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f38972,f431]) ).
fof(f38974,plain,
sQ1766_spl,
inference(contradiction_clause,[status(thm)],[f38973]) ).
fof(f38975,plain,
$false,
inference(sat_refutation,[status(thm)],[f453,f587,f589,f626,f645,f675,f738,f826,f1748,f1757,f1897,f2043,f2049,f2104,f2724,f3786,f8456,f18188,f18350,f28898,f38964,f38971,f38974]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC075-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n014.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 07:53:20 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.47 % Drodi V4.1.1
% 159.44/20.67 % Refutation found
% 159.44/20.67 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 159.44/20.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 41.21/20.76 % Elapsed time: 20.301372 seconds
% 41.21/20.76 % CPU time: 160.338384 seconds
% 41.21/20.76 % Total memory used: 594.894 MB
% 41.21/20.76 % Net memory used: 549.763 MB
%------------------------------------------------------------------------------