%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC112-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 02:40:01 PM UTC 2026
% Result : Unsatisfiable 0.16s 10.43s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 62
% Syntax : Number of formulae : 199 ( 32 unt; 39 def)
% Number of atoms : 569 ( 89 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 698 ( 328 ~; 331 |; 0 &)
% ( 39 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 44 ( 42 usr; 40 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 120 ( 120 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [U] :
( segmentP(U,nil)
| ~ ssList(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(f80,axiom,
! [U] :
( nil = U
| ~ ssList(U)
| ~ segmentP(nil,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(f100,axiom,
! [U,V] :
( V = U
| neq(V,U)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f115,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f127,axiom,
! [U,V] :
( V = U
| ~ ssList(V)
| ~ ssList(U)
| ~ segmentP(V,U)
| ~ segmentP(U,V) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f152,axiom,
! [U,V,W] :
( segmentP(U,W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ segmentP(V,W)
| ~ segmentP(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f172,axiom,
! [U,V,W,X] :
( segmentP(app(app(X,U),W),V)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X)
| ~ ssList(W)
| ~ segmentP(U,V) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f186,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f187,negated_conjecture,
ssList(sk2),
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,
ssList(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
app(app(sk5,sk3),sk6) = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
( nil != sk3
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f200,negated_conjecture,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil)
| nil = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f201,negated_conjecture,
( neq(sk2,nil)
| nil != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f210,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f258,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f276,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f277,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f283,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f288,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f305,plain,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f323,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ~ neq(U,V)
| U != V ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f324,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f323]) ).
fof(f342,plain,
! [X0,X1] :
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f371,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(f376,plain,
! [U,W] :
( segmentP(U,W)
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ~ ssList(W)
| ~ segmentP(V,W)
| ~ segmentP(U,V) ) ),
inference(miniscoping,[status(thm)],[f152]) ).
fof(f377,plain,
! [X0,X1,X2] :
( segmentP(X0,X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f376]) ).
fof(f407,plain,
! [X0,X1,X2,X3] :
( segmentP(app(app(X3,X0),X2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f408,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(f409,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)],[f408]) ).
fof(f433,plain,
ssList(sk1),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f434,plain,
ssList(sk2),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f437,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f438,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f439,plain,
ssList(sk5),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f440,plain,
ssList(sk6),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f441,plain,
app(app(sk5,sk3),sk6) = sk4,
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f447,plain,
( nil != sk3
| nil = sk4 ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f449,plain,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil)
| nil = sk2 ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f450,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f459,definition,
( sQ2_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f460,plain,
( ~ sQ2_spl
| nil = sk4 ),
inference(component_clause,[status(thm)],[f459]) ).
fof(f462,definition,
( sQ3_spl
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f464,plain,
( sQ3_spl
| nil != sk3 ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f465,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f447,f459,f462]) ).
fof(f466,definition,
( sQ4_spl
<=> nil = sk2 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f467,plain,
( ~ sQ4_spl
| nil = sk2 ),
inference(component_clause,[status(thm)],[f466]) ).
fof(f469,definition,
( sQ5_spl
<=> neq(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f470,plain,
( ~ sQ5_spl
| neq(sk2,nil) ),
inference(component_clause,[status(thm)],[f469]) ).
fof(f473,definition,
( sQ6_spl
<=> neq(sk1,nil) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f475,plain,
( sQ6_spl
| ~ neq(sk1,nil) ),
inference(component_clause,[status(thm)],[f473]) ).
fof(f476,definition,
( sQ7_spl
<=> segmentP(sk2,sk1) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f478,plain,
( sQ7_spl
| ~ segmentP(sk2,sk1) ),
inference(component_clause,[status(thm)],[f476]) ).
fof(f479,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f449,f466,f473,f476]) ).
fof(f480,definition,
( sQ8_spl
<=> nil = sk1 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f481,plain,
( ~ sQ8_spl
| nil = sk1 ),
inference(component_clause,[status(thm)],[f480]) ).
fof(f483,plain,
( sQ5_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f450,f480,f469]) ).
fof(f492,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f324]) ).
fof(f493,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f492]) ).
fof(f503,plain,
! [X0,X1,X2] :
( segmentP(app(app(X1,X2),X0),X2)
| ~ ssList(app(app(X1,X2),X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f409]) ).
fof(f520,plain,
app(sk6,nil) = sk6,
inference(resolution,[status(thm)],[f276,f440]) ).
fof(f521,plain,
app(sk5,nil) = sk5,
inference(resolution,[status(thm)],[f276,f439]) ).
fof(f524,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[f276,f210]) ).
fof(f525,plain,
app(sk2,nil) = sk2,
inference(resolution,[status(thm)],[f276,f434]) ).
fof(f526,plain,
app(sk1,nil) = sk1,
inference(resolution,[status(thm)],[f276,f433]) ).
fof(f527,plain,
app(nil,sk6) = sk6,
inference(resolution,[status(thm)],[f277,f440]) ).
fof(f528,plain,
app(nil,sk5) = sk5,
inference(resolution,[status(thm)],[f277,f439]) ).
fof(f533,plain,
app(nil,sk1) = sk1,
inference(resolution,[status(thm)],[f277,f433]) ).
fof(f540,plain,
app(app(sk5,sk1),sk6) = sk4,
inference(forward_demodulation,[status(thm)],[f438,f441]) ).
fof(f542,plain,
( ~ ssList(nil)
| nil = nil
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f283,f258]) ).
fof(f544,definition,
( sQ9_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f546,plain,
( sQ9_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f544]) ).
fof(f547,definition,
( sQ10_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f550,plain,
( sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f542,f544,f547]) ).
fof(f552,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f546,f210]) ).
fof(f553,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f552]) ).
fof(f570,definition,
( sQ11_spl
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f572,plain,
( sQ11_spl
| ~ ssList(sk6) ),
inference(component_clause,[status(thm)],[f570]) ).
fof(f574,definition,
( sQ12_spl
<=> ssList(app(sk5,sk1)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f576,plain,
( sQ12_spl
| ~ ssList(app(sk5,sk1)) ),
inference(component_clause,[status(thm)],[f574]) ).
fof(f578,plain,
( sQ3_spl
| nil != sk1 ),
inference(forward_demodulation,[status(thm)],[f438,f464]) ).
fof(f590,definition,
( sQ13_spl
<=> ssList(sk5) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f592,plain,
( sQ13_spl
| ~ ssList(sk5) ),
inference(component_clause,[status(thm)],[f590]) ).
fof(f632,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f572,f440]) ).
fof(f633,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f632]) ).
fof(f634,plain,
app(nil,sk2) = sk2,
inference(resolution,[status(thm)],[f434,f277]) ).
fof(f658,definition,
( sQ14_spl
<=> ssList(sk1) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f660,plain,
( sQ14_spl
| ~ ssList(sk1) ),
inference(component_clause,[status(thm)],[f658]) ).
fof(f679,plain,
app(app(sk5,sk1),sk6) = sk2,
inference(forward_demodulation,[status(thm)],[f437,f540]) ).
fof(f680,plain,
( ssList(sk2)
| ~ ssList(app(sk5,sk1))
| ~ ssList(sk6) ),
inference(paramodulation,[status(thm)],[f679,f288]) ).
fof(f681,definition,
( sQ15_spl
<=> ssList(sk2) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f684,plain,
( sQ15_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f680,f570,f574,f681]) ).
fof(f800,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| neq(nil,nil) ),
inference(backward_demodulation,[status(thm)],[f467,f470]) ).
fof(f811,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f800,f493]) ).
fof(f812,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f811,f544,f466,f469]) ).
fof(f819,plain,
( sQ6_spl
| sk1 = nil
| ~ ssList(sk1)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f475,f305]) ).
fof(f827,plain,
( sQ6_spl
| sQ8_spl
| ~ sQ14_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f819,f544,f658,f480,f473]) ).
fof(f828,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f660,f433]) ).
fof(f829,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f828]) ).
fof(f830,plain,
( ~ sQ8_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f481,f578]) ).
fof(f831,plain,
( ~ sQ8_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f830]) ).
fof(f845,plain,
! [X0] :
( ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(nil,X0) ),
inference(resolution,[status(thm)],[f342,f258]) ).
fof(f847,definition,
! [X0] :
( sQ25_spl
<=> ( ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f850,plain,
( ~ sQ9_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f845,f847,f544]) ).
fof(f852,plain,
( ~ sQ2_spl
| sk2 = nil ),
inference(backward_demodulation,[status(thm)],[f460,f437]) ).
fof(f853,plain,
( ~ sQ2_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f852,f466,f459]) ).
fof(f870,plain,
! [X0] :
( app(sk5,X0) = app(nil,app(sk5,X0))
| ~ ssList(nil)
| ~ ssList(sk5)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f528,f371]) ).
fof(f871,plain,
! [X0] :
( app(sk6,X0) = app(nil,app(sk6,X0))
| ~ ssList(nil)
| ~ ssList(sk6)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f527,f371]) ).
fof(f872,plain,
! [X0] :
( app(nil,X0) = app(nil,app(nil,X0))
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f524,f371]) ).
fof(f873,plain,
! [X0] :
( app(app(X0,app(sk5,sk1)),sk6) = app(X0,sk2)
| ~ ssList(X0)
| ~ ssList(app(sk5,sk1))
| ~ ssList(sk6) ),
inference(paramodulation,[status(thm)],[f679,f371]) ).
fof(f874,plain,
! [X0] :
( app(app(X0,nil),sk5) = app(X0,sk5)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sk5) ),
inference(paramodulation,[status(thm)],[f528,f371]) ).
fof(f875,plain,
! [X0] :
( app(app(X0,nil),sk6) = app(X0,sk6)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sk6) ),
inference(paramodulation,[status(thm)],[f527,f371]) ).
fof(f876,plain,
! [X0] :
( app(app(X0,nil),nil) = app(X0,nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f524,f371]) ).
fof(f877,plain,
! [X0] :
( app(app(X0,sk5),nil) = app(X0,sk5)
| ~ ssList(X0)
| ~ ssList(sk5)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f521,f371]) ).
fof(f878,plain,
! [X0] :
( app(app(X0,sk6),nil) = app(X0,sk6)
| ~ ssList(X0)
| ~ ssList(sk6)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f520,f371]) ).
fof(f879,definition,
! [X0] :
( sQ27_spl
<=> ( app(sk5,X0) = app(nil,app(sk5,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f882,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f870,f879,f590,f544]) ).
fof(f883,definition,
! [X0] :
( sQ28_spl
<=> ( app(sk6,X0) = app(nil,app(sk6,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f886,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f871,f883,f570,f544]) ).
fof(f887,definition,
! [X0] :
( sQ29_spl
<=> ( app(nil,X0) = app(nil,app(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f890,plain,
( ~ sQ9_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f872,f887,f544]) ).
fof(f891,definition,
! [X0] :
( sQ30_spl
<=> ( app(app(X0,app(sk5,sk1)),sk6) = app(X0,sk2)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f894,plain,
( sQ30_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f873,f570,f574,f891]) ).
fof(f895,definition,
! [X0] :
( sQ31_spl
<=> ( app(app(X0,nil),sk5) = app(X0,sk5)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f898,plain,
( sQ31_spl
| ~ sQ9_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f874,f590,f544,f895]) ).
fof(f899,definition,
! [X0] :
( sQ32_spl
<=> ( app(app(X0,nil),sk6) = app(X0,sk6)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f902,plain,
( sQ32_spl
| ~ sQ9_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f875,f570,f544,f899]) ).
fof(f903,definition,
! [X0] :
( sQ33_spl
<=> ( app(app(X0,nil),nil) = app(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f906,plain,
( sQ33_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f876,f544,f903]) ).
fof(f907,definition,
! [X0] :
( sQ34_spl
<=> ( app(app(X0,sk5),nil) = app(X0,sk5)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f910,plain,
( sQ34_spl
| ~ sQ13_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f877,f544,f590,f907]) ).
fof(f911,definition,
! [X0] :
( sQ35_spl
<=> ( app(app(X0,sk6),nil) = app(X0,sk6)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f914,plain,
( sQ35_spl
| ~ sQ11_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f878,f544,f570,f911]) ).
fof(f915,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f592,f439]) ).
fof(f916,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f915]) ).
fof(f924,plain,
( sQ12_spl
| ~ ssList(sk5)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f576,f288]) ).
fof(f925,plain,
( sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f924,f658,f590,f574]) ).
fof(f1067,plain,
! [X0] :
( app(app(X0,sk2),nil) = app(X0,sk2)
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f525,f371]) ).
fof(f1069,definition,
! [X0] :
( sQ36_spl
<=> ( app(app(X0,sk2),nil) = app(X0,sk2)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f1072,plain,
( sQ36_spl
| ~ sQ15_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f1067,f544,f681,f1069]) ).
fof(f1074,plain,
! [X0] :
( app(app(X0,nil),sk2) = app(X0,sk2)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(paramodulation,[status(thm)],[f634,f371]) ).
fof(f1075,plain,
! [X0] :
( app(sk2,X0) = app(nil,app(sk2,X0))
| ~ ssList(nil)
| ~ ssList(sk2)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f634,f371]) ).
fof(f1077,definition,
! [X0] :
( sQ37_spl
<=> ( app(app(X0,nil),sk2) = app(X0,sk2)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f1080,plain,
( sQ37_spl
| ~ sQ9_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f1074,f681,f544,f1077]) ).
fof(f1081,definition,
! [X0] :
( sQ38_spl
<=> ( app(sk2,X0) = app(nil,app(sk2,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f1084,plain,
( ~ sQ9_spl
| ~ sQ15_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f1075,f1081,f681,f544]) ).
fof(f1086,plain,
! [X0,X1] :
( ~ ssList(X1)
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ segmentP(X0,X1) ),
inference(resolution,[status(thm)],[f377,f258]) ).
fof(f1088,definition,
! [X0,X1] :
( sQ39_spl
<=> ( ~ ssList(X1)
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f1091,plain,
( ~ sQ9_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f1086,f1088,f544]) ).
fof(f1170,plain,
! [X0] :
( app(app(X0,nil),sk1) = app(X0,sk1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sk1) ),
inference(paramodulation,[status(thm)],[f533,f371]) ).
fof(f1171,plain,
! [X0] :
( app(sk1,X0) = app(nil,app(sk1,X0))
| ~ ssList(nil)
| ~ ssList(sk1)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f533,f371]) ).
fof(f1173,definition,
! [X0] :
( sQ45_spl
<=> ( app(app(X0,nil),sk1) = app(X0,sk1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f1176,plain,
( sQ45_spl
| ~ sQ9_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1170,f658,f544,f1173]) ).
fof(f1177,definition,
! [X0] :
( sQ46_spl
<=> ( app(sk1,X0) = app(nil,app(sk1,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f1180,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f1171,f1177,f658,f544]) ).
fof(f1182,plain,
! [X0] :
( app(app(X0,sk1),nil) = app(X0,sk1)
| ~ ssList(X0)
| ~ ssList(sk1)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f526,f371]) ).
fof(f1184,definition,
! [X0] :
( sQ47_spl
<=> ( app(app(X0,sk1),nil) = app(X0,sk1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f1187,plain,
( sQ47_spl
| ~ sQ14_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f1182,f544,f658,f1184]) ).
fof(f1245,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| segmentP(app(app(X1,X2),X0),nil)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f407,f258]) ).
fof(f1247,definition,
! [X0,X1,X2] :
( sQ48_spl
<=> ( ~ ssList(X2)
| segmentP(app(app(X1,X2),X0),nil)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f1250,plain,
( ~ sQ9_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f1245,f1247,f544]) ).
fof(f1254,plain,
! [X0] :
( segmentP(app(app(sk1,nil),X0),nil)
| ~ ssList(app(sk1,X0))
| ~ ssList(nil)
| ~ ssList(sk1)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f526,f503]) ).
fof(f1255,plain,
! [X0] :
( segmentP(app(app(nil,sk1),X0),sk1)
| ~ ssList(app(sk1,X0))
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f533,f503]) ).
fof(f1256,plain,
! [X0] :
( segmentP(app(app(nil,nil),X0),nil)
| ~ ssList(app(nil,X0))
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f524,f503]) ).
fof(f1259,definition,
! [X0] :
( sQ49_spl
<=> ( segmentP(app(app(sk1,nil),X0),nil)
| ~ ssList(app(sk1,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f1262,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f1254,f1259,f658,f544]) ).
fof(f1263,definition,
! [X0] :
( sQ50_spl
<=> ( segmentP(app(app(nil,sk1),X0),sk1)
| ~ ssList(app(sk1,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f1266,plain,
( ~ sQ14_spl
| ~ sQ9_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f1255,f1263,f544,f658]) ).
fof(f1267,definition,
! [X0] :
( sQ51_spl
<=> ( segmentP(app(app(nil,nil),X0),nil)
| ~ ssList(app(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f1270,plain,
( ~ sQ9_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f1256,f1267,f544]) ).
fof(f1342,plain,
! [X0] :
( segmentP(app(app(nil,sk2),X0),sk2)
| ~ ssList(app(sk2,X0))
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f634,f503]) ).
fof(f1346,definition,
! [X0] :
( sQ52_spl
<=> ( segmentP(app(app(nil,sk2),X0),sk2)
| ~ ssList(app(sk2,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f1349,plain,
( ~ sQ15_spl
| ~ sQ9_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f1342,f1346,f544,f681]) ).
fof(f1354,plain,
! [X0] :
( segmentP(app(app(sk2,nil),X0),nil)
| ~ ssList(app(sk2,X0))
| ~ ssList(nil)
| ~ ssList(sk2)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f525,f503]) ).
fof(f1357,definition,
! [X0] :
( sQ53_spl
<=> ( segmentP(app(app(sk2,nil),X0),nil)
| ~ ssList(app(sk2,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f1360,plain,
( ~ sQ9_spl
| ~ sQ15_spl
| sQ53_spl ),
inference(split_clause,[status(thm)],[f1354,f1357,f681,f544]) ).
fof(f1364,plain,
( segmentP(app(app(sk5,sk1),sk6),sk1)
| ~ ssList(sk2)
| ~ ssList(sk1)
| ~ ssList(sk5)
| ~ ssList(sk6) ),
inference(paramodulation,[status(thm)],[f679,f503]) ).
fof(f1365,plain,
! [X0] :
( segmentP(app(app(app(sk5,sk1),sk6),X0),sk6)
| ~ ssList(app(sk2,X0))
| ~ ssList(sk6)
| ~ ssList(app(sk5,sk1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f679,f503]) ).
fof(f1368,definition,
( sQ54_spl
<=> segmentP(app(app(sk5,sk1),sk6),sk1) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f1369,plain,
( ~ sQ54_spl
| segmentP(app(app(sk5,sk1),sk6),sk1) ),
inference(component_clause,[status(thm)],[f1368]) ).
fof(f1371,plain,
( sQ54_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1364,f570,f590,f658,f681,f1368]) ).
fof(f1372,definition,
! [X0] :
( sQ55_spl
<=> ( segmentP(app(app(app(sk5,sk1),sk6),X0),sk6)
| ~ ssList(app(sk2,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f1375,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f1365,f1372,f574,f570]) ).
fof(f1378,plain,
( ~ sQ54_spl
| segmentP(sk2,sk1) ),
inference(forward_demodulation,[status(thm)],[f679,f1369]) ).
fof(f1379,plain,
( ~ sQ54_spl
| sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1378,f478]) ).
fof(f1380,plain,
( ~ sQ54_spl
| sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1379]) ).
fof(f1550,plain,
( ~ sQ54_spl
| ~ sQ4_spl
| segmentP(nil,sk1) ),
inference(forward_demodulation,[status(thm)],[f467,f1378]) ).
fof(f1551,plain,
( ~ sQ54_spl
| ~ sQ4_spl
| nil = sk1
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f1550,f283]) ).
fof(f1555,plain,
( ~ sQ54_spl
| ~ sQ4_spl
| sQ8_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1551,f658,f480,f466,f1368]) ).
fof(f1568,plain,
$false,
inference(sat_refutation,[status(thm)],[f465,f479,f483,f550,f553,f633,f684,f812,f827,f829,f831,f850,f853,f882,f886,f890,f894,f898,f902,f906,f910,f914,f916,f925,f1072,f1080,f1084,f1091,f1176,f1180,f1187,f1250,f1262,f1266,f1270,f1349,f1360,f1371,f1375,f1380,f1555]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC112-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/10.39 % Computer : n016.cluster.edu
% 0.12/10.39 % Model : x86_64 x86_64
% 0.12/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.39 % Memory : 8046.5625MB
% 0.12/10.39 % OS : Linux 6.8.0-71-generic
% 0.12/10.39 % CPULimit : 300
% 0.12/10.39 % WCLimit : 300
% 0.12/10.39 % DateTime : Mon Sep 21 08:01:19 UTC 2026
% 0.12/10.39 % CPUTime :
% 0.16/10.40 % Drodi V4.1.1
% 0.16/10.43 % Refutation found
% 0.16/10.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/10.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/10.47 % Elapsed time: 0.063094 seconds
% 0.16/10.47 % CPU time: 0.266958 seconds
% 0.16/10.47 % Total memory used: 112.056 MB
% 0.16/10.47 % Net memory used: 111.788 MB
%------------------------------------------------------------------------------