%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC389-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 02:41:03 PM UTC 2026
% Result : Unsatisfiable 0.02s 0.62s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 63
% Syntax : Number of formulae : 190 ( 16 unt; 30 def)
% Number of atoms : 564 ( 123 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 701 ( 327 ~; 344 |; 0 &)
% ( 30 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 37 ( 35 usr; 31 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 120 ( 120 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [U] :
( segmentP(U,nil)
| ~ 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(f79,axiom,
! [U] :
( segmentP(nil,U)
| ~ ssList(U)
| nil != U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f80,axiom,
! [U] :
( nil = U
| ~ ssList(U)
| ~ segmentP(nil,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(f115,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f116,axiom,
! [U,V] :
( singletonP(V)
| ~ ssList(V)
| ~ ssItem(U)
| cons(U,nil) != V ),
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(f120,axiom,
! [U,V] :
( app(cons(U,nil),V) = cons(U,V)
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f127,axiom,
! [U,V] :
( V = U
| ~ ssList(V)
| ~ ssList(U)
| ~ segmentP(V,U)
| ~ segmentP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f145,axiom,
! [U,V] :
( app(U,V) = nil
| ~ ssList(U)
| ~ ssList(V)
| nil != V
| nil != 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(f152,axiom,
! [U,V,W] :
( segmentP(U,W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ segmentP(V,W)
| ~ segmentP(U,V) ),
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(f186,negated_conjecture,
ssList(sk1),
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,
( nil = sk4
| ssItem(sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
( nil = sk3
| ssItem(sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
( nil = sk4
| ssList(sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
( nil = sk4
| ssList(sk7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
( nil = sk4
| cons(sk5,nil) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( nil = sk4
| app(app(sk6,sk3),sk7) = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f200,negated_conjecture,
( nil = sk3
| ssList(sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f201,negated_conjecture,
( nil = sk3
| ssList(sk7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f202,negated_conjecture,
( nil = sk3
| cons(sk5,nil) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f203,negated_conjecture,
( nil = sk3
| app(app(sk6,sk3),sk7) = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f206,negated_conjecture,
( neq(sk2,nil)
| ~ segmentP(sk2,sk1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f207,negated_conjecture,
( ~ singletonP(sk1)
| ~ segmentP(sk2,sk1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f215,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f218,plain,
~ singletonP(nil),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f263,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f281,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f282,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f287,plain,
! [X0] :
( segmentP(nil,X0)
| ~ ssList(X0)
| nil != X0 ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f288,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f293,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f328,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ~ neq(U,V)
| U != V ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f329,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f328]) ).
fof(f330,plain,
! [V] :
( singletonP(V)
| ~ ssList(V)
| ! [U] :
( ~ ssItem(U)
| cons(U,nil) != V ) ),
inference(miniscoping,[status(thm)],[f116]) ).
fof(f331,plain,
! [X0,X1] :
( singletonP(X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,nil) != X1 ),
inference(cnf_transformation,[status(thm)],[f330]) ).
fof(f336,plain,
! [V] :
( nil = V
| ! [U] :
( ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f119]) ).
fof(f337,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f336]) ).
fof(f338,plain,
! [X0,X1] :
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f347,plain,
! [X0,X1] :
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f369,plain,
! [X0,X1] :
( app(X0,X1) = nil
| ~ ssList(X0)
| ~ ssList(X1)
| nil != X1
| nil != X0 ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f377,plain,
! [V,W] :
( V = W
| ~ ssList(W)
| ! [U] :
( ~ ssList(U)
| ~ ssList(V)
| app(U,V) != app(U,W) ) ),
inference(miniscoping,[status(thm)],[f150]) ).
fof(f378,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != app(X0,X2) ),
inference(cnf_transformation,[status(thm)],[f377]) ).
fof(f379,plain,
! [U,W] :
( U = W
| ~ ssList(W)
| ! [V] :
( ~ ssList(V)
| ~ ssList(U)
| app(U,V) != app(W,V) ) ),
inference(miniscoping,[status(thm)],[f151]) ).
fof(f380,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) != app(X2,X1) ),
inference(cnf_transformation,[status(thm)],[f379]) ).
fof(f381,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(f382,plain,
! [X0,X1,X2] :
( segmentP(X0,X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f381]) ).
fof(f413,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(f414,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)],[f413]) ).
fof(f438,plain,
ssList(sk1),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f442,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f443,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f444,plain,
( nil = sk4
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f445,plain,
( nil = sk3
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f446,plain,
( nil = sk4
| ssList(sk6) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f447,plain,
( nil = sk4
| ssList(sk7) ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f448,plain,
( nil = sk4
| cons(sk5,nil) = sk3 ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f449,plain,
( nil = sk4
| app(app(sk6,sk3),sk7) = sk4 ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f454,plain,
( nil = sk3
| ssList(sk6) ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f455,plain,
( nil = sk3
| ssList(sk7) ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f456,plain,
( nil = sk3
| cons(sk5,nil) = sk3 ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f457,plain,
( nil = sk3
| app(app(sk6,sk3),sk7) = sk4 ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f462,plain,
( neq(sk2,nil)
| ~ segmentP(sk2,sk1) ),
inference(cnf_transformation,[status(thm)],[f206]) ).
fof(f463,plain,
( ~ singletonP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(cnf_transformation,[status(thm)],[f207]) ).
fof(f471,definition,
( sQ2_spl
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f474,definition,
( sQ3_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f475,plain,
( ~ sQ3_spl
| nil = sk4 ),
inference(component_clause,[status(thm)],[f474]) ).
fof(f477,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f444,f471,f474]) ).
fof(f478,definition,
( sQ4_spl
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f479,plain,
( ~ sQ4_spl
| nil = sk3 ),
inference(component_clause,[status(thm)],[f478]) ).
fof(f481,plain,
( sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f445,f471,f478]) ).
fof(f482,definition,
( sQ5_spl
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f485,plain,
( sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f446,f482,f474]) ).
fof(f486,definition,
( sQ6_spl
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f489,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f447,f486,f474]) ).
fof(f490,definition,
( sQ7_spl
<=> cons(sk5,nil) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f491,plain,
( ~ sQ7_spl
| cons(sk5,nil) = sk3 ),
inference(component_clause,[status(thm)],[f490]) ).
fof(f493,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f448,f490,f474]) ).
fof(f494,definition,
( sQ8_spl
<=> app(app(sk6,sk3),sk7) = sk4 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f495,plain,
( ~ sQ8_spl
| app(app(sk6,sk3),sk7) = sk4 ),
inference(component_clause,[status(thm)],[f494]) ).
fof(f497,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f449,f494,f474]) ).
fof(f506,plain,
( sQ4_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f454,f482,f478]) ).
fof(f507,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f455,f486,f478]) ).
fof(f508,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f456,f490,f478]) ).
fof(f509,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f457,f494,f478]) ).
fof(f512,definition,
( sQ11_spl
<=> segmentP(sk2,sk1) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f514,plain,
( sQ11_spl
| ~ segmentP(sk2,sk1) ),
inference(component_clause,[status(thm)],[f512]) ).
fof(f515,definition,
( sQ12_spl
<=> neq(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f516,plain,
( ~ sQ12_spl
| neq(sk2,nil) ),
inference(component_clause,[status(thm)],[f515]) ).
fof(f518,plain,
( sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f462,f512,f515]) ).
fof(f519,definition,
( sQ13_spl
<=> singletonP(sk1) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f522,plain,
( ~ sQ13_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f463,f512,f519]) ).
fof(f525,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f329]) ).
fof(f526,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f525]) ).
fof(f535,plain,
( ~ sQ4_spl
| sk1 = nil ),
inference(backward_demodulation,[status(thm)],[f479,f443]) ).
fof(f536,plain,
( ~ sQ3_spl
| sk2 = nil ),
inference(backward_demodulation,[status(thm)],[f475,f442]) ).
fof(f539,plain,
( sQ11_spl
| ~ sQ3_spl
| ~ segmentP(nil,sk1) ),
inference(forward_demodulation,[status(thm)],[f536,f514]) ).
fof(f540,plain,
( sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ segmentP(nil,nil) ),
inference(forward_demodulation,[status(thm)],[f535,f539]) ).
fof(f541,plain,
( sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f540,f263]) ).
fof(f543,plain,
( sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f541,f215]) ).
fof(f544,plain,
( sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f543]) ).
fof(f546,plain,
( ~ ssList(nil)
| nil = nil
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f288,f263]) ).
fof(f548,definition,
( sQ14_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f550,plain,
( sQ14_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f548]) ).
fof(f551,definition,
( sQ15_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f554,plain,
( sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f546,f548,f551]) ).
fof(f556,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f550,f215]) ).
fof(f557,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f556]) ).
fof(f559,plain,
( ~ sQ7_spl
| cons(sk5,nil) = sk1 ),
inference(forward_demodulation,[status(thm)],[f443,f491]) ).
fof(f561,definition,
( sQ16_spl
<=> ssList(sk1) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f563,plain,
( sQ16_spl
| ~ ssList(sk1) ),
inference(component_clause,[status(thm)],[f561]) ).
fof(f565,plain,
( ~ sQ8_spl
| app(app(sk6,sk1),sk7) = sk4 ),
inference(forward_demodulation,[status(thm)],[f443,f495]) ).
fof(f566,plain,
( ~ sQ8_spl
| app(app(sk6,sk1),sk7) = sk2 ),
inference(forward_demodulation,[status(thm)],[f442,f565]) ).
fof(f567,plain,
( ~ sQ8_spl
| ssList(sk2)
| ~ ssList(app(sk6,sk1))
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f566,f293]) ).
fof(f568,definition,
( sQ17_spl
<=> ssList(app(sk6,sk1)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f570,plain,
( sQ17_spl
| ~ ssList(app(sk6,sk1)) ),
inference(component_clause,[status(thm)],[f568]) ).
fof(f571,definition,
( sQ18_spl
<=> ssList(sk2) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f574,plain,
( ~ sQ8_spl
| sQ18_spl
| ~ sQ17_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f567,f486,f568,f571,f494]) ).
fof(f576,definition,
( sQ19_spl
<=> sk1 = nil ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f582,plain,
( sQ17_spl
| ~ ssList(sk6)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f570,f293]) ).
fof(f583,plain,
( sQ17_spl
| ~ sQ5_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f582,f561,f482,f568]) ).
fof(f596,plain,
! [X0] :
( ~ sQ7_spl
| singletonP(X0)
| ~ ssList(X0)
| ~ ssItem(sk5)
| sk1 != X0 ),
inference(paramodulation,[status(thm)],[f559,f331]) ).
fof(f599,definition,
! [X0] :
( sQ21_spl
<=> ( singletonP(X0)
| ~ ssList(X0)
| sk1 != X0 ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f600,plain,
! [X0] :
( ~ sQ21_spl
| singletonP(X0)
| ~ ssList(X0)
| sk1 != X0 ),
inference(component_clause,[status(thm)],[f599]) ).
fof(f602,plain,
( ~ sQ7_spl
| ~ sQ2_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f596,f599,f471,f490]) ).
fof(f644,plain,
( ~ sQ21_spl
| singletonP(sk1)
| sk1 != sk1 ),
inference(resolution,[status(thm)],[f600,f438]) ).
fof(f652,plain,
( ~ sQ21_spl
| singletonP(nil)
| sk1 != nil ),
inference(resolution,[status(thm)],[f600,f215]) ).
fof(f668,definition,
( sQ29_spl
<=> sk1 = sk1 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f670,plain,
( sQ29_spl
| sk1 != sk1 ),
inference(component_clause,[status(thm)],[f668]) ).
fof(f671,plain,
( ~ sQ21_spl
| sQ13_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f644,f668,f519,f599]) ).
fof(f686,definition,
( sQ34_spl
<=> singletonP(nil) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f687,plain,
( ~ sQ34_spl
| singletonP(nil) ),
inference(component_clause,[status(thm)],[f686]) ).
fof(f689,plain,
( ~ sQ21_spl
| sQ34_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f652,f576,f686,f599]) ).
fof(f691,plain,
( ~ sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f687,f218]) ).
fof(f692,plain,
~ sQ34_spl,
inference(contradiction_clause,[status(thm)],[f691]) ).
fof(f693,plain,
( sQ29_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f670]) ).
fof(f694,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f693]) ).
fof(f697,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f563,f438]) ).
fof(f698,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f697]) ).
fof(f699,plain,
! [X0] :
( singletonP(app(cons(X0,nil),nil))
| ~ ssList(app(cons(X0,nil),nil))
| ~ ssItem(X0)
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f338,f331]) ).
fof(f700,definition,
! [X0] :
( sQ35_spl
<=> ( singletonP(app(cons(X0,nil),nil))
| ~ ssList(app(cons(X0,nil),nil))
| ~ ssItem(X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f703,plain,
( ~ sQ14_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f699,f700,f548]) ).
fof(f705,plain,
! [X0] :
( ~ ssList(X0)
| nil != X0
| nil = X0
| ~ ssList(nil)
| ~ ssList(X0)
| ~ segmentP(X0,nil) ),
inference(resolution,[status(thm)],[f347,f287]) ).
fof(f706,plain,
! [X0] :
( ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(nil,X0) ),
inference(resolution,[status(thm)],[f347,f263]) ).
fof(f708,definition,
! [X0] :
( sQ36_spl
<=> ( ~ ssList(X0)
| nil != X0
| nil = X0
| ~ ssList(X0)
| ~ segmentP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f711,plain,
( ~ sQ14_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f705,f708,f548]) ).
fof(f712,definition,
! [X0] :
( sQ37_spl
<=> ( ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f715,plain,
( ~ sQ14_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f706,f712,f548]) ).
fof(f725,plain,
( ~ sQ12_spl
| ~ sQ3_spl
| neq(nil,nil) ),
inference(backward_demodulation,[status(thm)],[f536,f516]) ).
fof(f736,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| nil != X1
| nil != X0 ),
inference(resolution,[status(thm)],[f369,f337]) ).
fof(f738,definition,
! [X0] :
( sQ39_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0)
| nil != X0 ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f739,plain,
! [X0] :
( ~ sQ39_spl
| ~ ssList(X0)
| ~ ssList(X0)
| nil != X0 ),
inference(component_clause,[status(thm)],[f738]) ).
fof(f741,definition,
! [X1] :
( sQ40_spl
<=> ( nil = X1
| ~ ssList(X1)
| ~ ssList(X1)
| nil != X1 ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f744,plain,
( sQ40_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f736,f738,f741]) ).
fof(f746,plain,
! [X0] :
( ~ sQ39_spl
| ~ ssList(X0)
| nil != X0 ),
inference(duplicate_literals_removal,[status(thm)],[f739]) ).
fof(f748,plain,
( ~ sQ12_spl
| ~ sQ3_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f725,f526]) ).
fof(f749,plain,
( ~ sQ12_spl
| ~ sQ3_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f748,f548,f474,f515]) ).
fof(f750,plain,
! [X0] :
( ~ ssList(app(nil,X0))
| app(nil,X0) = X0
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(app(nil,X0)) ),
inference(resolution,[status(thm)],[f378,f282]) ).
fof(f753,definition,
! [X0] :
( sQ41_spl
<=> ( ~ ssList(app(nil,X0))
| app(nil,X0) = X0
| ~ ssList(X0)
| ~ ssList(app(nil,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f756,plain,
( ~ sQ14_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f750,f753,f548]) ).
fof(f766,plain,
! [X0] :
( ~ ssList(app(X0,nil))
| app(X0,nil) = X0
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(app(X0,nil)) ),
inference(resolution,[status(thm)],[f380,f281]) ).
fof(f769,definition,
! [X0] :
( sQ44_spl
<=> ( ~ ssList(app(X0,nil))
| app(X0,nil) = X0
| ~ ssList(X0)
| ~ ssList(app(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f772,plain,
( ~ sQ14_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f766,f769,f548]) ).
fof(f776,plain,
! [X0,X1] :
( ~ ssList(X1)
| nil != X1
| segmentP(X0,X1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ segmentP(X0,nil) ),
inference(resolution,[status(thm)],[f382,f287]) ).
fof(f777,plain,
! [X0,X1] :
( ~ ssList(X1)
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ segmentP(X0,X1) ),
inference(resolution,[status(thm)],[f382,f263]) ).
fof(f780,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X0,X1)
| ~ segmentP(nil,X0) ),
inference(resolution,[status(thm)],[f382,f288]) ).
fof(f783,definition,
! [X0,X1] :
( sQ45_spl
<=> ( ~ ssList(X1)
| nil != X1
| segmentP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f786,plain,
( ~ sQ14_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f776,f783,f548]) ).
fof(f787,definition,
! [X0,X1] :
( sQ46_spl
<=> ( ~ ssList(X1)
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f790,plain,
( ~ sQ14_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f777,f787,f548]) ).
fof(f792,definition,
! [X0,X1] :
( sQ47_spl
<=> ( nil = X1
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X0,X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f795,plain,
( ~ sQ14_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f780,f792,f548]) ).
fof(f1037,plain,
( ~ sQ39_spl
| nil != nil ),
inference(resolution,[status(thm)],[f746,f215]) ).
fof(f1038,plain,
( ~ sQ39_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1037]) ).
fof(f1039,plain,
~ sQ39_spl,
inference(contradiction_clause,[status(thm)],[f1038]) ).
fof(f1054,plain,
( ~ sQ8_spl
| segmentP(sk2,sk1)
| ~ ssList(sk2)
| ~ ssList(sk1)
| ~ ssList(sk6)
| ~ ssList(sk7) ),
inference(resolution,[status(thm)],[f414,f566]) ).
fof(f1056,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| segmentP(app(X0,X1),X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f414,f281]) ).
fof(f1063,plain,
( ~ sQ8_spl
| sQ11_spl
| ~ sQ18_spl
| ~ sQ16_spl
| ~ sQ5_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1054,f486,f482,f561,f571,f512,f494]) ).
fof(f1065,definition,
! [X0,X1] :
( sQ74_spl
<=> ( ~ ssList(app(X0,X1))
| segmentP(app(X0,X1),X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f1068,plain,
( sQ74_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1056,f548,f1065]) ).
fof(f1078,plain,
$false,
inference(sat_refutation,[status(thm)],[f477,f481,f485,f489,f493,f497,f506,f507,f508,f509,f518,f522,f544,f554,f557,f574,f583,f602,f671,f689,f692,f694,f698,f703,f711,f715,f744,f749,f756,f772,f786,f790,f795,f1039,f1063,f1068]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC389-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.55 % Computer : n016.cluster.edu
% 0.09/0.55 % Model : x86_64 x86_64
% 0.09/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.55 % Memory : 8046.5625MB
% 0.09/0.55 % OS : Linux 6.8.0-71-generic
% 0.09/0.55 % CPULimit : 300
% 0.09/0.55 % WCLimit : 300
% 0.09/0.55 % DateTime : Mon Sep 21 08:25:23 UTC 2026
% 0.02/0.56 % CPUTime :
% 0.02/0.57 % Drodi V4.1.1
% 0.02/0.62 % Refutation found
% 0.02/0.62 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.02/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.64 % Elapsed time: 0.074096 seconds
% 0.13/0.64 % CPU time: 0.245719 seconds
% 0.13/0.64 % Total memory used: 111.261 MB
% 0.13/0.64 % Net memory used: 111.043 MB
%------------------------------------------------------------------------------