%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC098-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 02:39:57 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 28
% Syntax : Number of formulae : 100 ( 8 unt; 13 def)
% Number of atoms : 286 ( 70 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 360 ( 174 ~; 173 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 14 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 33 ( 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f71,axiom,
! [U] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f98,axiom,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f188,negated_conjecture,
ssList(sk3),
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,
! [A] :
( ~ memberP(sk2,A)
| ssItem(sk5(A))
| cons(A,nil) != sk1
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
! [A] :
( ~ memberP(sk2,A)
| memberP(sk2,sk5(A))
| cons(A,nil) != sk1
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
! [A] :
( ~ memberP(sk2,A)
| leq(A,sk5(A))
| cons(A,nil) != sk1
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
! [A] :
( ~ memberP(sk2,A)
| A != sk5(A)
| cons(A,nil) != sk1
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
( nil != sk1
| nil != sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( nil = sk4
| ssItem(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
( nil = sk3
| ssItem(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f199,negated_conjecture,
( nil = sk4
| cons(sk6,nil) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f201,negated_conjecture,
! [A] :
( nil = sk4
| ~ leq(sk6,A)
| ~ memberP(sk4,A)
| sk6 = A
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f203,negated_conjecture,
( nil = sk3
| memberP(sk4,sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f275,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f303,plain,
! [V] :
( ~ ssList(V)
| ! [U] :
( ~ ssItem(U)
| cons(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f98]) ).
fof(f304,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f303]) ).
fof(f437,plain,
ssList(sk3),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f439,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f440,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f441,plain,
! [X0] :
( ~ memberP(sk2,X0)
| ssItem(sk5(X0))
| cons(X0,nil) != sk1
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f442,plain,
! [X0] :
( ~ memberP(sk2,X0)
| memberP(sk2,sk5(X0))
| cons(X0,nil) != sk1
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f443,plain,
! [X0] :
( ~ memberP(sk2,X0)
| leq(X0,sk5(X0))
| cons(X0,nil) != sk1
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f444,plain,
! [X0] :
( ~ memberP(sk2,X0)
| X0 != sk5(X0)
| cons(X0,nil) != sk1
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f445,plain,
( nil != sk1
| nil != sk2 ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f446,plain,
( nil = sk4
| ssItem(sk6) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f447,plain,
( nil = sk3
| ssItem(sk6) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f448,plain,
( nil = sk4
| cons(sk6,nil) = sk3 ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f450,plain,
( nil = sk4
| ! [A] :
( ~ leq(sk6,A)
| ~ memberP(sk4,A)
| sk6 = A
| ~ ssItem(A) ) ),
inference(miniscoping,[status(thm)],[f201]) ).
fof(f451,plain,
! [X0] :
( nil = sk4
| ~ leq(sk6,X0)
| ~ memberP(sk4,X0)
| sk6 = X0
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f450]) ).
fof(f453,plain,
( nil = sk3
| memberP(sk4,sk6) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f463,definition,
( sQ2_spl
<=> nil = sk2 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f465,plain,
( sQ2_spl
| nil != sk2 ),
inference(component_clause,[status(thm)],[f463]) ).
fof(f466,definition,
( sQ3_spl
<=> nil = sk1 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f468,plain,
( sQ3_spl
| nil != sk1 ),
inference(component_clause,[status(thm)],[f466]) ).
fof(f469,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f445,f463,f466]) ).
fof(f470,definition,
( sQ4_spl
<=> ssItem(sk6) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f471,plain,
( ~ sQ4_spl
| ssItem(sk6) ),
inference(component_clause,[status(thm)],[f470]) ).
fof(f473,definition,
( sQ5_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f474,plain,
( ~ sQ5_spl
| nil = sk4 ),
inference(component_clause,[status(thm)],[f473]) ).
fof(f476,plain,
( sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f446,f470,f473]) ).
fof(f477,definition,
( sQ6_spl
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f478,plain,
( ~ sQ6_spl
| nil = sk3 ),
inference(component_clause,[status(thm)],[f477]) ).
fof(f480,plain,
( sQ6_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f447,f470,f477]) ).
fof(f481,definition,
( sQ7_spl
<=> cons(sk6,nil) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f482,plain,
( ~ sQ7_spl
| cons(sk6,nil) = sk3 ),
inference(component_clause,[status(thm)],[f481]) ).
fof(f484,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f448,f481,f473]) ).
fof(f485,definition,
( sQ8_spl
<=> memberP(sk4,sk6) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f486,plain,
( ~ sQ8_spl
| memberP(sk4,sk6) ),
inference(component_clause,[status(thm)],[f485]) ).
fof(f489,definition,
! [X0] :
( sQ9_spl
<=> ( ~ leq(sk6,X0)
| ~ memberP(sk4,X0)
| sk6 = X0
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f490,plain,
! [X0] :
( ~ sQ9_spl
| ~ leq(sk6,X0)
| ~ memberP(sk4,X0)
| sk6 = X0
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f489]) ).
fof(f492,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f451,f489,f473]) ).
fof(f494,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f453,f485,f477]) ).
fof(f528,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| nil = sk4 ),
inference(backward_demodulation,[status(thm)],[f531,f478]) ).
fof(f531,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk3 = sk4 ),
inference(forward_demodulation,[status(thm)],[f478,f474]) ).
fof(f532,plain,
( sQ2_spl
| nil != sk4 ),
inference(forward_demodulation,[status(thm)],[f439,f465]) ).
fof(f533,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f528,f532]) ).
fof(f534,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f533]) ).
fof(f535,plain,
( sQ3_spl
| ~ sQ6_spl
| sk3 != sk1 ),
inference(backward_demodulation,[status(thm)],[f478,f468]) ).
fof(f546,plain,
( sQ3_spl
| ~ sQ6_spl
| sk3 != sk3 ),
inference(forward_demodulation,[status(thm)],[f440,f535]) ).
fof(f547,plain,
( sQ3_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f546]) ).
fof(f548,plain,
( sQ3_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f547]) ).
fof(f555,plain,
! [X0] :
( ~ memberP(sk2,X0)
| ssItem(sk5(X0))
| cons(X0,nil) != sk3
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f440,f441]) ).
fof(f556,plain,
! [X0] :
( ~ memberP(sk4,X0)
| ssItem(sk5(X0))
| cons(X0,nil) != sk3
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f439,f555]) ).
fof(f557,plain,
( ~ sQ7_spl
| ~ memberP(sk4,sk6)
| ssItem(sk5(sk6))
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f556,f482]) ).
fof(f559,definition,
( sQ11_spl
<=> ssItem(sk5(sk6)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f562,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f557,f470,f559,f485,f481]) ).
fof(f569,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| cons(sk6,sk3) = sk3 ),
inference(backward_demodulation,[status(thm)],[f478,f482]) ).
fof(f573,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != sk3 ),
inference(forward_demodulation,[status(thm)],[f478,f304]) ).
fof(f580,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ ssList(sk3)
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f569,f573]) ).
fof(f583,definition,
( sQ13_spl
<=> ssList(sk3) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f585,plain,
( sQ13_spl
| ~ ssList(sk3) ),
inference(component_clause,[status(thm)],[f583]) ).
fof(f586,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f580,f470,f583,f481,f477]) ).
fof(f589,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f585,f437]) ).
fof(f590,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f589]) ).
fof(f600,plain,
! [X0] :
( ~ sQ5_spl
| ~ ssItem(X0)
| ~ memberP(sk4,X0) ),
inference(forward_demodulation,[status(thm)],[f474,f275]) ).
fof(f601,plain,
( ~ sQ8_spl
| ~ sQ5_spl
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f600,f486]) ).
fof(f602,plain,
( ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f601,f471]) ).
fof(f603,plain,
( ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f602]) ).
fof(f604,plain,
! [X0] :
( ~ memberP(sk2,X0)
| memberP(sk2,sk5(X0))
| cons(X0,nil) != sk3
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f440,f442]) ).
fof(f605,plain,
! [X0] :
( ~ memberP(sk2,X0)
| memberP(sk4,sk5(X0))
| cons(X0,nil) != sk3
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f439,f604]) ).
fof(f606,plain,
! [X0] :
( ~ memberP(sk4,X0)
| memberP(sk4,sk5(X0))
| cons(X0,nil) != sk3
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f439,f605]) ).
fof(f617,plain,
! [X0] :
( ~ memberP(sk2,X0)
| X0 != sk5(X0)
| cons(X0,nil) != sk3
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f440,f444]) ).
fof(f618,plain,
! [X0] :
( ~ memberP(sk4,X0)
| X0 != sk5(X0)
| cons(X0,nil) != sk3
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f439,f617]) ).
fof(f619,plain,
( ~ sQ7_spl
| ~ memberP(sk4,sk6)
| sk6 != sk5(sk6)
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f618,f482]) ).
fof(f621,definition,
( sQ15_spl
<=> sk6 = sk5(sk6) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f624,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f619,f470,f621,f485,f481]) ).
fof(f630,plain,
! [X0] :
( ~ memberP(sk2,X0)
| leq(X0,sk5(X0))
| cons(X0,nil) != sk3
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f440,f443]) ).
fof(f631,plain,
! [X0] :
( ~ memberP(sk4,X0)
| leq(X0,sk5(X0))
| cons(X0,nil) != sk3
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f439,f630]) ).
fof(f632,plain,
( ~ sQ7_spl
| ~ memberP(sk4,sk6)
| leq(sk6,sk5(sk6))
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f631,f482]) ).
fof(f634,definition,
( sQ16_spl
<=> leq(sk6,sk5(sk6)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f635,plain,
( ~ sQ16_spl
| leq(sk6,sk5(sk6)) ),
inference(component_clause,[status(thm)],[f634]) ).
fof(f637,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sQ16_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f632,f470,f634,f485,f481]) ).
fof(f639,plain,
( ~ sQ7_spl
| ~ memberP(sk4,sk6)
| memberP(sk4,sk5(sk6))
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f606,f482]) ).
fof(f641,definition,
( sQ17_spl
<=> memberP(sk4,sk5(sk6)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f644,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sQ17_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f639,f470,f641,f485,f481]) ).
fof(f646,plain,
( ~ sQ9_spl
| ~ sQ16_spl
| ~ memberP(sk4,sk5(sk6))
| sk6 = sk5(sk6)
| ~ ssItem(sk5(sk6)) ),
inference(resolution,[status(thm)],[f635,f490]) ).
fof(f648,plain,
( ~ sQ9_spl
| ~ sQ16_spl
| ~ sQ17_spl
| sQ15_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f646,f559,f621,f641,f634,f489]) ).
fof(f653,plain,
$false,
inference(sat_refutation,[status(thm)],[f469,f476,f480,f484,f492,f494,f534,f548,f562,f586,f590,f603,f624,f637,f644,f648]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC098-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 07:50:58 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.38 % Refutation found
% 0.14/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.044939 seconds
% 0.14/0.41 % CPU time: 0.105745 seconds
% 0.14/0.41 % Total memory used: 24.089 MB
% 0.14/0.41 % Net memory used: 24.064 MB
%------------------------------------------------------------------------------