%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC279-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 02:40:37 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 36
% Syntax : Number of formulae : 107 ( 21 unt; 18 def)
% Number of atoms : 292 ( 36 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 347 ( 162 ~; 167 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 19 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 60 ( 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
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(f85,axiom,
! [U,V] :
( ssList(app(V,U))
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f86,axiom,
! [U,V] :
( ssList(cons(U,V))
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f118,axiom,
! [U,V] :
( nil = U
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f119,axiom,
! [U,V] :
( nil = V
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ),
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,B,C,D] :
( ~ memberP(C,D)
| leq(A,D)
| ~ ssItem(D)
| app(app(B,cons(A,nil)),C) != sk3
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
! [A,B,C,D] :
( ~ memberP(B,D)
| leq(D,A)
| ~ ssItem(D)
| app(app(B,cons(A,nil)),C) != sk3
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
ssItem(sk8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f199,negated_conjecture,
( memberP(sk7,sk8)
| memberP(sk6,sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f200,negated_conjecture,
( ~ leq(sk5,sk8)
| memberP(sk6,sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f201,negated_conjecture,
( memberP(sk7,sk8)
| ~ leq(sk8,sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f202,negated_conjecture,
( ~ leq(sk5,sk8)
| ~ leq(sk8,sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f210,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f276,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f288,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f289,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f329,plain,
! [U] :
( nil = U
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f118]) ).
fof(f330,plain,
! [X0,X1] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f329]) ).
fof(f331,plain,
! [V] :
( nil = V
| ! [U] :
( ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f119]) ).
fof(f332,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f331]) ).
fof(f438,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f439,plain,
! [C,D] :
( ~ memberP(C,D)
| ! [A] :
( leq(A,D)
| ~ ssItem(D)
| ! [B] :
( app(app(B,cons(A,nil)),C) != sk3
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ) ) ),
inference(miniscoping,[status(thm)],[f192]) ).
fof(f440,plain,
! [X0,X1,X2,X3] :
( ~ memberP(X2,X3)
| leq(X0,X3)
| ~ ssItem(X3)
| app(app(X1,cons(X0,nil)),X2) != sk3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f439]) ).
fof(f441,plain,
! [B,D] :
( ~ memberP(B,D)
| ! [A] :
( leq(D,A)
| ~ ssItem(D)
| ! [C] :
( app(app(B,cons(A,nil)),C) != sk3
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ) ) ),
inference(miniscoping,[status(thm)],[f193]) ).
fof(f442,plain,
! [X0,X1,X2,X3] :
( ~ memberP(X1,X3)
| leq(X3,X0)
| ~ ssItem(X3)
| app(app(X1,cons(X0,nil)),X2) != sk3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f441]) ).
fof(f443,plain,
ssItem(sk5),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f444,plain,
ssList(sk6),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f445,plain,
ssList(sk7),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f446,plain,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f447,plain,
ssItem(sk8),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f448,plain,
( memberP(sk7,sk8)
| memberP(sk6,sk8) ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f449,plain,
( ~ leq(sk5,sk8)
| memberP(sk6,sk8) ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f450,plain,
( memberP(sk7,sk8)
| ~ leq(sk8,sk5) ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f451,plain,
( ~ leq(sk5,sk8)
| ~ leq(sk8,sk5) ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f459,definition,
( sQ2_spl
<=> memberP(sk6,sk8) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f462,definition,
( sQ3_spl
<=> memberP(sk7,sk8) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f465,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f448,f459,f462]) ).
fof(f466,definition,
( sQ4_spl
<=> leq(sk5,sk8) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f468,plain,
( sQ4_spl
| ~ leq(sk5,sk8) ),
inference(component_clause,[status(thm)],[f466]) ).
fof(f469,plain,
( ~ sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f449,f459,f466]) ).
fof(f470,definition,
( sQ5_spl
<=> leq(sk8,sk5) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f472,plain,
( sQ5_spl
| ~ leq(sk8,sk5) ),
inference(component_clause,[status(thm)],[f470]) ).
fof(f473,plain,
( sQ3_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f450,f470,f462]) ).
fof(f474,plain,
( ~ sQ4_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f451,f470,f466]) ).
fof(f509,plain,
! [X0,X1,X2,X3] :
( ~ memberP(X2,X3)
| leq(X0,X3)
| ~ ssItem(X3)
| app(app(X1,cons(X0,nil)),X2) != sk1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f438,f440]) ).
fof(f513,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[f276,f210]) ).
fof(f532,plain,
! [X0,X1,X2,X3] :
( ~ memberP(X1,X3)
| leq(X3,X0)
| ~ ssItem(X3)
| app(app(X1,cons(X0,nil)),X2) != sk1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f438,f442]) ).
fof(f537,definition,
( sQ6_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f539,plain,
( sQ6_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f537]) ).
fof(f540,definition,
( sQ7_spl
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f542,plain,
( sQ7_spl
| ~ ssList(sk6) ),
inference(component_clause,[status(thm)],[f540]) ).
fof(f544,definition,
( sQ8_spl
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f546,plain,
( sQ8_spl
| ~ ssList(sk7) ),
inference(component_clause,[status(thm)],[f544]) ).
fof(f571,definition,
( sQ10_spl
<=> ssList(sk1) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f575,plain,
! [X0] :
( ~ memberP(sk6,X0)
| leq(X0,sk5)
| ~ ssItem(X0)
| ~ ssList(sk7)
| ~ ssList(sk6)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f446,f532]) ).
fof(f576,plain,
! [X0] :
( ~ memberP(sk7,X0)
| leq(sk5,X0)
| ~ ssItem(X0)
| ~ ssList(sk7)
| ~ ssList(sk6)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f446,f509]) ).
fof(f579,plain,
( ssList(sk1)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f446,f288]) ).
fof(f580,definition,
( sQ11_spl
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f582,plain,
( sQ11_spl
| ~ ssItem(sk5) ),
inference(component_clause,[status(thm)],[f580]) ).
fof(f583,definition,
! [X0] :
( sQ12_spl
<=> ( ~ memberP(sk6,X0)
| leq(X0,sk5)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f584,plain,
! [X0] :
( ~ sQ12_spl
| ~ memberP(sk6,X0)
| leq(X0,sk5)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f583]) ).
fof(f586,plain,
( sQ12_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f575,f580,f540,f544,f583]) ).
fof(f587,definition,
! [X0] :
( sQ13_spl
<=> ( ~ memberP(sk7,X0)
| leq(sk5,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f588,plain,
! [X0] :
( ~ sQ13_spl
| ~ memberP(sk7,X0)
| leq(sk5,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f587]) ).
fof(f590,plain,
( sQ13_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f576,f580,f540,f544,f587]) ).
fof(f596,definition,
( sQ15_spl
<=> ssList(app(sk6,cons(sk5,nil))) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f598,plain,
( sQ15_spl
| ~ ssList(app(sk6,cons(sk5,nil))) ),
inference(component_clause,[status(thm)],[f596]) ).
fof(f599,plain,
( sQ10_spl
| ~ sQ15_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f579,f544,f596,f571]) ).
fof(f600,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f546,f445]) ).
fof(f601,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f600]) ).
fof(f602,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f542,f444]) ).
fof(f603,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f602]) ).
fof(f604,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f582,f443]) ).
fof(f605,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f604]) ).
fof(f644,plain,
( sQ15_spl
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil)) ),
inference(resolution,[status(thm)],[f598,f288]) ).
fof(f645,definition,
( sQ16_spl
<=> ssList(cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f647,plain,
( sQ16_spl
| ~ ssList(cons(sk5,nil)) ),
inference(component_clause,[status(thm)],[f645]) ).
fof(f648,plain,
( sQ15_spl
| ~ sQ7_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f644,f645,f540,f596]) ).
fof(f649,plain,
( nil = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f330,f513]) ).
fof(f655,plain,
( nil = app(sk6,cons(sk5,nil))
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk7)
| sk1 != nil ),
inference(paramodulation,[status(thm)],[f446,f330]) ).
fof(f660,definition,
( sQ17_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f663,plain,
( sQ17_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f649,f537,f660]) ).
fof(f664,definition,
( sQ18_spl
<=> sk1 = nil ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f676,definition,
( sQ21_spl
<=> sk7 = nil ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f681,definition,
( sQ22_spl
<=> nil = app(sk6,cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f684,plain,
( sQ22_spl
| ~ sQ15_spl
| ~ sQ8_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f655,f664,f544,f596,f681]) ).
fof(f689,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f539,f210]) ).
fof(f690,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f689]) ).
fof(f697,plain,
( nil = sk7
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk7)
| sk1 != nil ),
inference(paramodulation,[status(thm)],[f446,f332]) ).
fof(f708,plain,
( sQ21_spl
| ~ sQ15_spl
| ~ sQ8_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f697,f664,f544,f596,f676]) ).
fof(f731,plain,
( sQ16_spl
| ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f647,f289]) ).
fof(f732,plain,
( sQ16_spl
| ~ sQ6_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f731,f580,f537,f645]) ).
fof(f733,plain,
( sQ5_spl
| ~ sQ12_spl
| ~ memberP(sk6,sk8)
| ~ ssItem(sk8) ),
inference(resolution,[status(thm)],[f584,f472]) ).
fof(f735,definition,
( sQ23_spl
<=> ssItem(sk8) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f737,plain,
( sQ23_spl
| ~ ssItem(sk8) ),
inference(component_clause,[status(thm)],[f735]) ).
fof(f738,plain,
( sQ5_spl
| ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f733,f735,f459,f583,f470]) ).
fof(f740,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f737,f447]) ).
fof(f741,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f740]) ).
fof(f815,plain,
( sQ4_spl
| ~ sQ13_spl
| ~ memberP(sk7,sk8)
| ~ ssItem(sk8) ),
inference(resolution,[status(thm)],[f588,f468]) ).
fof(f817,plain,
( sQ4_spl
| ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f815,f735,f462,f587,f466]) ).
fof(f819,plain,
$false,
inference(sat_refutation,[status(thm)],[f465,f469,f473,f474,f586,f590,f599,f601,f603,f605,f648,f663,f684,f690,f708,f732,f738,f741,f817]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC279-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 08:11:44 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.42 % Elapsed time: 0.055446 seconds
% 0.09/0.42 % CPU time: 0.145580 seconds
% 0.09/0.42 % Total memory used: 65.137 MB
% 0.09/0.42 % Net memory used: 65.050 MB
%------------------------------------------------------------------------------