%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC320-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 02:40:46 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 35
% Syntax : Number of formulae : 111 ( 11 unt; 17 def)
% Number of atoms : 287 ( 83 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 337 ( 161 ~; 159 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 18 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 44 ( 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
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(f86,axiom,
! [U,V] :
( ssList(cons(U,V))
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f99,axiom,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != V ),
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(f145,axiom,
! [U,V] :
( app(U,V) = nil
| ~ ssList(U)
| ~ ssList(V)
| nil != V
| nil != U ),
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,
( nil != sk4
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( neq(sk2,nil)
| nil = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
! [A,B] :
( app(B,cons(A,nil)) != sk2
| app(cons(A,nil),B) != sk1
| ~ ssList(B)
| ~ ssItem(A)
| nil = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f199,negated_conjecture,
( neq(sk2,nil)
| nil != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f208,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f275,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f287,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f301,plain,
! [V] :
( ~ ssList(V)
| ! [U] :
( ~ ssItem(U)
| cons(U,V) != V ) ),
inference(miniscoping,[status(thm)],[f99]) ).
fof(f302,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != X1 ),
inference(cnf_transformation,[status(thm)],[f301]) ).
fof(f327,plain,
! [U] :
( nil = U
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f118]) ).
fof(f328,plain,
! [X0,X1] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f327]) ).
fof(f329,plain,
! [V] :
( nil = V
| ! [U] :
( ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f119]) ).
fof(f330,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f329]) ).
fof(f362,plain,
! [X0,X1] :
( app(X0,X1) = nil
| ~ ssList(X0)
| ~ ssList(X1)
| nil != X1
| nil != X0 ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f433,plain,
ssList(sk3),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f435,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f436,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f437,plain,
( nil != sk4
| nil = sk3 ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f438,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f439,plain,
( ~ neq(sk4,nil)
| ssList(sk6) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f440,plain,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk3 ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f441,plain,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk4 ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f442,plain,
( neq(sk2,nil)
| nil = sk2 ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f443,plain,
! [X0,X1] :
( app(X1,cons(X0,nil)) != sk2
| app(cons(X0,nil),X1) != sk1
| ~ ssList(X1)
| ~ ssItem(X0)
| nil = sk2 ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f444,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f453,definition,
( sQ2_spl
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f454,plain,
( ~ sQ2_spl
| nil = sk3 ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f456,definition,
( sQ3_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f458,plain,
( sQ3_spl
| nil != sk4 ),
inference(component_clause,[status(thm)],[f456]) ).
fof(f459,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f437,f453,f456]) ).
fof(f460,definition,
( sQ4_spl
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f463,definition,
( sQ5_spl
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f465,plain,
( sQ5_spl
| ~ neq(sk4,nil) ),
inference(component_clause,[status(thm)],[f463]) ).
fof(f466,plain,
( ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f438,f460,f463]) ).
fof(f467,definition,
( sQ6_spl
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f470,plain,
( ~ sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f439,f467,f463]) ).
fof(f471,definition,
( sQ7_spl
<=> app(cons(sk5,nil),sk6) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f472,plain,
( ~ sQ7_spl
| app(cons(sk5,nil),sk6) = sk3 ),
inference(component_clause,[status(thm)],[f471]) ).
fof(f474,plain,
( ~ sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f440,f471,f463]) ).
fof(f475,definition,
( sQ8_spl
<=> app(sk6,cons(sk5,nil)) = sk4 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f478,plain,
( ~ sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f441,f475,f463]) ).
fof(f479,definition,
( sQ9_spl
<=> nil = sk2 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f480,plain,
( ~ sQ9_spl
| nil = sk2 ),
inference(component_clause,[status(thm)],[f479]) ).
fof(f482,definition,
( sQ10_spl
<=> neq(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f483,plain,
( ~ sQ10_spl
| neq(sk2,nil) ),
inference(component_clause,[status(thm)],[f482]) ).
fof(f485,plain,
( sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f442,f479,f482]) ).
fof(f486,definition,
! [X0,X1] :
( sQ11_spl
<=> ( app(X1,cons(X0,nil)) != sk2
| app(cons(X0,nil),X1) != sk1
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f487,plain,
! [X0,X1] :
( ~ sQ11_spl
| app(X1,cons(X0,nil)) != sk2
| app(cons(X0,nil),X1) != sk1
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f486]) ).
fof(f489,plain,
( sQ11_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f443,f479,f486]) ).
fof(f490,definition,
( sQ12_spl
<=> nil = sk1 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f492,plain,
( sQ12_spl
| nil != sk1 ),
inference(component_clause,[status(thm)],[f490]) ).
fof(f493,plain,
( sQ10_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f444,f490,f482]) ).
fof(f511,plain,
( app(nil,nil) = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(destructive_equality_resolution,[status(thm)],[f362]) ).
fof(f512,plain,
( app(nil,nil) = nil
| ~ ssList(nil) ),
inference(duplicate_literals_removal,[status(thm)],[f511]) ).
fof(f526,plain,
( sQ12_spl
| nil != sk3 ),
inference(forward_demodulation,[status(thm)],[f436,f492]) ).
fof(f527,plain,
( sQ12_spl
| ~ sQ9_spl
| sk4 != sk3 ),
inference(backward_demodulation,[status(thm)],[f529,f526]) ).
fof(f529,plain,
( ~ sQ9_spl
| nil = sk4 ),
inference(forward_demodulation,[status(thm)],[f435,f480]) ).
fof(f532,plain,
( ~ sQ2_spl
| ~ sQ9_spl
| sk4 = sk3 ),
inference(forward_demodulation,[status(thm)],[f529,f454]) ).
fof(f533,plain,
( sQ12_spl
| ~ sQ9_spl
| ~ sQ2_spl
| sk4 != sk4 ),
inference(forward_demodulation,[status(thm)],[f532,f527]) ).
fof(f534,plain,
( sQ12_spl
| ~ sQ9_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f533]) ).
fof(f535,plain,
( sQ12_spl
| ~ sQ9_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f534]) ).
fof(f536,plain,
( ~ sQ10_spl
| neq(sk4,nil) ),
inference(forward_demodulation,[status(thm)],[f435,f483]) ).
fof(f537,plain,
! [X0,X1] :
( ~ sQ11_spl
| app(X1,cons(X0,nil)) != sk4
| app(cons(X0,nil),X1) != sk1
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f435,f487]) ).
fof(f539,plain,
( ~ sQ10_spl
| sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f536,f465]) ).
fof(f540,plain,
( ~ sQ10_spl
| sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f539]) ).
fof(f541,plain,
( ~ sQ9_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f529,f458]) ).
fof(f542,plain,
( ~ sQ9_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f541]) ).
fof(f595,plain,
( ~ sQ7_spl
| ~ sQ2_spl
| app(cons(sk5,sk3),sk6) = sk3 ),
inference(forward_demodulation,[status(thm)],[f454,f472]) ).
fof(f597,definition,
( sQ15_spl
<=> ssList(cons(sk5,sk3)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f599,plain,
( sQ15_spl
| ~ ssList(cons(sk5,sk3)) ),
inference(component_clause,[status(thm)],[f597]) ).
fof(f600,definition,
( sQ16_spl
<=> ssList(sk3) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f602,plain,
( sQ16_spl
| ~ ssList(sk3) ),
inference(component_clause,[status(thm)],[f600]) ).
fof(f607,plain,
( sQ15_spl
| ~ ssList(sk3)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f599,f287]) ).
fof(f608,plain,
( sQ15_spl
| ~ sQ16_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f607,f460,f600,f597]) ).
fof(f609,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f602,f433]) ).
fof(f610,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f609]) ).
fof(f619,plain,
! [X0,X1] :
( ~ sQ2_spl
| nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != sk3 ),
inference(forward_demodulation,[status(thm)],[f454,f328]) ).
fof(f620,plain,
! [X0,X1] :
( ~ sQ2_spl
| sk3 = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != sk3 ),
inference(forward_demodulation,[status(thm)],[f454,f619]) ).
fof(f621,plain,
( ~ sQ7_spl
| ~ sQ2_spl
| sk3 = cons(sk5,sk3)
| ~ ssList(cons(sk5,sk3))
| ~ ssList(sk6) ),
inference(resolution,[status(thm)],[f620,f595]) ).
fof(f626,definition,
( sQ17_spl
<=> sk3 = cons(sk5,sk3) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f627,plain,
( ~ sQ17_spl
| sk3 = cons(sk5,sk3) ),
inference(component_clause,[status(thm)],[f626]) ).
fof(f629,plain,
( ~ sQ7_spl
| ~ sQ2_spl
| sQ17_spl
| ~ sQ15_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f621,f467,f597,f626,f453,f471]) ).
fof(f647,plain,
( ~ sQ17_spl
| ~ ssList(sk3)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f627,f302]) ).
fof(f652,plain,
( ~ sQ17_spl
| ~ sQ16_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f647,f460,f600,f626]) ).
fof(f656,definition,
( sQ21_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f658,plain,
( sQ21_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f656]) ).
fof(f659,definition,
( sQ22_spl
<=> app(nil,nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f662,plain,
( sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f512,f656,f659]) ).
fof(f663,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f658,f208]) ).
fof(f664,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f663]) ).
fof(f675,plain,
! [X0,X1] :
( ~ sQ11_spl
| app(X1,cons(X0,nil)) != sk4
| app(cons(X0,nil),X1) != sk3
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f436,f537]) ).
fof(f679,definition,
( sQ25_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f685,plain,
( nil = nil
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f275,f330]) ).
fof(f687,plain,
( sQ25_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f685,f656,f679]) ).
fof(f693,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| app(sk6,cons(sk5,nil)) != sk4
| ~ ssList(sk6)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f472,f675]) ).
fof(f698,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f693,f460,f467,f475,f471,f486]) ).
fof(f709,plain,
$false,
inference(sat_refutation,[status(thm)],[f459,f466,f470,f474,f478,f485,f489,f493,f535,f540,f542,f608,f610,f629,f652,f662,f664,f687,f698]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC320-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 08:15:25 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 0.15/0.39 % Refutation found
% 0.15/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.41 % Elapsed time: 0.042105 seconds
% 0.15/0.41 % CPU time: 0.098076 seconds
% 0.15/0.41 % Total memory used: 24.266 MB
% 0.15/0.41 % Net memory used: 24.223 MB
%------------------------------------------------------------------------------