%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC012-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 02:39:35 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 19
% Syntax : Number of formulae : 59 ( 15 unt; 9 def)
% Number of atoms : 148 ( 33 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 175 ( 86 ~; 80 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 10 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
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(f188,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f189,negated_conjecture,
ssList(sk4),
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,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
! [A,B,C] :
( ~ neq(sk4,nil)
| app(B,C) != sk1
| app(app(B,cons(A,nil)),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f199,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk3,cons(sk5,nil)) = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f207,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f273,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f432,plain,
ssList(sk3),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f433,plain,
ssList(sk4),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f434,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f435,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f436,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f442,plain,
( ~ neq(sk4,nil)
| ! [B,C] :
( app(B,C) != sk1
| ! [A] :
( app(app(B,cons(A,nil)),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ) ) ),
inference(miniscoping,[status(thm)],[f197]) ).
fof(f443,plain,
! [X0,X1,X2] :
( ~ neq(sk4,nil)
| app(X1,X2) != sk1
| app(app(X1,cons(X0,nil)),X2) != sk2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f442]) ).
fof(f444,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f445,plain,
( ~ neq(sk4,nil)
| app(sk3,cons(sk5,nil)) = sk4 ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f453,definition,
( sQ2_spl
<=> neq(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f454,plain,
( ~ sQ2_spl
| neq(sk2,nil) ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f456,plain,
sQ2_spl,
inference(split_clause,[status(thm)],[f436,f453]) ).
fof(f457,definition,
( sQ3_spl
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f459,plain,
( sQ3_spl
| ~ neq(sk4,nil) ),
inference(component_clause,[status(thm)],[f457]) ).
fof(f461,definition,
! [X0,X1,X2] :
( sQ4_spl
<=> ( app(X1,X2) != sk1
| app(app(X1,cons(X0,nil)),X2) != sk2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f462,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| app(X1,X2) != sk1
| app(app(X1,cons(X0,nil)),X2) != sk2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f461]) ).
fof(f465,definition,
( sQ5_spl
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f469,definition,
( sQ6_spl
<=> app(sk3,cons(sk5,nil)) = sk4 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f470,plain,
( ~ sQ6_spl
| app(sk3,cons(sk5,nil)) = sk4 ),
inference(component_clause,[status(thm)],[f469]) ).
fof(f473,plain,
( ~ sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f443,f461,f457]) ).
fof(f474,plain,
( ~ sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f444,f465,f457]) ).
fof(f475,plain,
( ~ sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f445,f469,f457]) ).
fof(f507,plain,
( ~ sQ2_spl
| neq(sk4,nil) ),
inference(forward_demodulation,[status(thm)],[f434,f454]) ).
fof(f508,plain,
( sQ3_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f459,f507]) ).
fof(f509,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f508]) ).
fof(f510,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| app(X1,X2) != sk1
| app(app(X1,cons(X0,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f434,f462]) ).
fof(f511,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| app(X1,X2) != sk3
| app(app(X1,cons(X0,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f435,f510]) ).
fof(f516,definition,
( sQ8_spl
<=> ssList(sk3) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f518,plain,
( sQ8_spl
| ~ ssList(sk3) ),
inference(component_clause,[status(thm)],[f516]) ).
fof(f523,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ4_spl
| app(sk3,X0) != sk3
| app(sk4,X0) != sk4
| ~ ssList(X0)
| ~ ssList(sk3)
| ~ ssItem(sk5) ),
inference(paramodulation,[status(thm)],[f470,f511]) ).
fof(f524,definition,
! [X0] :
( sQ10_spl
<=> ( app(sk3,X0) != sk3
| app(sk4,X0) != sk4
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f525,plain,
! [X0] :
( ~ sQ10_spl
| app(sk3,X0) != sk3
| app(sk4,X0) != sk4
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f524]) ).
fof(f527,plain,
( ~ sQ6_spl
| ~ sQ4_spl
| sQ10_spl
| ~ sQ8_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f523,f465,f516,f524,f461,f469]) ).
fof(f528,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f518,f432]) ).
fof(f529,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f528]) ).
fof(f531,definition,
( sQ11_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f533,plain,
( sQ11_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f531]) ).
fof(f535,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f533,f207]) ).
fof(f536,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f535]) ).
fof(f537,plain,
( ~ sQ10_spl
| ~ ssList(sk3)
| app(sk4,nil) != sk4
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f525,f273]) ).
fof(f539,definition,
( sQ12_spl
<=> app(sk4,nil) = sk4 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f541,plain,
( sQ12_spl
| app(sk4,nil) != sk4 ),
inference(component_clause,[status(thm)],[f539]) ).
fof(f542,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f537,f531,f539,f516,f524]) ).
fof(f550,plain,
( sQ12_spl
| ~ ssList(sk4) ),
inference(resolution,[status(thm)],[f541,f273]) ).
fof(f551,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f550,f433]) ).
fof(f552,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f551]) ).
fof(f553,plain,
$false,
inference(sat_refutation,[status(thm)],[f456,f473,f474,f475,f509,f527,f529,f536,f542,f552]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC012-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n011.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 07:48:55 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.37 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.056761 seconds
% 0.12/0.42 % CPU time: 0.168185 seconds
% 0.12/0.42 % Total memory used: 108.980 MB
% 0.12/0.42 % Net memory used: 108.858 MB
%------------------------------------------------------------------------------