%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC013-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 22
% Syntax : Number of formulae : 77 ( 14 unt; 10 def)
% Number of atoms : 233 ( 54 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 308 ( 152 ~; 146 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 11 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 42 ( 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f76,axiom,
! [U] :
( nil = U
| ssItem(hd(U))
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f86,axiom,
! [U,V] :
( ssList(cons(U,V))
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f100,axiom,
! [U,V] :
( V = U
| neq(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(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(f196,negated_conjecture,
! [A,B] :
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| hd(sk4) != B
| cons(B,nil) != A
| ~ ssItem(B)
| sk3 = A
| ~ ssList(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
! [A,B] :
( ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| hd(sk2) != B
| cons(B,nil) != A
| ~ ssItem(B)
| sk1 != A
| ~ ssList(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f205,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f274,plain,
! [X0] :
( nil = X0
| ssItem(hd(X0))
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f284,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f300,plain,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f318,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ~ neq(U,V)
| U != V ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f319,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f318]) ).
fof(f430,plain,
ssList(sk3),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f431,plain,
ssList(sk4),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f432,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f433,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f434,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f440,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| ! [B] :
( hd(sk4) != B
| ! [A] :
( cons(B,nil) != A
| ~ ssItem(B)
| sk3 = A
| ~ ssList(A) ) ) ),
inference(miniscoping,[status(thm)],[f196]) ).
fof(f441,plain,
! [X0,X1] :
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| hd(sk4) != X1
| cons(X1,nil) != X0
| ~ ssItem(X1)
| sk3 = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f440]) ).
fof(f442,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| ! [B] :
( hd(sk2) != B
| ! [A] :
( cons(B,nil) != A
| ~ ssItem(B)
| sk1 != A
| ~ ssList(A) ) ) ),
inference(miniscoping,[status(thm)],[f197]) ).
fof(f443,plain,
! [X0,X1] :
( ~ neq(sk4,nil)
| ~ neq(nil,sk2)
| hd(sk2) != X1
| cons(X1,nil) != X0
| ~ ssItem(X1)
| sk1 != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f442]) ).
fof(f451,definition,
( sQ2_spl
<=> neq(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f452,plain,
( ~ sQ2_spl
| neq(sk2,nil) ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f454,plain,
sQ2_spl,
inference(split_clause,[status(thm)],[f434,f451]) ).
fof(f455,definition,
( sQ3_spl
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( sQ3_spl
| ~ neq(sk4,nil) ),
inference(component_clause,[status(thm)],[f455]) ).
fof(f459,definition,
! [X0,X1] :
( sQ4_spl
<=> ( hd(sk4) != X1
| cons(X1,nil) != X0
| ~ ssItem(X1)
| sk3 = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f460,plain,
! [X0,X1] :
( ~ sQ4_spl
| hd(sk4) != X1
| cons(X1,nil) != X0
| ~ ssItem(X1)
| sk3 = X0
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f459]) ).
fof(f462,definition,
( sQ5_spl
<=> neq(nil,sk4) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f464,plain,
( sQ5_spl
| ~ neq(nil,sk4) ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f466,definition,
! [X0,X1] :
( sQ6_spl
<=> ( hd(sk2) != X1
| cons(X1,nil) != X0
| ~ ssItem(X1)
| sk1 != X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f467,plain,
! [X0,X1] :
( ~ sQ6_spl
| hd(sk2) != X1
| cons(X1,nil) != X0
| ~ ssItem(X1)
| sk1 != X0
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f466]) ).
fof(f469,definition,
( sQ7_spl
<=> neq(nil,sk2) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f471,plain,
( sQ7_spl
| ~ neq(nil,sk2) ),
inference(component_clause,[status(thm)],[f469]) ).
fof(f473,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f441,f459,f462,f455]) ).
fof(f474,plain,
( ~ sQ3_spl
| ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f443,f466,f469,f455]) ).
fof(f482,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f319]) ).
fof(f483,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f482]) ).
fof(f506,plain,
( ~ sQ2_spl
| neq(sk4,nil) ),
inference(forward_demodulation,[status(thm)],[f432,f452]) ).
fof(f507,plain,
( sQ3_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f457,f506]) ).
fof(f508,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f507]) ).
fof(f509,plain,
( ~ sQ4_spl
| ~ ssItem(hd(sk4))
| sk3 = cons(hd(sk4),nil)
| ~ ssList(cons(hd(sk4),nil)) ),
inference(destructive_equality_resolution,[status(thm)],[f460]) ).
fof(f510,plain,
! [X0,X1] :
( ~ sQ6_spl
| hd(sk2) != X1
| cons(X1,nil) != X0
| ~ ssItem(X1)
| sk3 != X0
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f433,f467]) ).
fof(f511,plain,
! [X0,X1] :
( ~ sQ6_spl
| hd(sk4) != X1
| cons(X1,nil) != X0
| ~ ssItem(X1)
| sk3 != X0
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f432,f510]) ).
fof(f512,plain,
( ~ sQ6_spl
| cons(hd(sk4),nil) != sk3
| ~ ssItem(hd(sk4))
| ~ ssList(sk3) ),
inference(destructive_equality_resolution,[status(thm)],[f511]) ).
fof(f513,plain,
( ~ sQ6_spl
| cons(hd(sk4),nil) != sk3
| ~ ssItem(hd(sk4)) ),
inference(forward_subsumption_resolution,[status(thm)],[f512,f430]) ).
fof(f516,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ ssItem(hd(sk4))
| ~ ssList(cons(hd(sk4),nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[f509,f513]) ).
fof(f517,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ ssList(nil)
| ~ ssItem(hd(sk4))
| ~ ssItem(hd(sk4)) ),
inference(resolution,[status(thm)],[f516,f284]) ).
fof(f518,definition,
( sQ8_spl
<=> ssItem(hd(sk4)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f520,plain,
( sQ8_spl
| ~ ssItem(hd(sk4)) ),
inference(component_clause,[status(thm)],[f518]) ).
fof(f521,definition,
( sQ9_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f523,plain,
( sQ9_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f521]) ).
fof(f524,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f517,f518,f521,f466,f459]) ).
fof(f525,plain,
( sQ7_spl
| ~ neq(nil,sk4) ),
inference(forward_demodulation,[status(thm)],[f432,f471]) ).
fof(f526,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f523,f205]) ).
fof(f527,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f526]) ).
fof(f528,plain,
( sQ5_spl
| nil = sk4
| ~ ssList(nil)
| ~ ssList(sk4) ),
inference(resolution,[status(thm)],[f464,f300]) ).
fof(f529,definition,
( sQ10_spl
<=> ssList(sk4) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f531,plain,
( sQ10_spl
| ~ ssList(sk4) ),
inference(component_clause,[status(thm)],[f529]) ).
fof(f532,definition,
( sQ11_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f533,plain,
( ~ sQ11_spl
| nil = sk4 ),
inference(component_clause,[status(thm)],[f532]) ).
fof(f535,plain,
( sQ5_spl
| sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f528,f529,f521,f532,f462]) ).
fof(f543,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f531,f431]) ).
fof(f544,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f543]) ).
fof(f555,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| neq(sk4,sk4) ),
inference(backward_demodulation,[status(thm)],[f533,f506]) ).
fof(f568,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ ssList(sk4) ),
inference(resolution,[status(thm)],[f555,f483]) ).
fof(f569,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f568,f529,f532,f451]) ).
fof(f570,plain,
( sQ7_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f525,f462,f469]) ).
fof(f575,plain,
( sQ8_spl
| nil = sk4
| ~ ssList(sk4) ),
inference(resolution,[status(thm)],[f274,f520]) ).
fof(f576,plain,
( sQ8_spl
| sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f575,f529,f532,f518]) ).
fof(f577,plain,
$false,
inference(sat_refutation,[status(thm)],[f454,f473,f474,f508,f524,f527,f535,f544,f569,f570,f576]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC013-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 07:51:15 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.39 % Refutation found
% 0.11/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.044375 seconds
% 0.14/0.42 % CPU time: 0.076892 seconds
% 0.14/0.42 % Total memory used: 20.621 MB
% 0.14/0.42 % Net memory used: 20.593 MB
%------------------------------------------------------------------------------