%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC366-1 : 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 02:40:57 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 27
% Syntax : Number of formulae : 92 ( 15 unt; 13 def)
% Number of atoms : 259 ( 42 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 316 ( 149 ~; 154 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 14 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 50 ( 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f76,axiom,
! [U] :
( nil = U
| ssItem(hd(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(f100,axiom,
! [U,V] :
( V = U
| neq(V,U)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f115,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f143,axiom,
! [U,V,W] :
( rearsegP(W,V)
| ~ ssList(W)
| ~ ssList(V)
| ~ ssList(U)
| app(U,V) != W ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f188,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f189,negated_conjecture,
ssList(sk4),
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,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
! [A,B,C] :
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| hd(sk4) != C
| cons(C,nil) != B
| ~ ssItem(C)
| app(B,sk3) != A
| ~ ssList(B)
| sk4 = A
| ~ ssList(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( ~ neq(sk4,nil)
| ~ rearsegP(sk2,sk1) ),
file('/export/starexec/sandbox2/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(f283,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
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(f355,plain,
! [V,W] :
( rearsegP(W,V)
| ~ ssList(W)
| ~ ssList(V)
| ! [U] :
( ~ ssList(U)
| app(U,V) != W ) ),
inference(miniscoping,[status(thm)],[f143]) ).
fof(f356,plain,
! [X0,X1,X2] :
( rearsegP(X2,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) != X2 ),
inference(cnf_transformation,[status(thm)],[f355]) ).
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(f439,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| ! [C] :
( hd(sk4) != C
| ! [B] :
( cons(C,nil) != B
| ~ ssItem(C)
| ! [A] :
( app(B,sk3) != A
| ~ ssList(B)
| sk4 = A
| ~ ssList(A) ) ) ) ),
inference(miniscoping,[status(thm)],[f196]) ).
fof(f440,plain,
! [X0,X1,X2] :
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| hd(sk4) != X2
| cons(X2,nil) != X1
| ~ ssItem(X2)
| app(X1,sk3) != X0
| ~ ssList(X1)
| sk4 = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f439]) ).
fof(f441,plain,
( ~ neq(sk4,nil)
| ~ rearsegP(sk2,sk1) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f449,definition,
( sQ2_spl
<=> neq(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f450,plain,
( ~ sQ2_spl
| neq(sk2,nil) ),
inference(component_clause,[status(thm)],[f449]) ).
fof(f452,plain,
sQ2_spl,
inference(split_clause,[status(thm)],[f434,f449]) ).
fof(f453,definition,
( sQ3_spl
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f455,plain,
( sQ3_spl
| ~ neq(sk4,nil) ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f457,definition,
! [X0,X1,X2] :
( sQ4_spl
<=> ( hd(sk4) != X2
| cons(X2,nil) != X1
| ~ ssItem(X2)
| app(X1,sk3) != X0
| ~ ssList(X1)
| sk4 = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f458,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| hd(sk4) != X2
| cons(X2,nil) != X1
| ~ ssItem(X2)
| app(X1,sk3) != X0
| ~ ssList(X1)
| sk4 = X0
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f457]) ).
fof(f460,definition,
( sQ5_spl
<=> neq(nil,sk4) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f462,plain,
( sQ5_spl
| ~ neq(nil,sk4) ),
inference(component_clause,[status(thm)],[f460]) ).
fof(f464,definition,
( sQ6_spl
<=> rearsegP(sk2,sk1) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f466,plain,
( sQ6_spl
| ~ rearsegP(sk2,sk1) ),
inference(component_clause,[status(thm)],[f464]) ).
fof(f468,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f440,f457,f460,f453]) ).
fof(f469,plain,
( ~ sQ3_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f441,f464,f453]) ).
fof(f477,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f319]) ).
fof(f478,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f477]) ).
fof(f484,plain,
! [X0,X1] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f356]) ).
fof(f501,plain,
( ~ sQ2_spl
| neq(sk4,nil) ),
inference(forward_demodulation,[status(thm)],[f432,f450]) ).
fof(f502,plain,
( sQ6_spl
| ~ rearsegP(sk4,sk1) ),
inference(forward_demodulation,[status(thm)],[f432,f466]) ).
fof(f503,plain,
( sQ6_spl
| ~ rearsegP(sk4,sk3) ),
inference(forward_demodulation,[status(thm)],[f433,f502]) ).
fof(f504,plain,
( sQ3_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f455,f501]) ).
fof(f505,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f504]) ).
fof(f506,plain,
( ~ sQ4_spl
| ~ ssItem(hd(sk4))
| ~ ssList(cons(hd(sk4),nil))
| sk4 = app(cons(hd(sk4),nil),sk3)
| ~ ssList(app(cons(hd(sk4),nil),sk3)) ),
inference(destructive_equality_resolution,[status(thm)],[f458]) ).
fof(f509,definition,
( sQ7_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f511,plain,
( sQ7_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f509]) ).
fof(f517,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f511,f205]) ).
fof(f518,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f517]) ).
fof(f519,plain,
( ~ sQ4_spl
| ~ ssItem(hd(sk4))
| ~ ssList(cons(hd(sk4),nil))
| sk4 = app(cons(hd(sk4),nil),sk3)
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(sk3) ),
inference(resolution,[status(thm)],[f283,f506]) ).
fof(f520,definition,
( sQ9_spl
<=> ssList(sk3) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f522,plain,
( sQ9_spl
| ~ ssList(sk3) ),
inference(component_clause,[status(thm)],[f520]) ).
fof(f523,definition,
( sQ10_spl
<=> ssList(cons(hd(sk4),nil)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f525,plain,
( sQ10_spl
| ~ ssList(cons(hd(sk4),nil)) ),
inference(component_clause,[status(thm)],[f523]) ).
fof(f526,definition,
( sQ11_spl
<=> sk4 = app(cons(hd(sk4),nil),sk3) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f527,plain,
( ~ sQ11_spl
| sk4 = app(cons(hd(sk4),nil),sk3) ),
inference(component_clause,[status(thm)],[f526]) ).
fof(f529,definition,
( sQ12_spl
<=> ssItem(hd(sk4)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f531,plain,
( sQ12_spl
| ~ ssItem(hd(sk4)) ),
inference(component_clause,[status(thm)],[f529]) ).
fof(f532,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f519,f520,f523,f526,f529,f457]) ).
fof(f533,plain,
( sQ12_spl
| nil = sk4
| ~ ssList(sk4) ),
inference(resolution,[status(thm)],[f531,f274]) ).
fof(f534,definition,
( sQ13_spl
<=> ssList(sk4) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f536,plain,
( sQ13_spl
| ~ ssList(sk4) ),
inference(component_clause,[status(thm)],[f534]) ).
fof(f537,definition,
( sQ14_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f538,plain,
( ~ sQ14_spl
| nil = sk4 ),
inference(component_clause,[status(thm)],[f537]) ).
fof(f540,plain,
( sQ12_spl
| sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f533,f534,f537,f529]) ).
fof(f541,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f536,f431]) ).
fof(f542,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f541]) ).
fof(f557,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| neq(sk4,sk4) ),
inference(backward_demodulation,[status(thm)],[f538,f501]) ).
fof(f567,plain,
( sQ10_spl
| ~ ssList(nil)
| ~ ssItem(hd(sk4)) ),
inference(resolution,[status(thm)],[f525,f284]) ).
fof(f568,plain,
( sQ10_spl
| ~ sQ7_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f567,f529,f509,f523]) ).
fof(f573,plain,
( sQ5_spl
| nil = sk4
| ~ ssList(nil)
| ~ ssList(sk4) ),
inference(resolution,[status(thm)],[f300,f462]) ).
fof(f576,plain,
( sQ5_spl
| sQ14_spl
| ~ sQ7_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f573,f534,f509,f537,f460]) ).
fof(f590,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f522,f430]) ).
fof(f591,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f590]) ).
fof(f719,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| ~ ssList(sk4) ),
inference(resolution,[status(thm)],[f557,f478]) ).
fof(f720,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f719,f534,f537,f449]) ).
fof(f728,plain,
! [X0,X1] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f484,f283]) ).
fof(f733,plain,
( ~ sQ11_spl
| rearsegP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(cons(hd(sk4),nil)) ),
inference(paramodulation,[status(thm)],[f527,f728]) ).
fof(f740,definition,
( sQ27_spl
<=> rearsegP(sk4,sk3) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f741,plain,
( ~ sQ27_spl
| rearsegP(sk4,sk3) ),
inference(component_clause,[status(thm)],[f740]) ).
fof(f743,plain,
( ~ sQ11_spl
| sQ27_spl
| ~ sQ9_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f733,f523,f520,f740,f526]) ).
fof(f749,plain,
( ~ sQ27_spl
| sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f741,f503]) ).
fof(f750,plain,
( ~ sQ27_spl
| sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f749]) ).
fof(f751,plain,
$false,
inference(sat_refutation,[status(thm)],[f452,f468,f469,f505,f518,f532,f540,f542,f568,f576,f591,f720,f743,f750]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC366-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n009.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % 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 08:19:12 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.44 % Elapsed time: 0.062165 seconds
% 0.10/0.44 % CPU time: 0.199762 seconds
% 0.10/0.44 % Total memory used: 110.109 MB
% 0.10/0.44 % Net memory used: 109.872 MB
%------------------------------------------------------------------------------