%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC106-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 02:39:59 PM UTC 2026
% Result : Unsatisfiable 0.14s 5.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 26
% Syntax : Number of formulae : 79 ( 12 unt; 12 def)
% Number of atoms : 187 ( 24 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 202 ( 94 ~; 96 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 13 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 27 ( 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
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(f99,axiom,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != V ),
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(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(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(f199,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f200,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f201,negated_conjecture,
( ~ neq(sk4,nil)
| cons(sk5,nil) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f202,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f203,negated_conjecture,
( ~ neq(sk4,nil)
| ~ rearsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f211,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f289,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f304,plain,
! [V] :
( ~ ssList(V)
| ! [U] :
( ~ ssItem(U)
| cons(U,V) != V ) ),
inference(miniscoping,[status(thm)],[f99]) ).
fof(f305,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != X1 ),
inference(cnf_transformation,[status(thm)],[f304]) ).
fof(f306,plain,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f361,plain,
! [V,W] :
( rearsegP(W,V)
| ~ ssList(W)
| ~ ssList(V)
| ! [U] :
( ~ ssList(U)
| app(U,V) != W ) ),
inference(miniscoping,[status(thm)],[f143]) ).
fof(f362,plain,
! [X0,X1,X2] :
( rearsegP(X2,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) != X2 ),
inference(cnf_transformation,[status(thm)],[f361]) ).
fof(f436,plain,
ssList(sk3),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f438,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f439,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f440,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f447,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f448,plain,
( ~ neq(sk4,nil)
| ssList(sk6) ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f449,plain,
( ~ neq(sk4,nil)
| cons(sk5,nil) = sk3 ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f450,plain,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk4 ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f451,plain,
( ~ neq(sk4,nil)
| ~ rearsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f459,definition,
( sQ2_spl
<=> neq(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f460,plain,
( ~ sQ2_spl
| neq(sk2,nil) ),
inference(component_clause,[status(thm)],[f459]) ).
fof(f462,plain,
sQ2_spl,
inference(split_clause,[status(thm)],[f440,f459]) ).
fof(f463,definition,
( sQ3_spl
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f465,plain,
( sQ3_spl
| ~ neq(sk4,nil) ),
inference(component_clause,[status(thm)],[f463]) ).
fof(f467,definition,
( sQ4_spl
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f471,definition,
( sQ5_spl
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f475,definition,
( sQ6_spl
<=> cons(sk5,nil) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f476,plain,
( ~ sQ6_spl
| cons(sk5,nil) = sk3 ),
inference(component_clause,[status(thm)],[f475]) ).
fof(f479,definition,
( sQ7_spl
<=> app(sk6,cons(sk5,nil)) = sk4 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f480,plain,
( ~ sQ7_spl
| app(sk6,cons(sk5,nil)) = sk4 ),
inference(component_clause,[status(thm)],[f479]) ).
fof(f483,definition,
( sQ8_spl
<=> neq(sk1,nil) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f485,plain,
( sQ8_spl
| ~ neq(sk1,nil) ),
inference(component_clause,[status(thm)],[f483]) ).
fof(f486,definition,
( sQ9_spl
<=> rearsegP(sk2,sk1) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f488,plain,
( sQ9_spl
| ~ rearsegP(sk2,sk1) ),
inference(component_clause,[status(thm)],[f486]) ).
fof(f490,plain,
( ~ sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f447,f467,f463]) ).
fof(f491,plain,
( ~ sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f448,f471,f463]) ).
fof(f492,plain,
( ~ sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f449,f475,f463]) ).
fof(f493,plain,
( ~ sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f450,f479,f463]) ).
fof(f494,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f451,f483,f486,f463]) ).
fof(f509,plain,
! [X0,X1] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f362]) ).
fof(f526,plain,
( ~ sQ2_spl
| neq(sk4,nil) ),
inference(forward_demodulation,[status(thm)],[f438,f460]) ).
fof(f527,plain,
( sQ3_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f465,f526]) ).
fof(f528,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f527]) ).
fof(f529,plain,
( sQ8_spl
| ~ neq(sk3,nil) ),
inference(forward_demodulation,[status(thm)],[f439,f485]) ).
fof(f530,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| app(sk6,sk3) = sk4 ),
inference(forward_demodulation,[status(thm)],[f476,f480]) ).
fof(f533,definition,
( sQ10_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f535,plain,
( sQ10_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f533]) ).
fof(f541,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f535,f211]) ).
fof(f542,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f541]) ).
fof(f543,plain,
( ~ sQ6_spl
| ~ ssList(nil)
| ~ ssItem(sk5)
| sk3 != nil ),
inference(paramodulation,[status(thm)],[f476,f305]) ).
fof(f544,definition,
( sQ12_spl
<=> sk3 = nil ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f547,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ4_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f543,f544,f467,f533,f475]) ).
fof(f549,definition,
( sQ13_spl
<=> ssList(sk3) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f551,plain,
( sQ13_spl
| ~ ssList(sk3) ),
inference(component_clause,[status(thm)],[f549]) ).
fof(f556,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f551,f436]) ).
fof(f557,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f556]) ).
fof(f562,plain,
( sQ8_spl
| sk3 = nil
| ~ ssList(sk3)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f306,f529]) ).
fof(f565,plain,
( sQ8_spl
| sQ12_spl
| ~ sQ13_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f562,f533,f549,f544,f483]) ).
fof(f566,plain,
( sQ9_spl
| ~ rearsegP(sk4,sk1) ),
inference(forward_demodulation,[status(thm)],[f438,f488]) ).
fof(f567,plain,
( sQ9_spl
| ~ rearsegP(sk4,sk3) ),
inference(forward_demodulation,[status(thm)],[f439,f566]) ).
fof(f617,plain,
! [X0,X1] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f509,f289]) ).
fof(f620,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| rearsegP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(sk6) ),
inference(paramodulation,[status(thm)],[f530,f617]) ).
fof(f627,definition,
( sQ22_spl
<=> rearsegP(sk4,sk3) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f628,plain,
( ~ sQ22_spl
| rearsegP(sk4,sk3) ),
inference(component_clause,[status(thm)],[f627]) ).
fof(f630,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| sQ22_spl
| ~ sQ13_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f620,f471,f549,f627,f475,f479]) ).
fof(f631,plain,
( ~ sQ22_spl
| sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f628,f567]) ).
fof(f632,plain,
( ~ sQ22_spl
| sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f631]) ).
fof(f633,plain,
$false,
inference(sat_refutation,[status(thm)],[f462,f490,f491,f492,f493,f494,f528,f542,f547,f557,f565,f630,f632]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC106-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n016.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Mon Sep 21 08:00:57 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.39 % Drodi V4.1.1
% 0.14/5.41 % Refutation found
% 0.14/5.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.44 % Elapsed time: 0.060447 seconds
% 0.14/5.44 % CPU time: 0.172414 seconds
% 0.14/5.44 % Total memory used: 99.084 MB
% 0.14/5.44 % Net memory used: 98.955 MB
%------------------------------------------------------------------------------