%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC127-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 02:40:04 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.49s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 17
% Syntax : Number of formulae : 56 ( 19 unt; 7 def)
% Number of atoms : 104 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 88 ( 40 ~; 41 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 4 ( 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
~ singletonP(nil),
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(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),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
segmentP(sk4,sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
( ~ neq(sk4,nil)
| singletonP(sk3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f203,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f206,plain,
~ singletonP(nil),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f298,plain,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f428,plain,
ssList(sk3),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f430,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f431,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f432,plain,
neq(sk2,nil),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f433,plain,
segmentP(sk4,sk3),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f434,plain,
( ~ neq(sk4,nil)
| singletonP(sk3) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f435,plain,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f443,definition,
( sQ2_spl
<=> singletonP(sk3) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f444,plain,
( ~ sQ2_spl
| singletonP(sk3) ),
inference(component_clause,[status(thm)],[f443]) ).
fof(f446,definition,
( sQ3_spl
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f448,plain,
( sQ3_spl
| ~ neq(sk4,nil) ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f449,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f434,f443,f446]) ).
fof(f450,definition,
( sQ4_spl
<=> neq(sk1,nil) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f452,plain,
( sQ4_spl
| ~ neq(sk1,nil) ),
inference(component_clause,[status(thm)],[f450]) ).
fof(f453,definition,
( sQ5_spl
<=> segmentP(sk2,sk1) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f455,plain,
( sQ5_spl
| ~ segmentP(sk2,sk1) ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f456,plain,
( ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f435,f450,f453]) ).
fof(f488,plain,
neq(sk4,nil),
inference(forward_demodulation,[status(thm)],[f430,f432]) ).
fof(f489,plain,
( sQ4_spl
| ~ neq(sk3,nil) ),
inference(forward_demodulation,[status(thm)],[f431,f452]) ).
fof(f492,definition,
( sQ6_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f494,plain,
( sQ6_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f492]) ).
fof(f500,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f494,f203]) ).
fof(f501,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f500]) ).
fof(f502,plain,
( sQ4_spl
| sk3 = nil
| ~ ssList(sk3)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f298,f489]) ).
fof(f505,definition,
( sQ8_spl
<=> ssList(sk3) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f507,plain,
( sQ8_spl
| ~ ssList(sk3) ),
inference(component_clause,[status(thm)],[f505]) ).
fof(f508,definition,
( sQ9_spl
<=> sk3 = nil ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f509,plain,
( ~ sQ9_spl
| sk3 = nil ),
inference(component_clause,[status(thm)],[f508]) ).
fof(f511,plain,
( sQ4_spl
| sQ9_spl
| ~ sQ8_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f502,f492,f505,f508,f450]) ).
fof(f512,plain,
( sQ5_spl
| ~ segmentP(sk4,sk1) ),
inference(forward_demodulation,[status(thm)],[f430,f455]) ).
fof(f513,plain,
( sQ5_spl
| ~ segmentP(sk4,sk3) ),
inference(forward_demodulation,[status(thm)],[f431,f512]) ).
fof(f514,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f513,f433]) ).
fof(f515,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f514]) ).
fof(f516,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f507,f428]) ).
fof(f517,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f516]) ).
fof(f530,plain,
( ~ sQ9_spl
| neq(sk4,sk3) ),
inference(backward_demodulation,[status(thm)],[f509,f488]) ).
fof(f531,plain,
( ~ sQ9_spl
| ~ singletonP(sk3) ),
inference(backward_demodulation,[status(thm)],[f509,f206]) ).
fof(f534,plain,
( ~ sQ9_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f531,f444]) ).
fof(f535,plain,
( ~ sQ9_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f534]) ).
fof(f536,plain,
( sQ3_spl
| ~ sQ9_spl
| ~ neq(sk4,sk3) ),
inference(forward_demodulation,[status(thm)],[f509,f448]) ).
fof(f543,plain,
( sQ3_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f536,f530]) ).
fof(f544,plain,
( sQ3_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f543]) ).
fof(f545,plain,
$false,
inference(sat_refutation,[status(thm)],[f449,f456,f501,f511,f515,f517,f535,f544]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC127-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n018.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 07:59:59 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.48 % Drodi V4.1.1
% 0.17/0.49 % Refutation found
% 0.17/0.49 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.54 % Elapsed time: 0.096523 seconds
% 0.17/0.54 % CPU time: 0.109612 seconds
% 0.17/0.54 % Total memory used: 6.894 MB
% 0.17/0.54 % Net memory used: 6.888 MB
%------------------------------------------------------------------------------