%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC384-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 02:41:01 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 28
% Syntax : Number of formulae : 85 ( 12 unt; 13 def)
% Number of atoms : 214 ( 41 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 244 ( 115 ~; 116 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 14 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 37 ( 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [U,V] :
( ssList(app(V,U))
| ~ ssList(V)
| ~ 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(f115,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f116,axiom,
! [U,V] :
( singletonP(V)
| ~ ssList(V)
| ~ ssItem(U)
| cons(U,nil) != V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f173,axiom,
! [U,V,W,X] :
( segmentP(X,V)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| app(app(U,V),W) != X ),
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),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
( nil = sk4
| ssItem(sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
( nil = sk4
| ssList(sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
( nil = sk4
| ssList(sk7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( nil = sk4
| cons(sk5,nil) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
( nil = sk4
| app(app(sk6,sk3),sk7) = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f207,negated_conjecture,
( ~ segmentP(sk2,sk1)
| ~ singletonP(sk1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f215,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f293,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f294,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f328,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ~ neq(U,V)
| U != V ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f329,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f328]) ).
fof(f330,plain,
! [V] :
( singletonP(V)
| ~ ssList(V)
| ! [U] :
( ~ ssItem(U)
| cons(U,nil) != V ) ),
inference(miniscoping,[status(thm)],[f116]) ).
fof(f331,plain,
! [X0,X1] :
( singletonP(X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,nil) != X1 ),
inference(cnf_transformation,[status(thm)],[f330]) ).
fof(f413,plain,
! [V,X] :
( segmentP(X,V)
| ~ ssList(X)
| ~ ssList(V)
| ! [U] :
( ~ ssList(U)
| ! [W] :
( ~ ssList(W)
| app(app(U,V),W) != X ) ) ),
inference(miniscoping,[status(thm)],[f173]) ).
fof(f414,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| app(app(X0,X1),X2) != X3 ),
inference(cnf_transformation,[status(thm)],[f413]) ).
fof(f442,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f443,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f444,plain,
neq(sk2,nil),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f445,plain,
( nil = sk4
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f447,plain,
( nil = sk4
| ssList(sk6) ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f448,plain,
( nil = sk4
| ssList(sk7) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f449,plain,
( nil = sk4
| cons(sk5,nil) = sk3 ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f450,plain,
( nil = sk4
| app(app(sk6,sk3),sk7) = sk4 ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f463,plain,
( ~ segmentP(sk2,sk1)
| ~ singletonP(sk1) ),
inference(cnf_transformation,[status(thm)],[f207]) ).
fof(f471,definition,
( sQ2_spl
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f474,definition,
( sQ3_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f475,plain,
( ~ sQ3_spl
| nil = sk4 ),
inference(component_clause,[status(thm)],[f474]) ).
fof(f477,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f445,f471,f474]) ).
fof(f482,definition,
( sQ5_spl
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f485,plain,
( sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f447,f482,f474]) ).
fof(f486,definition,
( sQ6_spl
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f489,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f448,f486,f474]) ).
fof(f490,definition,
( sQ7_spl
<=> cons(sk5,nil) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f491,plain,
( ~ sQ7_spl
| cons(sk5,nil) = sk3 ),
inference(component_clause,[status(thm)],[f490]) ).
fof(f493,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f449,f490,f474]) ).
fof(f494,definition,
( sQ8_spl
<=> app(app(sk6,sk3),sk7) = sk4 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f495,plain,
( ~ sQ8_spl
| app(app(sk6,sk3),sk7) = sk4 ),
inference(component_clause,[status(thm)],[f494]) ).
fof(f497,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f450,f494,f474]) ).
fof(f512,definition,
( sQ11_spl
<=> singletonP(sk1) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f515,definition,
( sQ12_spl
<=> segmentP(sk2,sk1) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f518,plain,
( ~ sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f463,f512,f515]) ).
fof(f521,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f329]) ).
fof(f522,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f521]) ).
fof(f532,plain,
( ~ sQ3_spl
| sk2 = nil ),
inference(backward_demodulation,[status(thm)],[f475,f442]) ).
fof(f535,plain,
( ~ sQ3_spl
| neq(nil,nil) ),
inference(backward_demodulation,[status(thm)],[f532,f444]) ).
fof(f537,plain,
( ~ sQ3_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f522,f535]) ).
fof(f538,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f537,f215]) ).
fof(f539,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f538]) ).
fof(f543,definition,
( sQ13_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f545,plain,
( sQ13_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f543]) ).
fof(f551,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f545,f215]) ).
fof(f552,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f551]) ).
fof(f554,plain,
( ~ sQ7_spl
| cons(sk5,nil) = sk1 ),
inference(forward_demodulation,[status(thm)],[f443,f491]) ).
fof(f556,plain,
( ~ sQ7_spl
| ssList(sk1)
| ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(paramodulation,[status(thm)],[f554,f294]) ).
fof(f561,definition,
( sQ16_spl
<=> ssList(sk1) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f564,plain,
( ~ sQ7_spl
| sQ16_spl
| ~ sQ13_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f556,f471,f543,f561,f490]) ).
fof(f569,plain,
( ~ sQ8_spl
| app(app(sk6,sk1),sk7) = sk4 ),
inference(forward_demodulation,[status(thm)],[f443,f495]) ).
fof(f570,plain,
( ~ sQ8_spl
| app(app(sk6,sk1),sk7) = sk2 ),
inference(forward_demodulation,[status(thm)],[f442,f569]) ).
fof(f571,plain,
( ~ sQ8_spl
| ssList(sk2)
| ~ ssList(app(sk6,sk1))
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f570,f293]) ).
fof(f572,definition,
( sQ17_spl
<=> ssList(app(sk6,sk1)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f574,plain,
( sQ17_spl
| ~ ssList(app(sk6,sk1)) ),
inference(component_clause,[status(thm)],[f572]) ).
fof(f575,definition,
( sQ18_spl
<=> ssList(sk2) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f578,plain,
( ~ sQ8_spl
| sQ18_spl
| ~ sQ17_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f571,f486,f572,f575,f494]) ).
fof(f579,plain,
( sQ17_spl
| ~ ssList(sk6)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f574,f293]) ).
fof(f580,plain,
( sQ17_spl
| ~ sQ5_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f579,f561,f482,f572]) ).
fof(f583,plain,
( ~ sQ7_spl
| singletonP(sk1)
| ~ ssList(sk1)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f331,f554]) ).
fof(f588,plain,
( ~ sQ7_spl
| sQ11_spl
| ~ sQ16_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f583,f471,f561,f512,f490]) ).
fof(f796,definition,
! [X0] :
( sQ46_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0)
| nil != X0 ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f797,plain,
! [X0] :
( ~ sQ46_spl
| ~ ssList(X0)
| ~ ssList(X0)
| nil != X0 ),
inference(component_clause,[status(thm)],[f796]) ).
fof(f805,plain,
! [X0] :
( ~ sQ46_spl
| ~ ssList(X0)
| nil != X0 ),
inference(duplicate_literals_removal,[status(thm)],[f797]) ).
fof(f854,plain,
( ~ sQ46_spl
| nil != nil ),
inference(resolution,[status(thm)],[f805,f215]) ).
fof(f855,plain,
( ~ sQ46_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f854]) ).
fof(f856,plain,
~ sQ46_spl,
inference(contradiction_clause,[status(thm)],[f855]) ).
fof(f1121,plain,
( ~ sQ8_spl
| segmentP(sk2,sk1)
| ~ ssList(sk2)
| ~ ssList(sk1)
| ~ ssList(sk6)
| ~ ssList(sk7) ),
inference(resolution,[status(thm)],[f414,f570]) ).
fof(f1132,plain,
( ~ sQ8_spl
| sQ12_spl
| ~ sQ18_spl
| ~ sQ16_spl
| ~ sQ5_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1121,f486,f482,f561,f575,f515,f494]) ).
fof(f1155,plain,
$false,
inference(sat_refutation,[status(thm)],[f477,f485,f489,f493,f497,f518,f539,f552,f564,f578,f580,f588,f856,f1132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC384-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 08:18:22 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.43 % Refutation found
% 0.14/0.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.46 % Elapsed time: 0.077615 seconds
% 0.14/0.46 % CPU time: 0.336218 seconds
% 0.14/0.46 % Total memory used: 114.178 MB
% 0.14/0.46 % Net memory used: 113.876 MB
%------------------------------------------------------------------------------