%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC252-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 02:40:31 PM UTC 2026
% Result : Unsatisfiable 0.34s 15.61s
% Output : CNFRefutation 0.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 27
% Syntax : Number of formulae : 82 ( 18 unt; 12 def)
% Number of atoms : 244 ( 38 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 313 ( 151 ~; 150 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 13 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 68 ( 68 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [U,V] : ssList(skaf48(U,V)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [U,V] : ssList(skaf47(U,V)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [U] :
( segmentP(U,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(f103,axiom,
! [U,V] :
( leq(U,V)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f168,axiom,
! [U,V] :
( app(app(skaf47(U,V),V),skaf48(V,U)) = U
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f186,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
nil != sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
! [A,B,C] :
( ssItem(sk5(C,B,A))
| app(app(B,cons(A,nil)),C) != sk1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
! [A,B,C] :
( lt(A,sk5(C,B,A))
| app(app(B,cons(A,nil)),C) != sk1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
! [A,B,C] :
( ~ leq(A,sk5(C,B,A))
| app(app(B,cons(A,nil)),C) != sk1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f199,negated_conjecture,
( nil = sk3
| ssItem(sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f202,negated_conjecture,
( nil = sk3
| cons(sk6,nil) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f211,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f251,plain,
! [X0,X1] : ssList(skaf48(X0,X1)),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f252,plain,
! [X0,X1] : ssList(skaf47(X0,X1)),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f260,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f290,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f309,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f402,plain,
! [X0,X1] :
( app(app(skaf47(X0,X1),X1),skaf48(X1,X0)) = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f168]) ).
fof(f434,plain,
ssList(sk1),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f439,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f440,plain,
nil != sk1,
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f441,plain,
! [X0,X1,X2] :
( ssItem(sk5(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sk1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f444,plain,
! [X0,X1,X2] :
( lt(X0,sk5(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sk1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f445,plain,
! [X0,X1,X2] :
( ~ leq(X0,sk5(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sk1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f447,plain,
( nil = sk3
| ssItem(sk6) ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f450,plain,
( nil = sk3
| cons(sk6,nil) = sk3 ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f459,definition,
( sQ2_spl
<=> ssItem(sk6) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f466,definition,
( sQ4_spl
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f467,plain,
( ~ sQ4_spl
| nil = sk3 ),
inference(component_clause,[status(thm)],[f466]) ).
fof(f469,plain,
( sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f447,f459,f466]) ).
fof(f470,definition,
( sQ5_spl
<=> cons(sk6,nil) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f471,plain,
( ~ sQ5_spl
| cons(sk6,nil) = sk3 ),
inference(component_clause,[status(thm)],[f470]) ).
fof(f478,plain,
( sQ4_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f450,f470,f466]) ).
fof(f492,plain,
( ~ sQ4_spl
| sk1 = nil ),
inference(backward_demodulation,[status(thm)],[f467,f439]) ).
fof(f493,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f492,f440]) ).
fof(f494,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f493]) ).
fof(f497,plain,
( ~ sQ5_spl
| cons(sk6,nil) = sk1 ),
inference(forward_demodulation,[status(thm)],[f439,f471]) ).
fof(f499,plain,
! [X0,X1] :
( ~ sQ5_spl
| ssItem(sk5(X1,X0,sk6))
| app(app(X0,sk1),X1) != sk1
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sk6) ),
inference(paramodulation,[status(thm)],[f497,f441]) ).
fof(f504,definition,
! [X0,X1] :
( sQ8_spl
<=> ( ssItem(sk5(X1,X0,sk6))
| app(app(X0,sk1),X1) != sk1
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f505,plain,
! [X0,X1] :
( ~ sQ8_spl
| ssItem(sk5(X1,X0,sk6))
| app(app(X0,sk1),X1) != sk1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f504]) ).
fof(f507,plain,
( ~ sQ5_spl
| sQ8_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f499,f459,f504,f470]) ).
fof(f508,plain,
( ~ sQ5_spl
| ssList(sk1)
| ~ ssList(nil)
| ~ ssItem(sk6) ),
inference(paramodulation,[status(thm)],[f497,f290]) ).
fof(f509,definition,
( sQ9_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f511,plain,
( sQ9_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f509]) ).
fof(f512,definition,
( sQ10_spl
<=> ssList(sk1) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f515,plain,
( ~ sQ5_spl
| sQ10_spl
| ~ sQ9_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f508,f459,f509,f512,f470]) ).
fof(f516,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f511,f211]) ).
fof(f517,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f516]) ).
fof(f535,plain,
! [X0,X1] :
( ~ sQ5_spl
| lt(sk6,sk5(X1,X0,sk6))
| app(app(X0,sk1),X1) != sk1
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sk6) ),
inference(paramodulation,[status(thm)],[f497,f444]) ).
fof(f536,definition,
! [X0,X1] :
( sQ14_spl
<=> ( lt(sk6,sk5(X1,X0,sk6))
| app(app(X0,sk1),X1) != sk1
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f537,plain,
! [X0,X1] :
( ~ sQ14_spl
| lt(sk6,sk5(X1,X0,sk6))
| app(app(X0,sk1),X1) != sk1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f536]) ).
fof(f539,plain,
( ~ sQ5_spl
| sQ14_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f535,f459,f536,f470]) ).
fof(f560,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ leq(sk6,sk5(X1,X0,sk6))
| app(app(X0,sk1),X1) != sk1
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sk6) ),
inference(paramodulation,[status(thm)],[f497,f445]) ).
fof(f561,definition,
! [X0,X1] :
( sQ17_spl
<=> ( ~ leq(sk6,sk5(X1,X0,sk6))
| app(app(X0,sk1),X1) != sk1
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f562,plain,
! [X0,X1] :
( ~ sQ17_spl
| ~ leq(sk6,sk5(X1,X0,sk6))
| app(app(X0,sk1),X1) != sk1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f561]) ).
fof(f564,plain,
( ~ sQ5_spl
| sQ17_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f560,f459,f561,f470]) ).
fof(f611,plain,
! [X0,X1] :
( ~ sQ14_spl
| leq(sk6,sk5(X1,X0,sk6))
| ~ ssItem(sk6)
| ~ ssItem(sk5(X1,X0,sk6))
| app(app(X0,sk1),X1) != sk1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f537,f309]) ).
fof(f624,definition,
! [X0,X1] :
( sQ26_spl
<=> ( leq(sk6,sk5(X1,X0,sk6))
| ~ ssItem(sk5(X1,X0,sk6))
| app(app(X0,sk1),X1) != sk1
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f625,plain,
! [X0,X1] :
( ~ sQ26_spl
| leq(sk6,sk5(X1,X0,sk6))
| ~ ssItem(sk5(X1,X0,sk6))
| app(app(X0,sk1),X1) != sk1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f624]) ).
fof(f627,plain,
( ~ sQ14_spl
| ~ sQ2_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f611,f624,f459,f536]) ).
fof(f631,plain,
! [X0,X1] :
( ~ sQ26_spl
| ~ sQ8_spl
| leq(sk6,sk5(X1,X0,sk6))
| app(app(X0,sk1),X1) != sk1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f625,f505]) ).
fof(f1192,plain,
! [X0,X1] :
( ~ sQ26_spl
| ~ sQ8_spl
| ~ sQ17_spl
| app(app(X0,sk1),X1) != sk1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f631,f562]) ).
fof(f2884,plain,
( ~ sQ26_spl
| ~ sQ8_spl
| ~ sQ17_spl
| ~ ssList(skaf48(sk1,sk1))
| ~ ssList(skaf47(sk1,sk1))
| ~ ssList(sk1)
| ~ ssList(sk1)
| ~ segmentP(sk1,sk1) ),
inference(resolution,[status(thm)],[f402,f1192]) ).
fof(f2912,definition,
( sQ208_spl
<=> segmentP(sk1,sk1) ),
introduced(definition,[new_symbols(definition,[sQ208_spl])],[split_symbol_definition]) ).
fof(f2914,plain,
( sQ208_spl
| ~ segmentP(sk1,sk1) ),
inference(component_clause,[status(thm)],[f2912]) ).
fof(f2915,definition,
( sQ209_spl
<=> ssList(skaf47(sk1,sk1)) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f2917,plain,
( sQ209_spl
| ~ ssList(skaf47(sk1,sk1)) ),
inference(component_clause,[status(thm)],[f2915]) ).
fof(f2918,definition,
( sQ210_spl
<=> ssList(skaf48(sk1,sk1)) ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f2920,plain,
( sQ210_spl
| ~ ssList(skaf48(sk1,sk1)) ),
inference(component_clause,[status(thm)],[f2918]) ).
fof(f2921,plain,
( ~ sQ26_spl
| ~ sQ8_spl
| ~ sQ17_spl
| ~ sQ210_spl
| ~ sQ209_spl
| ~ sQ10_spl
| ~ sQ208_spl ),
inference(split_clause,[status(thm)],[f2884,f2912,f512,f2915,f2918,f561,f504,f624]) ).
fof(f2949,plain,
( sQ210_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2920,f251]) ).
fof(f2950,plain,
sQ210_spl,
inference(contradiction_clause,[status(thm)],[f2949]) ).
fof(f2954,plain,
( sQ208_spl
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f2914,f260]) ).
fof(f2959,plain,
( sQ208_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2954,f434]) ).
fof(f2960,plain,
sQ208_spl,
inference(contradiction_clause,[status(thm)],[f2959]) ).
fof(f2961,plain,
( sQ209_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2917,f252]) ).
fof(f2962,plain,
sQ209_spl,
inference(contradiction_clause,[status(thm)],[f2961]) ).
fof(f2963,plain,
$false,
inference(sat_refutation,[status(thm)],[f469,f478,f494,f507,f515,f517,f539,f564,f627,f2921,f2950,f2960,f2962]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC252-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/15.41 % CPULimit : 300
% 0.09/15.41 % WCLimit : 300
% 0.09/15.41 % DateTime : Mon Sep 21 08:10:02 UTC 2026
% 0.09/15.41 % CPUTime :
% 0.09/15.43 % Drodi V4.1.1
% 0.34/15.61 % Refutation found
% 0.34/15.61 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.34/15.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.34/15.64 % Elapsed time: 0.224428 seconds
% 0.34/15.64 % CPU time: 1.447078 seconds
% 0.34/15.64 % Total memory used: 136.329 MB
% 0.34/15.64 % Net memory used: 134.997 MB
%------------------------------------------------------------------------------