%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC081-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 02:39:53 PM UTC 2026
% Result : Unsatisfiable 12.69s 2.07s
% Output : CNFRefutation 12.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 32
% Syntax : Number of formulae : 107 ( 21 unt; 16 def)
% Number of atoms : 274 ( 31 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 313 ( 146 ~; 151 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 17 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 41 ( 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [U,V] : ssList(skaf45(U,V)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f74,axiom,
! [U] :
( app(nil,U) = U
| ~ ssList(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(f132,axiom,
! [U,V] :
( app(V,skaf45(U,V)) = U
| ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,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(f188,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f189,negated_conjecture,
ssList(sk4),
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,
! [A] :
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
( nil = sk4
| ssList(sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
( nil = sk4
| neq(sk5,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( nil = sk4
| frontsegP(sk4,sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
( nil = sk4
| frontsegP(sk3,sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f209,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f252,plain,
! [X0,X1] : ssList(skaf45(X0,X1)),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f276,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f322,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ~ neq(U,V)
| U != V ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f323,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f322]) ).
fof(f346,plain,
! [X0,X1] :
( app(X1,skaf45(X0,X1)) = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f407,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(f408,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)],[f407]) ).
fof(f434,plain,
ssList(sk3),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f435,plain,
ssList(sk4),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f436,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f437,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f438,plain,
neq(sk2,nil),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f439,plain,
! [X0] :
( ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f440,plain,
( nil = sk4
| ssList(sk5) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f442,plain,
( nil = sk4
| neq(sk5,nil) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f443,plain,
( nil = sk4
| frontsegP(sk4,sk5) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f444,plain,
( nil = sk4
| frontsegP(sk3,sk5) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f455,definition,
( sQ2_spl
<=> ssList(sk5) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f456,plain,
( ~ sQ2_spl
| ssList(sk5) ),
inference(component_clause,[status(thm)],[f455]) ).
fof(f458,definition,
( sQ3_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f459,plain,
( ~ sQ3_spl
| nil = sk4 ),
inference(component_clause,[status(thm)],[f458]) ).
fof(f461,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f440,f455,f458]) ).
fof(f466,definition,
( sQ5_spl
<=> neq(sk5,nil) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f469,plain,
( sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f442,f466,f458]) ).
fof(f470,definition,
( sQ6_spl
<=> frontsegP(sk4,sk5) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f471,plain,
( ~ sQ6_spl
| frontsegP(sk4,sk5) ),
inference(component_clause,[status(thm)],[f470]) ).
fof(f473,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f443,f470,f458]) ).
fof(f474,definition,
( sQ7_spl
<=> frontsegP(sk3,sk5) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f475,plain,
( ~ sQ7_spl
| frontsegP(sk3,sk5) ),
inference(component_clause,[status(thm)],[f474]) ).
fof(f477,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f444,f474,f458]) ).
fof(f488,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f323]) ).
fof(f489,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f488]) ).
fof(f499,plain,
! [X0,X1,X2] :
( segmentP(app(app(X1,X2),X0),X2)
| ~ ssList(app(app(X1,X2),X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f408]) ).
fof(f517,definition,
( sQ8_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f519,plain,
( sQ8_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f517]) ).
fof(f525,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f519,f209]) ).
fof(f526,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f525]) ).
fof(f544,plain,
neq(sk4,nil),
inference(backward_demodulation,[status(thm)],[f436,f438]) ).
fof(f576,plain,
! [X0] :
( ~ segmentP(sk1,X0)
| ~ segmentP(sk4,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f436,f439]) ).
fof(f577,plain,
! [X0] :
( ~ segmentP(sk3,X0)
| ~ segmentP(sk4,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f437,f576]) ).
fof(f586,definition,
( sQ15_spl
<=> ssList(sk4) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f588,plain,
( sQ15_spl
| ~ ssList(sk4) ),
inference(component_clause,[status(thm)],[f586]) ).
fof(f597,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f588,f435]) ).
fof(f598,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f597]) ).
fof(f618,plain,
( ~ sQ3_spl
| neq(nil,nil) ),
inference(backward_demodulation,[status(thm)],[f459,f544]) ).
fof(f638,plain,
( ~ sQ3_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f618,f489]) ).
fof(f643,plain,
( ~ sQ3_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f638,f517,f458]) ).
fof(f709,definition,
( sQ31_spl
<=> ssList(sk3) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f711,plain,
( sQ31_spl
| ~ ssList(sk3) ),
inference(component_clause,[status(thm)],[f709]) ).
fof(f744,plain,
( ~ sQ2_spl
| app(nil,sk5) = sk5 ),
inference(resolution,[status(thm)],[f456,f276]) ).
fof(f902,plain,
! [X0] :
( ~ sQ2_spl
| segmentP(app(app(nil,sk5),X0),sk5)
| ~ ssList(app(sk5,X0))
| ~ ssList(sk5)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f744,f499]) ).
fof(f905,definition,
! [X0] :
( sQ63_spl
<=> ( segmentP(app(app(nil,sk5),X0),sk5)
| ~ ssList(app(sk5,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f906,plain,
! [X0] :
( ~ sQ63_spl
| segmentP(app(app(nil,sk5),X0),sk5)
| ~ ssList(app(sk5,X0))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f905]) ).
fof(f908,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f902,f905,f517,f455]) ).
fof(f917,plain,
! [X0] :
( ~ sQ63_spl
| ~ sQ2_spl
| segmentP(app(sk5,X0),sk5)
| ~ ssList(app(sk5,X0))
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f744,f906]) ).
fof(f1022,plain,
( sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f711,f434]) ).
fof(f1023,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f1022]) ).
fof(f3649,plain,
( ~ sQ7_spl
| app(sk5,skaf45(sk3,sk5)) = sk3
| ~ ssList(sk3)
| ~ ssList(sk5) ),
inference(resolution,[status(thm)],[f346,f475]) ).
fof(f3661,plain,
( ~ sQ6_spl
| app(sk5,skaf45(sk4,sk5)) = sk4
| ~ ssList(sk4)
| ~ ssList(sk5) ),
inference(resolution,[status(thm)],[f346,f471]) ).
fof(f3680,definition,
( sQ373_spl
<=> app(sk5,skaf45(sk3,sk5)) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ373_spl])],[split_symbol_definition]) ).
fof(f3681,plain,
( ~ sQ373_spl
| app(sk5,skaf45(sk3,sk5)) = sk3 ),
inference(component_clause,[status(thm)],[f3680]) ).
fof(f3683,plain,
( ~ sQ7_spl
| sQ373_spl
| ~ sQ31_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f3649,f455,f709,f3680,f474]) ).
fof(f3718,definition,
( sQ381_spl
<=> app(sk5,skaf45(sk4,sk5)) = sk4 ),
introduced(definition,[new_symbols(definition,[sQ381_spl])],[split_symbol_definition]) ).
fof(f3719,plain,
( ~ sQ381_spl
| app(sk5,skaf45(sk4,sk5)) = sk4 ),
inference(component_clause,[status(thm)],[f3718]) ).
fof(f3721,plain,
( ~ sQ6_spl
| sQ381_spl
| ~ sQ15_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f3661,f455,f586,f3718,f470]) ).
fof(f4204,definition,
( sQ434_spl
<=> ssList(skaf45(sk4,sk5)) ),
introduced(definition,[new_symbols(definition,[sQ434_spl])],[split_symbol_definition]) ).
fof(f4206,plain,
( sQ434_spl
| ~ ssList(skaf45(sk4,sk5)) ),
inference(component_clause,[status(thm)],[f4204]) ).
fof(f4234,plain,
( sQ434_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4206,f252]) ).
fof(f4235,plain,
sQ434_spl,
inference(contradiction_clause,[status(thm)],[f4234]) ).
fof(f4248,definition,
( sQ441_spl
<=> ssList(skaf45(sk3,sk5)) ),
introduced(definition,[new_symbols(definition,[sQ441_spl])],[split_symbol_definition]) ).
fof(f4250,plain,
( sQ441_spl
| ~ ssList(skaf45(sk3,sk5)) ),
inference(component_clause,[status(thm)],[f4248]) ).
fof(f4278,plain,
( sQ441_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4250,f252]) ).
fof(f4279,plain,
sQ441_spl,
inference(contradiction_clause,[status(thm)],[f4278]) ).
fof(f4941,plain,
( ~ sQ373_spl
| ~ sQ63_spl
| ~ sQ2_spl
| segmentP(app(sk5,skaf45(sk3,sk5)),sk5)
| ~ ssList(sk3)
| ~ ssList(skaf45(sk3,sk5)) ),
inference(paramodulation,[status(thm)],[f3681,f917]) ).
fof(f4942,plain,
( ~ sQ381_spl
| ~ sQ63_spl
| ~ sQ2_spl
| segmentP(app(sk5,skaf45(sk4,sk5)),sk5)
| ~ ssList(sk4)
| ~ ssList(skaf45(sk4,sk5)) ),
inference(paramodulation,[status(thm)],[f3719,f917]) ).
fof(f4948,definition,
( sQ535_spl
<=> segmentP(app(sk5,skaf45(sk3,sk5)),sk5) ),
introduced(definition,[new_symbols(definition,[sQ535_spl])],[split_symbol_definition]) ).
fof(f4949,plain,
( ~ sQ535_spl
| segmentP(app(sk5,skaf45(sk3,sk5)),sk5) ),
inference(component_clause,[status(thm)],[f4948]) ).
fof(f4951,plain,
( ~ sQ373_spl
| ~ sQ63_spl
| ~ sQ2_spl
| sQ535_spl
| ~ sQ31_spl
| ~ sQ441_spl ),
inference(split_clause,[status(thm)],[f4941,f4248,f709,f4948,f455,f905,f3680]) ).
fof(f4952,definition,
( sQ536_spl
<=> segmentP(app(sk5,skaf45(sk4,sk5)),sk5) ),
introduced(definition,[new_symbols(definition,[sQ536_spl])],[split_symbol_definition]) ).
fof(f4953,plain,
( ~ sQ536_spl
| segmentP(app(sk5,skaf45(sk4,sk5)),sk5) ),
inference(component_clause,[status(thm)],[f4952]) ).
fof(f4955,plain,
( ~ sQ381_spl
| ~ sQ63_spl
| ~ sQ2_spl
| sQ536_spl
| ~ sQ15_spl
| ~ sQ434_spl ),
inference(split_clause,[status(thm)],[f4942,f4204,f586,f4952,f455,f905,f3718]) ).
fof(f4962,plain,
( ~ sQ536_spl
| ~ sQ381_spl
| segmentP(sk4,sk5) ),
inference(forward_demodulation,[status(thm)],[f3719,f4953]) ).
fof(f4963,plain,
( ~ sQ535_spl
| ~ sQ373_spl
| segmentP(sk3,sk5) ),
inference(forward_demodulation,[status(thm)],[f3681,f4949]) ).
fof(f7843,plain,
( ~ sQ535_spl
| ~ sQ373_spl
| ~ segmentP(sk4,sk5)
| ~ neq(sk5,nil)
| ~ ssList(sk5) ),
inference(resolution,[status(thm)],[f577,f4963]) ).
fof(f7844,definition,
( sQ686_spl
<=> segmentP(sk4,sk5) ),
introduced(definition,[new_symbols(definition,[sQ686_spl])],[split_symbol_definition]) ).
fof(f7846,plain,
( sQ686_spl
| ~ segmentP(sk4,sk5) ),
inference(component_clause,[status(thm)],[f7844]) ).
fof(f7847,plain,
( ~ sQ535_spl
| ~ sQ373_spl
| ~ sQ686_spl
| ~ sQ5_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f7843,f455,f466,f7844,f3680,f4948]) ).
fof(f7848,plain,
( sQ686_spl
| ~ sQ536_spl
| ~ sQ381_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7846,f4962]) ).
fof(f7849,plain,
( sQ686_spl
| ~ sQ536_spl
| ~ sQ381_spl ),
inference(contradiction_clause,[status(thm)],[f7848]) ).
fof(f7850,plain,
$false,
inference(sat_refutation,[status(thm)],[f461,f469,f473,f477,f526,f598,f643,f908,f1023,f3683,f3721,f4235,f4279,f4951,f4955,f7847,f7849]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC081-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 07:54:35 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 12.69/2.07 % Refutation found
% 12.69/2.07 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 12.69/2.07 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.79/2.10 % Elapsed time: 1.737280 seconds
% 8.79/2.10 % CPU time: 13.426903 seconds
% 8.79/2.10 % Total memory used: 236.739 MB
% 8.79/2.10 % Net memory used: 223.042 MB
%------------------------------------------------------------------------------