%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC357-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 02:40:55 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.86s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 28
% Syntax : Number of formulae : 94 ( 22 unt; 12 def)
% Number of atoms : 245 ( 26 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 291 ( 140 ~; 139 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 13 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 54 ( 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [U,V] : ssList(skaf45(U,V)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [U] :
( segmentP(U,nil)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [U] :
( segmentP(U,U)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f74,axiom,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
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(f132,axiom,
! [U,V] :
( app(V,skaf45(U,V)) = U
| ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f152,axiom,
! [U,V,W] :
( segmentP(U,W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ segmentP(V,W)
| ~ segmentP(U,V) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f188,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f189,negated_conjecture,
ssList(sk4),
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(f193,negated_conjecture,
~ segmentP(sk2,sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
( frontsegP(sk4,sk3)
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( frontsegP(sk4,sk3)
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f205,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f248,plain,
! [X0,X1] : ssList(skaf45(X0,X1)),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f253,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f254,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f272,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f283,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f342,plain,
! [X0,X1] :
( app(X1,skaf45(X0,X1)) = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f371,plain,
! [U,W] :
( segmentP(U,W)
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ~ ssList(W)
| ~ segmentP(V,W)
| ~ segmentP(U,V) ) ),
inference(miniscoping,[status(thm)],[f152]) ).
fof(f372,plain,
! [X0,X1,X2] :
( segmentP(X0,X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f403,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(f404,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)],[f403]) ).
fof(f430,plain,
ssList(sk3),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f431,plain,
ssList(sk4),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f432,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f433,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f435,plain,
~ segmentP(sk2,sk1),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f437,plain,
( frontsegP(sk4,sk3)
| nil = sk4 ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f439,plain,
( frontsegP(sk4,sk3)
| nil = sk3 ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f447,definition,
( sQ2_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f448,plain,
( ~ sQ2_spl
| nil = sk4 ),
inference(component_clause,[status(thm)],[f447]) ).
fof(f454,definition,
( sQ4_spl
<=> frontsegP(sk4,sk3) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f455,plain,
( ~ sQ4_spl
| frontsegP(sk4,sk3) ),
inference(component_clause,[status(thm)],[f454]) ).
fof(f457,plain,
( sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f437,f447,f454]) ).
fof(f458,definition,
( sQ5_spl
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f459,plain,
( ~ sQ5_spl
| nil = sk3 ),
inference(component_clause,[status(thm)],[f458]) ).
fof(f462,plain,
( sQ4_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f439,f458,f454]) ).
fof(f481,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)],[f404]) ).
fof(f495,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| nil = sk4 ),
inference(backward_demodulation,[status(thm)],[f498,f459]) ).
fof(f496,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| sk1 = sk4 ),
inference(backward_demodulation,[status(thm)],[f498,f433]) ).
fof(f498,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| sk3 = sk4 ),
inference(forward_demodulation,[status(thm)],[f459,f448]) ).
fof(f501,plain,
~ segmentP(sk4,sk1),
inference(forward_demodulation,[status(thm)],[f432,f435]) ).
fof(f502,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ segmentP(sk4,sk4) ),
inference(forward_demodulation,[status(thm)],[f496,f501]) ).
fof(f503,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ2_spl
| segmentP(X0,sk4)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f495,f253]) ).
fof(f504,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| segmentP(sk4,sk4) ),
inference(resolution,[status(thm)],[f503,f431]) ).
fof(f505,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f504,f502]) ).
fof(f506,plain,
( ~ sQ5_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f505]) ).
fof(f507,plain,
~ segmentP(sk4,sk3),
inference(forward_demodulation,[status(thm)],[f433,f501]) ).
fof(f510,definition,
( sQ6_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f512,plain,
( sQ6_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f510]) ).
fof(f518,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f512,f205]) ).
fof(f519,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f518]) ).
fof(f579,definition,
( sQ10_spl
<=> ssList(sk3) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f581,plain,
( sQ10_spl
| ~ ssList(sk3) ),
inference(component_clause,[status(thm)],[f579]) ).
fof(f582,definition,
( sQ11_spl
<=> ssList(sk4) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f584,plain,
( sQ11_spl
| ~ ssList(sk4) ),
inference(component_clause,[status(thm)],[f582]) ).
fof(f646,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f584,f431]) ).
fof(f647,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f646]) ).
fof(f657,plain,
! [X0] :
( ~ ssList(sk4)
| ~ ssList(X0)
| ~ ssList(sk3)
| ~ segmentP(X0,sk3)
| ~ segmentP(sk4,X0) ),
inference(resolution,[status(thm)],[f372,f507]) ).
fof(f665,definition,
! [X0] :
( sQ15_spl
<=> ( ~ ssList(X0)
| ~ segmentP(X0,sk3)
| ~ segmentP(sk4,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f666,plain,
! [X0] :
( ~ sQ15_spl
| ~ ssList(X0)
| ~ segmentP(X0,sk3)
| ~ segmentP(sk4,X0) ),
inference(component_clause,[status(thm)],[f665]) ).
fof(f668,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f657,f665,f579,f582]) ).
fof(f671,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f581,f430]) ).
fof(f672,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f671]) ).
fof(f675,plain,
( ~ sQ15_spl
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk4,sk3) ),
inference(resolution,[status(thm)],[f666,f254]) ).
fof(f680,definition,
( sQ17_spl
<=> segmentP(sk4,sk3) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f683,plain,
( ~ sQ15_spl
| ~ sQ10_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f675,f680,f579,f665]) ).
fof(f838,plain,
app(nil,sk3) = sk3,
inference(resolution,[status(thm)],[f272,f430]) ).
fof(f1017,plain,
! [X0] :
( segmentP(app(app(nil,sk3),X0),sk3)
| ~ ssList(app(sk3,X0))
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f838,f481]) ).
fof(f1020,definition,
! [X0] :
( sQ51_spl
<=> ( segmentP(app(app(nil,sk3),X0),sk3)
| ~ ssList(app(sk3,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f1021,plain,
! [X0] :
( ~ sQ51_spl
| segmentP(app(app(nil,sk3),X0),sk3)
| ~ ssList(app(sk3,X0))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1020]) ).
fof(f1023,plain,
( ~ sQ10_spl
| ~ sQ6_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f1017,f1020,f510,f579]) ).
fof(f1026,plain,
! [X0] :
( ~ sQ51_spl
| segmentP(app(sk3,X0),sk3)
| ~ ssList(app(sk3,X0))
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f838,f1021]) ).
fof(f1551,plain,
! [X0] :
( ~ sQ51_spl
| ~ ssList(sk3)
| ~ ssList(X0)
| segmentP(app(sk3,X0),sk3)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1026,f283]) ).
fof(f1553,definition,
! [X0] :
( sQ79_spl
<=> ( ~ ssList(X0)
| segmentP(app(sk3,X0),sk3)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f1554,plain,
! [X0] :
( ~ sQ79_spl
| ~ ssList(X0)
| segmentP(app(sk3,X0),sk3)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1553]) ).
fof(f1556,plain,
( ~ sQ51_spl
| ~ sQ10_spl
| sQ79_spl ),
inference(split_clause,[status(thm)],[f1551,f1553,f579,f1020]) ).
fof(f1561,plain,
! [X0] :
( ~ sQ79_spl
| segmentP(app(sk3,X0),sk3)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1554]) ).
fof(f4355,plain,
( ~ sQ4_spl
| app(sk3,skaf45(sk4,sk3)) = sk4
| ~ ssList(sk4)
| ~ ssList(sk3) ),
inference(resolution,[status(thm)],[f342,f455]) ).
fof(f4385,definition,
( sQ370_spl
<=> app(sk3,skaf45(sk4,sk3)) = sk4 ),
introduced(definition,[new_symbols(definition,[sQ370_spl])],[split_symbol_definition]) ).
fof(f4386,plain,
( ~ sQ370_spl
| app(sk3,skaf45(sk4,sk3)) = sk4 ),
inference(component_clause,[status(thm)],[f4385]) ).
fof(f4388,plain,
( ~ sQ4_spl
| sQ370_spl
| ~ sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f4355,f579,f582,f4385,f454]) ).
fof(f4780,plain,
( ~ sQ370_spl
| ~ sQ79_spl
| segmentP(sk4,sk3)
| ~ ssList(skaf45(sk4,sk3)) ),
inference(paramodulation,[status(thm)],[f4386,f1561]) ).
fof(f4783,definition,
( sQ420_spl
<=> ssList(skaf45(sk4,sk3)) ),
introduced(definition,[new_symbols(definition,[sQ420_spl])],[split_symbol_definition]) ).
fof(f4785,plain,
( sQ420_spl
| ~ ssList(skaf45(sk4,sk3)) ),
inference(component_clause,[status(thm)],[f4783]) ).
fof(f4793,plain,
( ~ sQ370_spl
| ~ sQ79_spl
| sQ17_spl
| ~ sQ420_spl ),
inference(split_clause,[status(thm)],[f4780,f4783,f680,f1553,f4385]) ).
fof(f4796,plain,
( sQ420_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4785,f248]) ).
fof(f4797,plain,
sQ420_spl,
inference(contradiction_clause,[status(thm)],[f4796]) ).
fof(f4798,plain,
$false,
inference(sat_refutation,[status(thm)],[f457,f462,f506,f519,f647,f668,f672,f683,f1023,f1556,f4388,f4793,f4797]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC357-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.54 % Computer : n012.cluster.edu
% 0.07/0.54 % Model : x86_64 x86_64
% 0.07/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.54 % Memory : 8046.5625MB
% 0.07/0.54 % OS : Linux 6.8.0-71-generic
% 0.07/0.54 % CPULimit : 300
% 0.07/0.54 % WCLimit : 300
% 0.07/0.54 % DateTime : Mon Sep 21 08:17:53 UTC 2026
% 0.07/0.55 % CPUTime :
% 0.11/0.56 % Drodi V4.1.1
% 0.11/0.86 % Refutation found
% 0.11/0.86 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.88 % Elapsed time: 0.319704 seconds
% 0.11/0.88 % CPU time: 2.126915 seconds
% 0.11/0.88 % Total memory used: 146.818 MB
% 0.11/0.88 % Net memory used: 143.841 MB
%------------------------------------------------------------------------------