%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC339+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 : n001.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 02:40:50 PM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 14 unt; 7 def)
% Number of atoms : 262 ( 55 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 318 ( 110 ~; 108 |; 77 &)
% ( 9 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 8 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 89 ( 55 !; 34 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( totalorderedP(U)
& segmentP(V,U) )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( leq(X7,X5)
& app(X8,cons(X7,nil)) = W
& ssList(X8) )
& ssItem(X7) )
& app(cons(X5,nil),X6) = Z
& ssList(X6) )
& ssItem(X5) )
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( leq(X1,X3)
& app(cons(X3,nil),X4) = W
& ssList(X4) )
& ssItem(X3) )
& app(X2,cons(X1,nil)) = Y
& ssList(X2) )
& ssItem(X1) )
| ~ totalorderedP(W)
| app(app(Y,W),Z) != X ) ) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( totalorderedP(U)
& segmentP(V,U) )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( leq(X7,X5)
& app(X8,cons(X7,nil)) = W
& ssList(X8) )
& ssItem(X7) )
& app(cons(X5,nil),X6) = Z
& ssList(X6) )
& ssItem(X5) )
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( leq(X1,X3)
& app(cons(X3,nil),X4) = W
& ssList(X4) )
& ssItem(X3) )
& app(X2,cons(X1,nil)) = Y
& ssList(X2) )
& ssItem(X1) )
| ~ totalorderedP(W)
| app(app(Y,W),Z) != X ) ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f131,plain,
! [U] :
( ! [V] :
( ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f132,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ( app(app(sK7_skl(V,U),V),sK8_skl(V,U)) = U
& ssList(sK8_skl(V,U))
& ssList(sK7_skl(V,U)) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132]) ).
fof(f137,plain,
! [X0,X1,X2,X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ totalorderedP(U)
| ~ segmentP(V,U) )
& ( nil != W
| nil = X )
& ? [Y] :
( ? [Z] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ leq(X7,X5)
| app(X8,cons(X7,nil)) != W
| ~ ssList(X8) )
| ~ ssItem(X7) )
| app(cons(X5,nil),X6) != Z
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ~ leq(X1,X3)
| app(cons(X3,nil),X4) != W
| ~ ssList(X4) )
| ~ ssItem(X3) )
| app(X2,cons(X1,nil)) != Y
| ~ ssList(X2) )
| ~ ssItem(X1) )
& totalorderedP(W)
& app(app(Y,W),Z) = X
& ssList(Z) )
& ssList(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ totalorderedP(U)
| ~ segmentP(V,U) )
& ( nil != W
| nil = X )
& ? [Y] :
( ? [Z] :
( ! [X5] :
( ! [X7] :
( ~ leq(X7,X5)
| ! [X8] :
( app(X8,cons(X7,nil)) != W
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ! [X6] :
( app(cons(X5,nil),X6) != Z
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X1] :
( ! [X3] :
( ~ leq(X1,X3)
| ! [X4] :
( app(cons(X3,nil),X4) != W
| ~ ssList(X4) )
| ~ ssItem(X3) )
| ! [X2] :
( app(X2,cons(X1,nil)) != Y
| ~ ssList(X2) )
| ~ ssItem(X1) )
& totalorderedP(W)
& app(app(Y,W),Z) = X
& ssList(Z) )
& ssList(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(miniscoping,[status(thm)],[f415]) ).
fof(f417,plain,
( ( ~ totalorderedP(sK47_skl)
| ~ segmentP(sK48_skl,sK47_skl) )
& ( nil != sK49_skl
| nil = sK50_skl )
& ! [X5] :
( ! [X7] :
( ~ leq(X7,X5)
| ! [X8] :
( app(X8,cons(X7,nil)) != sK49_skl
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ! [X6] :
( app(cons(X5,nil),X6) != sK52_skl
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X1] :
( ! [X3] :
( ~ leq(X1,X3)
| ! [X4] :
( app(cons(X3,nil),X4) != sK49_skl
| ~ ssList(X4) )
| ~ ssItem(X3) )
| ! [X2] :
( app(X2,cons(X1,nil)) != sK51_skl
| ~ ssList(X2) )
| ~ ssItem(X1) )
& totalorderedP(sK49_skl)
& app(app(sK51_skl,sK49_skl),sK52_skl) = sK50_skl
& ssList(sK52_skl)
& ssList(sK51_skl)
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& ssList(sK50_skl)
& ssList(sK49_skl)
& ssList(sK48_skl)
& ssList(sK47_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl,sK51_skl,sK52_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl),skolemize(Z,sK52_skl)],[f416]) ).
fof(f420,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f421,plain,
ssList(sK50_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f422,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f423,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f424,plain,
ssList(sK51_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f425,plain,
ssList(sK52_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f426,plain,
app(app(sK51_skl,sK49_skl),sK52_skl) = sK50_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f427,plain,
totalorderedP(sK49_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f431,plain,
( ~ totalorderedP(sK47_skl)
| ~ segmentP(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f439,definition,
( sQ2_spl
<=> segmentP(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f441,plain,
( sQ2_spl
| ~ segmentP(sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f442,definition,
( sQ3_spl
<=> totalorderedP(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f444,plain,
( sQ3_spl
| ~ totalorderedP(sK47_skl) ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f431,f439,f442]) ).
fof(f452,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X0)
| segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X1)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f137]) ).
fof(f480,plain,
( sQ2_spl
| ~ segmentP(sK50_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f422,f441]) ).
fof(f481,plain,
( sQ2_spl
| ~ segmentP(sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f480]) ).
fof(f491,plain,
( ~ ssList(sK52_skl)
| ~ ssList(sK51_skl)
| segmentP(sK50_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(app(app(sK51_skl,sK49_skl),sK52_skl)) ),
inference(paramodulation,[status(thm)],[f426,f452]) ).
fof(f493,definition,
( sQ4_spl
<=> ssList(app(app(sK51_skl,sK49_skl),sK52_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f495,plain,
( sQ4_spl
| ~ ssList(app(app(sK51_skl,sK49_skl),sK52_skl)) ),
inference(component_clause,[status(thm)],[f493]) ).
fof(f496,definition,
( sQ5_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f498,plain,
( sQ5_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f496]) ).
fof(f499,definition,
( sQ6_spl
<=> segmentP(sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f500,plain,
( ~ sQ6_spl
| segmentP(sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f499]) ).
fof(f502,definition,
( sQ7_spl
<=> ssList(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f504,plain,
( sQ7_spl
| ~ ssList(sK51_skl) ),
inference(component_clause,[status(thm)],[f502]) ).
fof(f505,definition,
( sQ8_spl
<=> ssList(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f507,plain,
( sQ8_spl
| ~ ssList(sK52_skl) ),
inference(component_clause,[status(thm)],[f505]) ).
fof(f508,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f491,f493,f496,f499,f502,f505]) ).
fof(f516,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f507,f425]) ).
fof(f517,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f516]) ).
fof(f519,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f504,f424]) ).
fof(f520,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f519]) ).
fof(f521,plain,
( ~ sQ6_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f500,f481]) ).
fof(f522,plain,
( ~ sQ6_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f521]) ).
fof(f523,plain,
( sQ3_spl
| ~ totalorderedP(sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f444]) ).
fof(f524,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f523,f427]) ).
fof(f525,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f524]) ).
fof(f526,plain,
( sQ4_spl
| ~ ssList(sK50_skl) ),
inference(forward_demodulation,[status(thm)],[f426,f495]) ).
fof(f527,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f526,f421]) ).
fof(f528,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f527]) ).
fof(f530,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f498,f420]) ).
fof(f531,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f530]) ).
fof(f532,plain,
$false,
inference(sat_refutation,[status(thm)],[f445,f508,f517,f520,f522,f525,f528,f531]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC339+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 08:22:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.46 % Elapsed time: 0.079255 seconds
% 0.10/0.46 % CPU time: 0.125927 seconds
% 0.10/0.46 % Total memory used: 27.827 MB
% 0.10/0.46 % Net memory used: 27.777 MB
%------------------------------------------------------------------------------