%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC331+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 : 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 02:40:49 PM UTC 2026
% Result : Theorem 0.07s 0.38s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 64 ( 16 unt; 8 def)
% Number of atoms : 238 ( 49 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 271 ( 97 ~; 96 |; 55 &)
% ( 10 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 9 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 67 ( 45 !; 22 ?)
% 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( equalelemsP(U)
& segmentP(V,U) )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( app(X2,cons(Z,nil)) = W
& ssList(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ equalelemsP(W)
| app(W,Y) != X ) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( equalelemsP(U)
& segmentP(V,U) )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( app(X2,cons(Z,nil)) = W
& ssList(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ equalelemsP(W)
| app(W,Y) != 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(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f248,plain,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f249,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f248]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ equalelemsP(U)
| ~ segmentP(V,U) )
& ( nil != W
| nil = X )
& ? [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( app(X2,cons(Z,nil)) != W
| ~ ssList(X2) )
| app(cons(Z,nil),X1) != Y
| ~ ssList(X1) )
| ~ ssItem(Z) )
& equalelemsP(W)
& app(W,Y) = X
& 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] :
( ( ~ equalelemsP(U)
| ~ segmentP(V,U) )
& ( nil != W
| nil = X )
& ? [Y] :
( ! [Z] :
( ! [X2] :
( app(X2,cons(Z,nil)) != W
| ~ ssList(X2) )
| ! [X1] :
( app(cons(Z,nil),X1) != Y
| ~ ssList(X1) )
| ~ ssItem(Z) )
& equalelemsP(W)
& app(W,Y) = X
& ssList(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(miniscoping,[status(thm)],[f415]) ).
fof(f417,plain,
( ( ~ equalelemsP(sK47_skl)
| ~ segmentP(sK48_skl,sK47_skl) )
& ( nil != sK49_skl
| nil = sK50_skl )
& ! [Z] :
( ! [X2] :
( app(X2,cons(Z,nil)) != sK49_skl
| ~ ssList(X2) )
| ! [X1] :
( app(cons(Z,nil),X1) != sK51_skl
| ~ ssList(X1) )
| ~ ssItem(Z) )
& equalelemsP(sK49_skl)
& app(sK49_skl,sK51_skl) = sK50_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]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_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,
app(sK49_skl,sK51_skl) = sK50_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f426,plain,
equalelemsP(sK49_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f429,plain,
( ~ equalelemsP(sK47_skl)
| ~ segmentP(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f437,definition,
( sQ2_spl
<=> segmentP(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f439,plain,
( sQ2_spl
| ~ segmentP(sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f437]) ).
fof(f440,definition,
( sQ3_spl
<=> equalelemsP(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( sQ3_spl
| ~ equalelemsP(sK47_skl) ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f443,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f429,f437,f440]) ).
fof(f450,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(f487,definition,
( sQ5_spl
<=> ssList(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f489,plain,
( sQ5_spl
| ~ ssList(sK51_skl) ),
inference(component_clause,[status(thm)],[f487]) ).
fof(f490,definition,
( sQ6_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f492,plain,
( sQ6_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f490]) ).
fof(f494,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f492,f420]) ).
fof(f495,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f494]) ).
fof(f496,plain,
( sQ2_spl
| ~ segmentP(sK48_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f439]) ).
fof(f497,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f489,f424]) ).
fof(f498,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f497]) ).
fof(f515,plain,
( sQ2_spl
| ~ segmentP(sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f422,f496]) ).
fof(f527,plain,
app(nil,sK49_skl) = sK49_skl,
inference(resolution,[status(thm)],[f249,f420]) ).
fof(f532,definition,
( sQ13_spl
<=> ssList(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f534,plain,
( sQ13_spl
| ~ ssList(sK50_skl) ),
inference(component_clause,[status(thm)],[f532]) ).
fof(f535,definition,
( sQ14_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f537,plain,
( sQ14_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f535]) ).
fof(f539,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f537,f223]) ).
fof(f540,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f539]) ).
fof(f557,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,sK49_skl),X0),sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(app(sK49_skl,X0)) ),
inference(paramodulation,[status(thm)],[f527,f450]) ).
fof(f558,definition,
! [X0] :
( sQ17_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,sK49_skl),X0),sK49_skl)
| ~ ssList(app(sK49_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f559,plain,
! [X0] :
( ~ sQ17_spl
| ~ ssList(X0)
| segmentP(app(app(nil,sK49_skl),X0),sK49_skl)
| ~ ssList(app(sK49_skl,X0)) ),
inference(component_clause,[status(thm)],[f558]) ).
fof(f561,plain,
( ~ sQ14_spl
| ~ sQ6_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f557,f558,f490,f535]) ).
fof(f562,plain,
! [X0] :
( ~ sQ17_spl
| ~ ssList(X0)
| segmentP(app(sK49_skl,X0),sK49_skl)
| ~ ssList(app(sK49_skl,X0)) ),
inference(forward_demodulation,[status(thm)],[f527,f559]) ).
fof(f575,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f534,f421]) ).
fof(f576,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f575]) ).
fof(f648,plain,
( ~ sQ17_spl
| ~ ssList(sK51_skl)
| segmentP(app(sK49_skl,sK51_skl),sK49_skl)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f425,f562]) ).
fof(f653,definition,
( sQ28_spl
<=> segmentP(app(sK49_skl,sK51_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f654,plain,
( ~ sQ28_spl
| segmentP(app(sK49_skl,sK51_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f653]) ).
fof(f656,plain,
( ~ sQ17_spl
| ~ sQ5_spl
| sQ28_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f648,f532,f653,f487,f558]) ).
fof(f658,plain,
( ~ sQ28_spl
| segmentP(sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f425,f654]) ).
fof(f659,plain,
( ~ sQ28_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f658,f515]) ).
fof(f660,plain,
( ~ sQ28_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f659]) ).
fof(f661,plain,
( sQ3_spl
| ~ equalelemsP(sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f442]) ).
fof(f662,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f661,f426]) ).
fof(f663,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f662]) ).
fof(f664,plain,
$false,
inference(sat_refutation,[status(thm)],[f443,f495,f498,f540,f561,f576,f656,f660,f663]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC331+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n019.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 08:16:20 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.37 % Drodi V4.1.1
% 0.07/0.38 % Refutation found
% 0.07/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.053794 seconds
% 0.13/0.41 % CPU time: 0.118733 seconds
% 0.13/0.41 % Total memory used: 24.850 MB
% 0.13/0.41 % Net memory used: 24.769 MB
%------------------------------------------------------------------------------