%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC059+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 : n020.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 02:39:48 PM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 85 ( 8 unt; 12 def)
% Number of atoms : 289 ( 62 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 342 ( 138 ~; 130 |; 49 &)
% ( 14 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 12 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 58 ( 48 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [U] :
( ssList(U)
=> segmentP(U,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( ( ~ segmentP(X,W)
| ~ neq(W,nil) )
& neq(X,nil) )
| ( nil = X
& nil != W )
| 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)
=> ( ( ( ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( ( ~ segmentP(X,W)
| ~ neq(W,nil) )
& neq(X,nil) )
| ( nil = X
& nil != W )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f217,plain,
! [U] :
( ! [V] :
( ( neq(U,V)
<=> U != V )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f218,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f217]) ).
fof(f219,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f318,plain,
! [U] :
( segmentP(U,U)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f55]) ).
fof(f319,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f318]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ! [Y] :
( ~ segmentP(U,Y)
| ~ segmentP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& ( ( segmentP(X,W)
& neq(W,nil) )
| ~ neq(X,nil) )
& ( nil != X
| nil = W )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [U,V] :
( sP0_prd(V,U)
<=> ( nil != U
& nil = V ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ! [Y] :
( ~ segmentP(U,Y)
| ~ segmentP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(V,nil) )
| sP0_prd(V,U) )
& ( ( segmentP(X,W)
& neq(W,nil) )
| ~ neq(X,nil) )
& ( nil != X
| nil = W )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ( ! [Y] :
( ~ segmentP(sK47_skl,Y)
| ~ segmentP(sK48_skl,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(sK48_skl,nil) )
| sP0_prd(sK48_skl,sK47_skl) )
& ( ( segmentP(sK50_skl,sK49_skl)
& neq(sK49_skl,nil) )
| ~ neq(sK50_skl,nil) )
& ( nil != sK50_skl
| nil = sK49_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]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl)],[f417]) ).
fof(f421,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f423,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f424,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f425,plain,
( nil != sK50_skl
| nil = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
( neq(sK49_skl,nil)
| ~ neq(sK50_skl,nil) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
( segmentP(sK50_skl,sK49_skl)
| ~ neq(sK50_skl,nil) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f428,plain,
( neq(sK48_skl,nil)
| sP0_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f429,plain,
! [X0] :
( ~ segmentP(sK47_skl,X0)
| ~ segmentP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0)
| sP0_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f430,plain,
! [U,V] :
( ( nil = U
| nil != V
| sP0_prd(V,U) )
& ( ( nil != U
& nil = V )
| ~ sP0_prd(V,U) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f431,plain,
( ! [U,V] :
( nil = U
| nil != V
| sP0_prd(V,U) )
& ! [U,V] :
( ( nil != U
& nil = V )
| ~ sP0_prd(V,U) ) ),
inference(miniscoping,[status(thm)],[f430]) ).
fof(f432,plain,
! [X0,X1] :
( nil = X0
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f431]) ).
fof(f433,plain,
! [X0,X1] :
( nil != X1
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f431]) ).
fof(f434,plain,
! [X0,X1] :
( nil = X1
| nil != X0
| sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f431]) ).
fof(f435,definition,
( sQ0_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f436,plain,
( ~ sQ0_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f435]) ).
fof(f438,definition,
( sQ1_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f439,plain,
( ~ sQ1_spl
| nil = sK50_skl ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f440,plain,
( sQ1_spl
| nil != sK50_skl ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f441,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f425,f435,f438]) ).
fof(f442,definition,
( sQ2_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( ~ sQ2_spl
| neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f444,plain,
( sQ2_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,definition,
( sQ3_spl
<=> neq(sK49_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f448,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f426,f442,f445]) ).
fof(f449,definition,
( sQ4_spl
<=> segmentP(sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f452,plain,
( sQ4_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f427,f442,f449]) ).
fof(f453,definition,
( sQ5_spl
<=> sP0_prd(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f454,plain,
( ~ sQ5_spl
| sP0_prd(sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f456,definition,
( sQ6_spl
<=> neq(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( ~ sQ6_spl
| neq(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f456]) ).
fof(f459,plain,
( sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f428,f453,f456]) ).
fof(f460,definition,
! [X0] :
( sQ7_spl
<=> ( ~ segmentP(sK47_skl,X0)
| ~ segmentP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f461,plain,
! [X0] :
( ~ sQ7_spl
| ~ segmentP(sK47_skl,X0)
| ~ segmentP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f460]) ).
fof(f463,plain,
( sQ7_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f429,f453,f460]) ).
fof(f479,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f219]) ).
fof(f480,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f479]) ).
fof(f494,plain,
! [X0] : ~ sP0_prd(X0,nil),
inference(destructive_equality_resolution,[status(thm)],[f433]) ).
fof(f495,plain,
! [X0] :
( nil = X0
| sP0_prd(nil,X0) ),
inference(destructive_equality_resolution,[status(thm)],[f434]) ).
fof(f498,plain,
( ~ sQ0_spl
| sK47_skl = nil ),
inference(backward_demodulation,[status(thm)],[f436,f424]) ).
fof(f500,plain,
( ~ sQ5_spl
| sP0_prd(sK50_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f454]) ).
fof(f501,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| sP0_prd(sK50_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f498,f500]) ).
fof(f502,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f501,f494]) ).
fof(f503,plain,
( ~ sQ5_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f502]) ).
fof(f504,plain,
( ~ sQ6_spl
| neq(sK50_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f423,f457]) ).
fof(f505,plain,
! [X0] :
( ~ sQ7_spl
| ~ segmentP(sK47_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f423,f461]) ).
fof(f511,plain,
( ~ sQ6_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f504,f444]) ).
fof(f512,plain,
( ~ sQ6_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f511]) ).
fof(f513,plain,
( ~ sQ5_spl
| sP0_prd(sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f500]) ).
fof(f514,plain,
( ~ sQ5_spl
| nil = sK50_skl ),
inference(resolution,[status(thm)],[f513,f432]) ).
fof(f515,plain,
( ~ sQ5_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f514,f440]) ).
fof(f516,plain,
( ~ sQ5_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f515]) ).
fof(f517,plain,
! [X0] :
( ~ sQ7_spl
| ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f424,f505]) ).
fof(f520,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| neq(nil,nil) ),
inference(backward_demodulation,[status(thm)],[f439,f443]) ).
fof(f529,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f520,f480]) ).
fof(f530,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f529,f223]) ).
fof(f531,plain,
( ~ sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f530]) ).
fof(f533,plain,
! [X0] :
( nil = nil
| nil = X0 ),
inference(resolution,[status(thm)],[f495,f432]) ).
fof(f534,definition,
! [X0] :
( sQ8_spl
<=> nil = X0 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f535,plain,
! [X0] :
( ~ sQ8_spl
| nil = X0 ),
inference(component_clause,[status(thm)],[f534]) ).
fof(f537,definition,
( sQ9_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f540,plain,
( sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f533,f534,f537]) ).
fof(f541,plain,
( sQ1_spl
| ~ sQ8_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f440,f535]) ).
fof(f555,plain,
( sQ1_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f541]) ).
fof(f556,plain,
( ~ sQ7_spl
| ~ segmentP(sK50_skl,sK49_skl)
| ~ neq(sK49_skl,nil)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f319,f517]) ).
fof(f557,definition,
( sQ10_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f559,plain,
( sQ10_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f557]) ).
fof(f560,plain,
( ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f556,f557,f445,f449,f460]) ).
fof(f561,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f559,f421]) ).
fof(f562,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f561]) ).
fof(f563,plain,
$false,
inference(sat_refutation,[status(thm)],[f441,f448,f452,f459,f463,f503,f512,f516,f531,f540,f555,f560,f562]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC059+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n020.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 07:53:02 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.047914 seconds
% 0.12/0.41 % CPU time: 0.159178 seconds
% 0.12/0.41 % Total memory used: 110.666 MB
% 0.12/0.41 % Net memory used: 110.531 MB
%------------------------------------------------------------------------------