%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC127+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 : n017.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 02:40:04 PM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 53 ( 15 unt; 7 def)
% Number of atoms : 147 ( 18 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 149 ( 55 ~; 52 |; 23 &)
% ( 9 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 20 ( 16 !; 4 ?)
% 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(f39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( segmentP(V,U)
& neq(U,nil) )
| ( neq(X,nil)
& ~ singletonP(W) )
| ~ segmentP(X,W)
| ~ neq(V,nil)
| 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)
=> ( ( segmentP(V,U)
& neq(U,nil) )
| ( neq(X,nil)
& ~ singletonP(W) )
| ~ segmentP(X,W)
| ~ neq(V,nil)
| 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(f220,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(f280,plain,
~ singletonP(nil),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ segmentP(V,U)
| ~ neq(U,nil) )
& ( ~ neq(X,nil)
| singletonP(W) )
& segmentP(X,W)
& neq(V,nil)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
( ( ~ segmentP(sK48_skl,sK47_skl)
| ~ neq(sK47_skl,nil) )
& ( ~ neq(sK50_skl,nil)
| singletonP(sK49_skl) )
& segmentP(sK50_skl,sK49_skl)
& neq(sK48_skl,nil)
& 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)],[f415]) ).
fof(f419,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f421,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f422,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f423,plain,
neq(sK48_skl,nil),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
segmentP(sK50_skl,sK49_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f425,plain,
( ~ neq(sK50_skl,nil)
| singletonP(sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f426,plain,
( ~ segmentP(sK48_skl,sK47_skl)
| ~ neq(sK47_skl,nil) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f427,definition,
( sQ0_spl
<=> singletonP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f428,plain,
( ~ sQ0_spl
| singletonP(sK49_skl) ),
inference(component_clause,[status(thm)],[f427]) ).
fof(f430,definition,
( sQ1_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f432,plain,
( sQ1_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f430]) ).
fof(f433,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f425,f427,f430]) ).
fof(f434,definition,
( sQ2_spl
<=> neq(sK47_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f436,plain,
( sQ2_spl
| ~ neq(sK47_skl,nil) ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f437,definition,
( sQ3_spl
<=> segmentP(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f439,plain,
( sQ3_spl
| ~ segmentP(sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f437]) ).
fof(f440,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f426,f434,f437]) ).
fof(f473,plain,
neq(sK50_skl,nil),
inference(forward_demodulation,[status(thm)],[f421,f423]) ).
fof(f474,plain,
( sQ2_spl
| ~ neq(sK49_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f422,f436]) ).
fof(f481,definition,
( sQ4_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f483,plain,
( sQ4_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f481]) ).
fof(f489,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f483,f223]) ).
fof(f490,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f489]) ).
fof(f528,plain,
( sQ2_spl
| sK49_skl = nil
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f220,f474]) ).
fof(f538,definition,
( sQ15_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f540,plain,
( sQ15_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f538]) ).
fof(f541,definition,
( sQ16_spl
<=> sK49_skl = nil ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f542,plain,
( ~ sQ16_spl
| sK49_skl = nil ),
inference(component_clause,[status(thm)],[f541]) ).
fof(f544,plain,
( sQ2_spl
| sQ16_spl
| ~ sQ4_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f528,f538,f481,f541,f434]) ).
fof(f545,plain,
( sQ3_spl
| ~ segmentP(sK50_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f421,f439]) ).
fof(f546,plain,
( sQ3_spl
| ~ segmentP(sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f422,f545]) ).
fof(f547,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f546,f424]) ).
fof(f548,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f547]) ).
fof(f549,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f540,f419]) ).
fof(f550,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f549]) ).
fof(f554,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| singletonP(nil) ),
inference(backward_demodulation,[status(thm)],[f542,f428]) ).
fof(f557,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f554,f280]) ).
fof(f558,plain,
( ~ sQ0_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f557]) ).
fof(f559,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f432,f473]) ).
fof(f560,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f559]) ).
fof(f561,plain,
$false,
inference(sat_refutation,[status(thm)],[f433,f440,f490,f544,f548,f550,f558,f560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC127+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 07:52:56 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.073935 seconds
% 0.13/0.44 % CPU time: 0.197835 seconds
% 0.13/0.44 % Total memory used: 110.500 MB
% 0.13/0.44 % Net memory used: 110.365 MB
%------------------------------------------------------------------------------