%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC348+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 : n026.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 02:40:53 PM UTC 2026
% Result : Theorem 0.11s 0.41s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 19
% Syntax : Number of formulae : 85 ( 14 unt; 12 def)
% Number of atoms : 239 ( 36 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 247 ( 93 ~; 95 |; 28 &)
% ( 18 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 13 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 38 ( 31 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [U] :
( ssList(U)
=> ( segmentP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,axiom,
! [U] :
( ssItem(U)
=> strictorderedP(cons(U,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f69,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( strictorderedP(U)
& segmentP(V,U) )
| ( neq(X,nil)
& ~ singletonP(W) )
| ~ segmentP(X,W)
| 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)
=> ( ( strictorderedP(U)
& segmentP(V,U) )
| ( neq(X,nil)
& ~ singletonP(W) )
| ~ segmentP(X,W)
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f113,plain,
! [U] :
( ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f114,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ? [V] :
( cons(V,nil) = U
& ssItem(V) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ( cons(sK4_skl(U),nil) = U
& ssItem(sK4_skl(U)) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114]) ).
fof(f116,plain,
! [X0] :
( ssItem(sK4_skl(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0] :
( cons(sK4_skl(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
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(f324,plain,
! [U] :
( ( segmentP(nil,U)
<=> nil = U )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f58]) ).
fof(f325,plain,
! [U] :
( ( ( nil != U
| segmentP(nil,U) )
& ( nil = U
| ~ segmentP(nil,U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f324]) ).
fof(f326,plain,
! [X0] :
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f325]) ).
fof(f347,plain,
! [U] :
( strictorderedP(cons(U,nil))
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f68]) ).
fof(f348,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f347]) ).
fof(f349,plain,
strictorderedP(nil),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ strictorderedP(U)
| ~ segmentP(V,U) )
& ( ~ neq(X,nil)
| singletonP(W) )
& segmentP(X,W)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
( ( ~ strictorderedP(sK47_skl)
| ~ segmentP(sK48_skl,sK47_skl) )
& ( ~ neq(sK50_skl,nil)
| singletonP(sK49_skl) )
& segmentP(sK50_skl,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)],[f415]) ).
fof(f419,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f420,plain,
ssList(sK50_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,
segmentP(sK50_skl,sK49_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
( ~ neq(sK50_skl,nil)
| singletonP(sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f425,plain,
( ~ strictorderedP(sK47_skl)
| ~ segmentP(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f426,definition,
( sQ0_spl
<=> singletonP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f427,plain,
( ~ sQ0_spl
| singletonP(sK49_skl) ),
inference(component_clause,[status(thm)],[f426]) ).
fof(f429,definition,
( sQ1_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f431,plain,
( sQ1_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f429]) ).
fof(f432,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f424,f426,f429]) ).
fof(f433,definition,
( sQ2_spl
<=> segmentP(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f435,plain,
( sQ2_spl
| ~ segmentP(sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f433]) ).
fof(f436,definition,
( sQ3_spl
<=> strictorderedP(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f438,plain,
( sQ3_spl
| ~ strictorderedP(sK47_skl) ),
inference(component_clause,[status(thm)],[f436]) ).
fof(f439,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f425,f433,f436]) ).
fof(f472,plain,
( sQ2_spl
| ~ segmentP(sK50_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f421,f435]) ).
fof(f473,plain,
( sQ2_spl
| ~ segmentP(sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f422,f472]) ).
fof(f474,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f473,f423]) ).
fof(f475,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f474]) ).
fof(f476,plain,
( sQ3_spl
| ~ strictorderedP(sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f422,f438]) ).
fof(f485,definition,
( sQ4_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f487,plain,
( sQ4_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f485]) ).
fof(f493,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f487,f223]) ).
fof(f494,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f493]) ).
fof(f558,definition,
( sQ17_spl
<=> ssList(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f560,plain,
( sQ17_spl
| ~ ssList(sK50_skl) ),
inference(component_clause,[status(thm)],[f558]) ).
fof(f563,plain,
( ~ sQ0_spl
| ssItem(sK4_skl(sK49_skl))
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f116,f427]) ).
fof(f564,definition,
( sQ18_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f566,plain,
( sQ18_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f564]) ).
fof(f567,definition,
( sQ19_spl
<=> ssItem(sK4_skl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f570,plain,
( ~ sQ0_spl
| sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f563,f564,f567,f426]) ).
fof(f571,plain,
( sQ1_spl
| sK50_skl = nil
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f431,f220]) ).
fof(f572,definition,
( sQ20_spl
<=> sK50_skl = nil ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f573,plain,
( ~ sQ20_spl
| sK50_skl = nil ),
inference(component_clause,[status(thm)],[f572]) ).
fof(f575,plain,
( sQ1_spl
| sQ20_spl
| ~ sQ4_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f571,f558,f485,f572,f429]) ).
fof(f576,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f560,f420]) ).
fof(f577,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f576]) ).
fof(f578,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f566,f419]) ).
fof(f579,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f578]) ).
fof(f580,plain,
( ~ sQ0_spl
| cons(sK4_skl(sK49_skl),nil) = sK49_skl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f427,f117]) ).
fof(f582,definition,
( sQ21_spl
<=> cons(sK4_skl(sK49_skl),nil) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f583,plain,
( ~ sQ21_spl
| cons(sK4_skl(sK49_skl),nil) = sK49_skl ),
inference(component_clause,[status(thm)],[f582]) ).
fof(f585,plain,
( ~ sQ0_spl
| sQ21_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f580,f564,f582,f426]) ).
fof(f588,plain,
( ~ sQ20_spl
| segmentP(nil,sK49_skl) ),
inference(backward_demodulation,[status(thm)],[f573,f423]) ).
fof(f592,plain,
( ~ sQ20_spl
| nil = sK49_skl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f588,f326]) ).
fof(f593,definition,
( sQ22_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f594,plain,
( ~ sQ22_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f593]) ).
fof(f596,plain,
( ~ sQ20_spl
| sQ22_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f592,f564,f593,f572]) ).
fof(f599,plain,
( sQ3_spl
| ~ sQ22_spl
| ~ strictorderedP(nil) ),
inference(backward_demodulation,[status(thm)],[f594,f476]) ).
fof(f604,plain,
( sQ3_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f599,f349]) ).
fof(f605,plain,
( sQ3_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f604]) ).
fof(f887,plain,
( ~ sQ21_spl
| strictorderedP(sK49_skl)
| ~ ssItem(sK4_skl(sK49_skl)) ),
inference(paramodulation,[status(thm)],[f583,f348]) ).
fof(f900,definition,
( sQ69_spl
<=> strictorderedP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f901,plain,
( ~ sQ69_spl
| strictorderedP(sK49_skl) ),
inference(component_clause,[status(thm)],[f900]) ).
fof(f903,plain,
( ~ sQ21_spl
| sQ69_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f887,f567,f900,f582]) ).
fof(f921,plain,
( ~ sQ69_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f901,f476]) ).
fof(f922,plain,
( ~ sQ69_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f921]) ).
fof(f923,plain,
$false,
inference(sat_refutation,[status(thm)],[f432,f439,f475,f494,f570,f575,f577,f579,f585,f596,f605,f903,f922]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC348+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 08:20:37 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 0.11/0.41 % Refutation found
% 0.11/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.44 % Elapsed time: 0.058662 seconds
% 0.11/0.44 % CPU time: 0.184455 seconds
% 0.11/0.44 % Total memory used: 76.870 MB
% 0.11/0.44 % Net memory used: 76.663 MB
%------------------------------------------------------------------------------