%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC086+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 : n003.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 02:39:54 PM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 9 unt; 6 def)
% Number of atoms : 188 ( 35 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 221 ( 85 ~; 75 |; 42 &)
% ( 8 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 47 ( 37 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
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)
=> ( ( ( ~ segmentP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ 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(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ 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(f219,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
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] :
( ( ( segmentP(X,W)
& neq(W,nil) )
| ( nil = W
& nil = X ) )
& ! [Y] :
( ~ segmentP(U,Y)
| ~ segmentP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(V,nil)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [W,X] :
( sP0_prd(X,W)
<=> ( nil = W
& nil = X ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( segmentP(X,W)
& neq(W,nil) )
| sP0_prd(X,W) )
& ! [Y] :
( ~ segmentP(U,Y)
| ~ segmentP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(V,nil)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ( segmentP(sK50_skl,sK49_skl)
& neq(sK49_skl,nil) )
| sP0_prd(sK50_skl,sK49_skl) )
& ! [Y] :
( ~ segmentP(sK47_skl,Y)
| ~ segmentP(sK48_skl,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& 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)],[f417]) ).
fof(f421,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f422,plain,
ssList(sK50_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,
neq(sK48_skl,nil),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
! [X0] :
( ~ segmentP(sK47_skl,X0)
| ~ segmentP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
( neq(sK49_skl,nil)
| sP0_prd(sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f428,plain,
( segmentP(sK50_skl,sK49_skl)
| sP0_prd(sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f429,plain,
! [W,X] :
( ( nil != W
| nil != X
| sP0_prd(X,W) )
& ( ( nil = W
& nil = X )
| ~ sP0_prd(X,W) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f430,plain,
( ! [W,X] :
( nil != W
| nil != X
| sP0_prd(X,W) )
& ! [W,X] :
( ( nil = W
& nil = X )
| ~ sP0_prd(X,W) ) ),
inference(miniscoping,[status(thm)],[f429]) ).
fof(f431,plain,
! [X0,X1] :
( nil = X0
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f430]) ).
fof(f434,definition,
( sQ0_spl
<=> sP0_prd(sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f435,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f437,definition,
( sQ1_spl
<=> neq(sK49_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f438,plain,
( ~ sQ1_spl
| neq(sK49_skl,nil) ),
inference(component_clause,[status(thm)],[f437]) ).
fof(f440,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f427,f434,f437]) ).
fof(f441,definition,
( sQ2_spl
<=> segmentP(sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f444,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f428,f434,f441]) ).
fof(f460,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f219]) ).
fof(f461,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f460]) ).
fof(f478,plain,
neq(sK50_skl,nil),
inference(forward_demodulation,[status(thm)],[f423,f425]) ).
fof(f479,plain,
( ~ sQ0_spl
| nil = sK50_skl ),
inference(resolution,[status(thm)],[f431,f435]) ).
fof(f483,plain,
( ~ sQ0_spl
| neq(sK50_skl,sK50_skl) ),
inference(backward_demodulation,[status(thm)],[f479,f478]) ).
fof(f496,plain,
( ~ sQ0_spl
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f483,f461]) ).
fof(f498,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f496,f422]) ).
fof(f499,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f498]) ).
fof(f500,plain,
! [X0] :
( ~ segmentP(sK47_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f423,f426]) ).
fof(f501,plain,
! [X0] :
( ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f424,f500]) ).
fof(f503,plain,
( ~ sQ1_spl
| ~ segmentP(sK49_skl,sK49_skl)
| ~ segmentP(sK50_skl,sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f501,f438]) ).
fof(f515,definition,
( sQ6_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f517,plain,
( sQ6_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f515]) ).
fof(f518,definition,
( sQ7_spl
<=> segmentP(sK49_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f520,plain,
( sQ7_spl
| ~ segmentP(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f518]) ).
fof(f521,plain,
( ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f503,f515,f441,f518,f437]) ).
fof(f529,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f517,f421]) ).
fof(f530,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f529]) ).
fof(f531,plain,
( sQ7_spl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f520,f319]) ).
fof(f532,plain,
( sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f531,f515,f518]) ).
fof(f533,plain,
$false,
inference(sat_refutation,[status(thm)],[f440,f444,f499,f521,f530,f532]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC086+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 07:56:15 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.13/0.38 % 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
% 0.13/0.43 % Elapsed time: 0.061311 seconds
% 0.13/0.43 % CPU time: 0.167502 seconds
% 0.13/0.43 % Total memory used: 110.636 MB
% 0.13/0.43 % Net memory used: 110.488 MB
%------------------------------------------------------------------------------