%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC047+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 : n012.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 02:39:44 PM UTC 2026
% Result : Theorem 0.08s 0.54s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 58 ( 11 unt; 7 def)
% Number of atoms : 195 ( 44 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 230 ( 93 ~; 79 |; 42 &)
% ( 7 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 7 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 50 ( 38 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
? [U] :
( ? [V] :
( U != V
& ssItem(V) )
& ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( ? [Y] :
( rearsegP(U,Y)
& rearsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| 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)
=> ( ( ( ? [Y] :
( rearsegP(U,Y)
& rearsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| X != W
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f102,plain,
( sK0_skl != sK1_skl
& ssItem(sK1_skl)
& ssItem(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl)],[f2]) ).
fof(f105,plain,
sK0_skl != sK1_skl,
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f304,plain,
! [U] :
( rearsegP(U,U)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f305,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f304]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ! [Y] :
( ~ rearsegP(U,Y)
| ~ rearsegP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& X = 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] :
( ~ rearsegP(U,Y)
| ~ rearsegP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(V,nil) )
| sP0_prd(V,U) )
& X = W
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ( ! [Y] :
( ~ rearsegP(sK47_skl,Y)
| ~ rearsegP(sK48_skl,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(sK48_skl,nil) )
| sP0_prd(sK48_skl,sK47_skl) )
& 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)],[f417]) ).
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,
sK50_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
( neq(sK48_skl,nil)
| sP0_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
! [X0] :
( ~ rearsegP(sK47_skl,X0)
| ~ rearsegP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0)
| sP0_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f428,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(f429,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)],[f428]) ).
fof(f430,plain,
! [X0,X1] :
( nil = X0
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f431,plain,
! [X0,X1] :
( nil != X1
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f433,definition,
( sQ0_spl
<=> sP0_prd(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f434,plain,
( ~ sQ0_spl
| sP0_prd(sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f433]) ).
fof(f436,definition,
( sQ1_spl
<=> neq(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f437,plain,
( ~ sQ1_spl
| neq(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f436]) ).
fof(f439,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f433,f436]) ).
fof(f440,definition,
! [X0] :
( sQ2_spl
<=> ( ~ rearsegP(sK47_skl,X0)
| ~ rearsegP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f441,plain,
! [X0] :
( ~ sQ2_spl
| ~ rearsegP(sK47_skl,X0)
| ~ rearsegP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f443,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f427,f433,f440]) ).
fof(f474,plain,
! [X0] : ~ sP0_prd(X0,nil),
inference(destructive_equality_resolution,[status(thm)],[f431]) ).
fof(f478,plain,
sK47_skl = sK50_skl,
inference(backward_demodulation,[status(thm)],[f425,f424]) ).
fof(f480,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f434]) ).
fof(f481,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK50_skl) ),
inference(forward_demodulation,[status(thm)],[f478,f480]) ).
fof(f482,plain,
( ~ sQ0_spl
| nil = sK50_skl ),
inference(resolution,[status(thm)],[f430,f481]) ).
fof(f484,plain,
! [X0] :
( ~ sQ0_spl
| ~ sP0_prd(X0,sK50_skl) ),
inference(backward_demodulation,[status(thm)],[f482,f474]) ).
fof(f496,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f481,f484]) ).
fof(f497,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f496]) ).
fof(f498,plain,
( ~ sQ1_spl
| neq(sK50_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f423,f437]) ).
fof(f499,plain,
! [X0] :
( ~ sQ2_spl
| ~ rearsegP(sK47_skl,X0)
| ~ rearsegP(sK50_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f423,f441]) ).
fof(f500,plain,
! [X0] :
( ~ sQ2_spl
| ~ rearsegP(sK50_skl,X0)
| ~ rearsegP(sK50_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f478,f499]) ).
fof(f501,plain,
! [X0] :
( ~ sQ2_spl
| ~ rearsegP(sK50_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f500]) ).
fof(f506,definition,
! [X0] :
( sQ3_spl
<=> nil = X0 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f507,plain,
! [X0] :
( ~ sQ3_spl
| nil = X0 ),
inference(component_clause,[status(thm)],[f506]) ).
fof(f513,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ rearsegP(sK50_skl,sK50_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f501,f498]) ).
fof(f515,definition,
( sQ5_spl
<=> ssList(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f517,plain,
( sQ5_spl
| ~ ssList(sK50_skl) ),
inference(component_clause,[status(thm)],[f515]) ).
fof(f518,definition,
( sQ6_spl
<=> rearsegP(sK50_skl,sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f520,plain,
( sQ6_spl
| ~ rearsegP(sK50_skl,sK50_skl) ),
inference(component_clause,[status(thm)],[f518]) ).
fof(f521,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f513,f515,f518,f440,f436]) ).
fof(f529,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f517,f422]) ).
fof(f530,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f529]) ).
fof(f531,plain,
! [X0,X1] :
( ~ sQ3_spl
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f507,f507]) ).
fof(f538,plain,
( ~ sQ3_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f105,f531]) ).
fof(f539,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f538]) ).
fof(f540,plain,
( sQ6_spl
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f520,f305]) ).
fof(f541,plain,
( sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f540,f515,f518]) ).
fof(f542,plain,
$false,
inference(sat_refutation,[status(thm)],[f439,f443,f497,f521,f530,f539,f541]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC047+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.50 % Computer : n012.cluster.edu
% 0.03/0.50 % Model : x86_64 x86_64
% 0.03/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.50 % Memory : 8046.5625MB
% 0.03/0.50 % OS : Linux 6.8.0-71-generic
% 0.03/0.50 % CPULimit : 300
% 0.03/0.50 % WCLimit : 300
% 0.03/0.50 % DateTime : Mon Sep 21 07:51:07 UTC 2026
% 0.03/0.51 % CPUTime :
% 0.03/0.52 % Drodi V4.1.1
% 0.08/0.54 % Refutation found
% 0.08/0.54 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.55 % Elapsed time: 0.044943 seconds
% 0.08/0.55 % CPU time: 0.112092 seconds
% 0.08/0.55 % Total memory used: 110.570 MB
% 0.08/0.55 % Net memory used: 110.419 MB
%------------------------------------------------------------------------------