%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC132+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 : 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 02:40:05 PM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 13 unt; 3 def)
% Number of atoms : 89 ( 17 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 89 ( 33 ~; 26 |; 15 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f60,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( cyclefreeP(V)
| neq(X,nil)
| 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)
=> ( cyclefreeP(V)
| neq(X,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(f330,plain,
cyclefreeP(nil),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ~ cyclefreeP(V)
& ~ neq(X,nil)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
( ~ cyclefreeP(sK48_skl)
& ~ neq(sK50_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(f418,plain,
ssList(sK48_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f421,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f423,plain,
~ neq(sK50_skl,nil),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
~ cyclefreeP(sK48_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f448,plain,
~ neq(sK48_skl,nil),
inference(forward_demodulation,[status(thm)],[f421,f423]) ).
fof(f456,definition,
( sQ2_spl
<=> sK48_skl = nil ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( ~ sQ2_spl
| sK48_skl = nil ),
inference(component_clause,[status(thm)],[f456]) ).
fof(f461,plain,
( ~ sQ2_spl
| ~ cyclefreeP(nil) ),
inference(backward_demodulation,[status(thm)],[f457,f424]) ).
fof(f464,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f461,f330]) ).
fof(f465,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f464]) ).
fof(f469,definition,
( sQ3_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f471,plain,
( sQ3_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f469]) ).
fof(f486,plain,
( sK48_skl = nil
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f448,f220]) ).
fof(f488,definition,
( sQ6_spl
<=> ssList(sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f490,plain,
( sQ6_spl
| ~ ssList(sK48_skl) ),
inference(component_clause,[status(thm)],[f488]) ).
fof(f491,plain,
( sQ2_spl
| ~ sQ3_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f486,f488,f469,f456]) ).
fof(f493,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f471,f223]) ).
fof(f494,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f493]) ).
fof(f495,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f490,f418]) ).
fof(f496,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f495]) ).
fof(f497,plain,
$false,
inference(sat_refutation,[status(thm)],[f465,f491,f494,f496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC132+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 07:59:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.058775 seconds
% 0.14/0.43 % CPU time: 0.161315 seconds
% 0.14/0.43 % Total memory used: 110.220 MB
% 0.14/0.43 % Net memory used: 110.077 MB
%------------------------------------------------------------------------------