%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC276+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 : n016.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 02:40:36 PM UTC 2026
% Result : Theorem 0.15s 10.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 7 unt; 6 def)
% Number of atoms : 151 ( 38 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 160 ( 55 ~; 52 |; 36 &)
% ( 6 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 6 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 41 ( 31 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f65,axiom,
! [U] :
( ssItem(U)
=> totalorderedP(cons(U,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ( ~ memberP(X,Y)
| cons(Y,nil) != W ) ) )
| totalorderedP(U)
| 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)
=> ( ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ( ~ memberP(X,Y)
| cons(Y,nil) != W ) ) )
| totalorderedP(U)
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f337,plain,
! [U] :
( totalorderedP(cons(U,nil))
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f65]) ).
fof(f338,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f337]) ).
fof(f339,plain,
totalorderedP(nil),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [Y] :
( memberP(X,Y)
& cons(Y,nil) = W
& ssItem(Y) ) )
& ~ totalorderedP(U)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [W,X,Y] :
( sP0_prd(Y,X,W)
<=> ( memberP(X,Y)
& cons(Y,nil) = W
& ssItem(Y) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [Y] : sP0_prd(Y,X,W) )
& ~ totalorderedP(U)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ( nil = sK49_skl
& nil = sK50_skl )
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) )
& ~ totalorderedP(sK47_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,sK51_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl)],[f417]) ).
fof(f424,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f425,plain,
~ totalorderedP(sK47_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
( nil = sK50_skl
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
( nil = sK49_skl
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f428,plain,
! [W,X,Y] :
( ( ~ memberP(X,Y)
| cons(Y,nil) != W
| ~ ssItem(Y)
| sP0_prd(Y,X,W) )
& ( ( memberP(X,Y)
& cons(Y,nil) = W
& ssItem(Y) )
| ~ sP0_prd(Y,X,W) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f429,plain,
( ! [W,X,Y] :
( ~ memberP(X,Y)
| cons(Y,nil) != W
| ~ ssItem(Y)
| sP0_prd(Y,X,W) )
& ! [W,X,Y] :
( ( memberP(X,Y)
& cons(Y,nil) = W
& ssItem(Y) )
| ~ sP0_prd(Y,X,W) ) ),
inference(miniscoping,[status(thm)],[f428]) ).
fof(f430,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f431,plain,
! [X0,X1,X2] :
( cons(X0,nil) = X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f434,definition,
( sQ0_spl
<=> sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f435,plain,
( ~ sQ0_spl
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f437,definition,
( sQ1_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f438,plain,
( ~ sQ1_spl
| nil = sK50_skl ),
inference(component_clause,[status(thm)],[f437]) ).
fof(f440,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f434,f437]) ).
fof(f441,definition,
( sQ2_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( ~ sQ2_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f427,f434,f441]) ).
fof(f478,plain,
~ totalorderedP(sK49_skl),
inference(forward_demodulation,[status(thm)],[f424,f425]) ).
fof(f479,plain,
( ~ sQ0_spl
| ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f435,f430]) ).
fof(f483,plain,
( ~ sQ0_spl
| cons(sK51_skl,nil) = sK49_skl ),
inference(resolution,[status(thm)],[f431,f435]) ).
fof(f484,plain,
( ~ sQ0_spl
| totalorderedP(sK49_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f483,f338]) ).
fof(f488,definition,
( sQ3_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f490,plain,
( sQ3_spl
| ~ ssItem(sK51_skl) ),
inference(component_clause,[status(thm)],[f488]) ).
fof(f491,definition,
( sQ4_spl
<=> totalorderedP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f492,plain,
( ~ sQ4_spl
| totalorderedP(sK49_skl) ),
inference(component_clause,[status(thm)],[f491]) ).
fof(f494,plain,
( ~ sQ0_spl
| sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f484,f488,f491,f434]) ).
fof(f510,plain,
( sQ3_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f490,f479]) ).
fof(f511,plain,
( sQ3_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f510]) ).
fof(f522,plain,
( ~ sQ1_spl
| totalorderedP(sK50_skl) ),
inference(backward_demodulation,[status(thm)],[f438,f339]) ).
fof(f524,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ totalorderedP(sK50_skl) ),
inference(backward_demodulation,[status(thm)],[f527,f478]) ).
fof(f527,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sK50_skl = sK49_skl ),
inference(forward_demodulation,[status(thm)],[f438,f442]) ).
fof(f531,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f524,f522]) ).
fof(f532,plain,
( ~ sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f531]) ).
fof(f533,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f478,f492]) ).
fof(f534,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f533]) ).
fof(f535,plain,
$false,
inference(sat_refutation,[status(thm)],[f440,f444,f494,f511,f532,f534]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC276+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/10.40 % Computer : n016.cluster.edu
% 0.12/10.40 % Model : x86_64 x86_64
% 0.12/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.40 % Memory : 8046.5625MB
% 0.12/10.40 % OS : Linux 6.8.0-71-generic
% 0.12/10.40 % CPULimit : 300
% 0.12/10.40 % WCLimit : 300
% 0.12/10.40 % DateTime : Mon Sep 21 08:16:05 UTC 2026
% 0.15/10.40 % CPUTime :
% 0.15/10.42 % Drodi V4.1.1
% 0.15/10.44 % Refutation found
% 0.15/10.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/10.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/10.47 % Elapsed time: 0.060962 seconds
% 0.15/10.47 % CPU time: 0.175982 seconds
% 0.15/10.47 % Total memory used: 110.642 MB
% 0.15/10.47 % Net memory used: 110.486 MB
%------------------------------------------------------------------------------