%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC007+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 : n007.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 02:39:33 PM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 13 unt; 4 def)
% Number of atoms : 121 ( 43 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 131 ( 51 ~; 44 |; 22 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 39 ( 29 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Y,X1) = U
& app(app(Y,Z),X1) = V
& ssList(X1) )
& ssList(Z) )
& ssList(Y) )
| U != W
| V != X
| nil != W ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Y,X1) = U
& app(app(Y,Z),X1) = V
& ssList(X1) )
& ssList(Z) )
& ssList(Y) )
| U != W
| V != X
| nil != W ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f248,plain,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f249,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f248]) ).
fof(f388,plain,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f84]) ).
fof(f389,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f388]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Y,X1) != U
| app(app(Y,Z),X1) != V
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssList(Y) )
& U = W
& V = X
& nil = W
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
( ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Y,X1) != sK47_skl
| app(app(Y,Z),X1) != sK48_skl
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssList(Y) )
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& nil = sK49_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,
nil = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f423,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
! [X0,X1,X2] :
( app(X0,X2) != sK47_skl
| app(app(X0,X1),X2) != sK48_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f462,plain,
sK47_skl = nil,
inference(forward_demodulation,[status(thm)],[f421,f423]) ).
fof(f463,plain,
! [X0,X1,X2] :
( app(X0,X2) != nil
| app(app(X0,X1),X2) != sK48_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f462,f424]) ).
fof(f470,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[f249,f223]) ).
fof(f471,plain,
app(nil,sK48_skl) = sK48_skl,
inference(resolution,[status(thm)],[f249,f418]) ).
fof(f472,plain,
! [X0] :
( app(app(nil,X0),nil) != sK48_skl
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f470,f463]) ).
fof(f475,definition,
( sQ0_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f477,plain,
( sQ0_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f475]) ).
fof(f478,definition,
! [X0] :
( sQ1_spl
<=> ( app(app(nil,X0),nil) != sK48_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f479,plain,
! [X0] :
( ~ sQ1_spl
| app(app(nil,X0),nil) != sK48_skl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f478]) ).
fof(f481,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f472,f475,f478]) ).
fof(f487,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f477,f223]) ).
fof(f488,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f487]) ).
fof(f494,definition,
( sQ4_spl
<=> ssList(sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f496,plain,
( sQ4_spl
| ~ ssList(sK48_skl) ),
inference(component_clause,[status(thm)],[f494]) ).
fof(f524,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f496,f418]) ).
fof(f525,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f524]) ).
fof(f573,plain,
app(sK48_skl,nil) = sK48_skl,
inference(resolution,[status(thm)],[f389,f418]) ).
fof(f650,plain,
( ~ sQ1_spl
| app(sK48_skl,nil) != sK48_skl
| ~ ssList(sK48_skl) ),
inference(paramodulation,[status(thm)],[f471,f479]) ).
fof(f652,definition,
( sQ16_spl
<=> app(sK48_skl,nil) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f654,plain,
( sQ16_spl
| app(sK48_skl,nil) != sK48_skl ),
inference(component_clause,[status(thm)],[f652]) ).
fof(f655,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f650,f494,f652,f478]) ).
fof(f660,plain,
( sQ16_spl
| sK48_skl != sK48_skl ),
inference(forward_demodulation,[status(thm)],[f573,f654]) ).
fof(f661,plain,
( sQ16_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f660]) ).
fof(f662,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f661]) ).
fof(f663,plain,
$false,
inference(sat_refutation,[status(thm)],[f481,f488,f525,f655,f662]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC007+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 07:46:35 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.051757 seconds
% 0.12/0.42 % CPU time: 0.163229 seconds
% 0.12/0.42 % Total memory used: 110.609 MB
% 0.12/0.42 % Net memory used: 110.432 MB
%------------------------------------------------------------------------------