%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC419+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 02:41:10 PM UTC 2026
% Result : Theorem 11.78s 1.99s
% Output : CNFRefutation 6.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 70 ( 11 unt; 10 def)
% Number of atoms : 223 ( 67 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 253 ( 100 ~; 95 |; 36 &)
% ( 10 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 11 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 48 ( 36 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( neq(X,nil)
& ! [X2] :
( ssItem(X2)
=> ! [X3] :
( app(X3,cons(X2,nil)) != W
| app(cons(X2,nil),X3) != X
| ~ ssList(X3) ) ) )
| ( nil = X
& nil != W )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(app(X1,cons(Y,nil)),Z) = U
& app(app(Z,cons(Y,nil)),X1) = V
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| ~ neq(V,nil)
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( neq(X,nil)
& ! [X2] :
( ssItem(X2)
=> ! [X3] :
( app(X3,cons(X2,nil)) != W
| app(cons(X2,nil),X3) != X
| ~ ssList(X3) ) ) )
| ( nil = X
& nil != W )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(app(X1,cons(Y,nil)),Z) = U
& app(app(Z,cons(Y,nil)),X1) = V
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| ~ neq(V,nil)
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f221,plain,
! [U] :
( ! [V] :
( ssList(cons(V,U))
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f222,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f221]) ).
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] :
( ( ~ neq(X,nil)
| ? [X2] :
( ? [X3] :
( app(X3,cons(X2,nil)) = W
& app(cons(X2,nil),X3) = X
& ssList(X3) )
& ssItem(X2) ) )
& ( nil != X
| nil = W )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(app(X1,cons(Y,nil)),Z) != U
| app(app(Z,cons(Y,nil)),X1) != V
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(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,plain,
( ( ~ neq(sK50_skl,nil)
| ( app(sK52_skl,cons(sK51_skl,nil)) = sK49_skl
& app(cons(sK51_skl,nil),sK52_skl) = sK50_skl
& ssList(sK52_skl)
& ssItem(sK51_skl) ) )
& ( nil != sK50_skl
| nil = sK49_skl )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(app(X1,cons(Y,nil)),Z) != sK47_skl
| app(app(Z,cons(Y,nil)),X1) != sK48_skl
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(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,sK51_skl,sK52_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(X2,sK51_skl),skolemize(X3,sK52_skl)],[f415]) ).
fof(f417,plain,
ssList(sK47_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f421,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f422,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f423,plain,
neq(sK48_skl,nil),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
! [X0,X1,X2] :
( app(app(X2,cons(X0,nil)),X1) != sK47_skl
| app(app(X1,cons(X0,nil)),X2) != sK48_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f426,plain,
( ~ neq(sK50_skl,nil)
| ssItem(sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f427,plain,
( ~ neq(sK50_skl,nil)
| ssList(sK52_skl) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f428,plain,
( ~ neq(sK50_skl,nil)
| app(cons(sK51_skl,nil),sK52_skl) = sK50_skl ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f429,plain,
( ~ neq(sK50_skl,nil)
| app(sK52_skl,cons(sK51_skl,nil)) = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f437,definition,
( sQ2_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f440,definition,
( sQ3_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( sQ3_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f443,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f426,f437,f440]) ).
fof(f444,definition,
( sQ4_spl
<=> ssList(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f447,plain,
( ~ sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f427,f444,f440]) ).
fof(f448,definition,
( sQ5_spl
<=> app(cons(sK51_skl,nil),sK52_skl) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f449,plain,
( ~ sQ5_spl
| app(cons(sK51_skl,nil),sK52_skl) = sK50_skl ),
inference(component_clause,[status(thm)],[f448]) ).
fof(f451,plain,
( ~ sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f428,f448,f440]) ).
fof(f452,definition,
( sQ6_spl
<=> app(sK52_skl,cons(sK51_skl,nil)) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f453,plain,
( ~ sQ6_spl
| app(sK52_skl,cons(sK51_skl,nil)) = sK49_skl ),
inference(component_clause,[status(thm)],[f452]) ).
fof(f455,plain,
( ~ sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f429,f452,f440]) ).
fof(f490,plain,
( sQ3_spl
| ~ neq(sK48_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f421,f442]) ).
fof(f491,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f490,f423]) ).
fof(f492,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f491]) ).
fof(f574,plain,
( ~ sQ6_spl
| app(sK52_skl,cons(sK51_skl,nil)) = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f422,f453]) ).
fof(f575,plain,
( ~ sQ5_spl
| app(cons(sK51_skl,nil),sK52_skl) = sK48_skl ),
inference(forward_demodulation,[status(thm)],[f421,f449]) ).
fof(f582,plain,
app(sK47_skl,nil) = sK47_skl,
inference(resolution,[status(thm)],[f389,f417]) ).
fof(f611,definition,
( sQ10_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f613,plain,
( sQ10_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f611]) ).
fof(f616,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f613,f223]) ).
fof(f617,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f616]) ).
fof(f636,plain,
! [X0] :
( ~ sQ6_spl
| app(sK47_skl,X0) != sK47_skl
| app(app(X0,cons(sK51_skl,nil)),sK52_skl) != sK48_skl
| ~ ssList(sK52_skl)
| ~ ssList(X0)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f574,f424]) ).
fof(f638,definition,
! [X0] :
( sQ13_spl
<=> ( app(sK47_skl,X0) != sK47_skl
| app(app(X0,cons(sK51_skl,nil)),sK52_skl) != sK48_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f639,plain,
! [X0] :
( ~ sQ13_spl
| app(sK47_skl,X0) != sK47_skl
| app(app(X0,cons(sK51_skl,nil)),sK52_skl) != sK48_skl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f638]) ).
fof(f641,plain,
( ~ sQ6_spl
| ~ sQ4_spl
| sQ13_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f636,f437,f638,f444,f452]) ).
fof(f729,definition,
( sQ24_spl
<=> ssList(cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f730,plain,
( ~ sQ24_spl
| ssList(cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f729]) ).
fof(f731,plain,
( sQ24_spl
| ~ ssList(cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f729]) ).
fof(f844,plain,
( sQ24_spl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f731,f222]) ).
fof(f845,plain,
( sQ24_spl
| ~ sQ2_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f844,f611,f437,f729]) ).
fof(f859,plain,
( ~ sQ24_spl
| app(nil,cons(sK51_skl,nil)) = cons(sK51_skl,nil) ),
inference(resolution,[status(thm)],[f730,f249]) ).
fof(f1544,plain,
( ~ sQ13_spl
| app(sK47_skl,nil) != sK47_skl
| app(app(nil,cons(sK51_skl,nil)),sK52_skl) != sK48_skl ),
inference(resolution,[status(thm)],[f639,f223]) ).
fof(f1558,definition,
( sQ93_spl
<=> app(app(nil,cons(sK51_skl,nil)),sK52_skl) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f1560,plain,
( sQ93_spl
| app(app(nil,cons(sK51_skl,nil)),sK52_skl) != sK48_skl ),
inference(component_clause,[status(thm)],[f1558]) ).
fof(f1561,definition,
( sQ94_spl
<=> app(sK47_skl,nil) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f1563,plain,
( sQ94_spl
| app(sK47_skl,nil) != sK47_skl ),
inference(component_clause,[status(thm)],[f1561]) ).
fof(f1564,plain,
( ~ sQ13_spl
| ~ sQ94_spl
| ~ sQ93_spl ),
inference(split_clause,[status(thm)],[f1544,f1558,f1561,f638]) ).
fof(f1586,plain,
( sQ93_spl
| ~ sQ24_spl
| app(cons(sK51_skl,nil),sK52_skl) != sK48_skl ),
inference(forward_demodulation,[status(thm)],[f859,f1560]) ).
fof(f1587,plain,
( sQ93_spl
| ~ sQ24_spl
| ~ sQ5_spl
| sK48_skl != sK48_skl ),
inference(forward_demodulation,[status(thm)],[f575,f1586]) ).
fof(f1588,plain,
( sQ93_spl
| ~ sQ24_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1587]) ).
fof(f1589,plain,
( sQ93_spl
| ~ sQ24_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f1588]) ).
fof(f1591,plain,
( sQ94_spl
| sK47_skl != sK47_skl ),
inference(forward_demodulation,[status(thm)],[f582,f1563]) ).
fof(f1592,plain,
( sQ94_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1591]) ).
fof(f1593,plain,
sQ94_spl,
inference(contradiction_clause,[status(thm)],[f1592]) ).
fof(f1594,plain,
$false,
inference(sat_refutation,[status(thm)],[f443,f447,f451,f455,f492,f617,f641,f845,f1564,f1589,f1593]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC419+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 : n016.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 08:27:52 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 11.78/1.99 % Refutation found
% 11.78/1.99 % SZS status Theorem for theBenchmark: Theorem is valid
% 11.78/1.99 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.22/2.03 % Elapsed time: 1.653914 seconds
% 6.22/2.03 % CPU time: 12.736770 seconds
% 6.22/2.03 % Total memory used: 215.515 MB
% 6.22/2.03 % Net memory used: 204.142 MB
%------------------------------------------------------------------------------