%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC008-1 : 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 02:39:34 PM UTC 2026
% Result : Unsatisfiable 57.03s 7.61s
% Output : CNFRefutation 57.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 17
% Syntax : Number of formulae : 59 ( 26 unt; 7 def)
% Number of atoms : 119 ( 32 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 116 ( 56 ~; 53 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 8 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [U,V] : ssList(skaf45(U,V)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f73,axiom,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f132,axiom,
! [U,V] :
( app(V,skaf45(U,V)) = U
| ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f188,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f189,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f190,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
frontsegP(sk4,sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
! [A,B,C] :
( app(A,C) != sk1
| app(app(A,B),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f203,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f246,plain,
! [X0,X1] : ssList(skaf45(X0,X1)),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f269,plain,
! [X0] :
( ~ ssList(X0)
| X0 = app(X0,nil) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f340,plain,
! [X0,X1] :
( X1 = app(X0,skaf45(X1,X0))
| ~ ssList(X1)
| ~ frontsegP(X1,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f428,plain,
ssList(sk3),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f429,plain,
ssList(sk4),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f430,plain,
sk4 = sk2,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f431,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f432,plain,
frontsegP(sk4,sk3),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f434,plain,
! [A,C] :
( app(A,C) != sk1
| ! [B] :
( app(app(A,B),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ) ),
inference(miniscoping,[status(thm)],[f194]) ).
fof(f435,plain,
! [X0,X1,X2] :
( app(app(X0,X2),X1) != sk2
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| sk1 != app(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
fof(f462,plain,
frontsegP(sk4,sk1),
inference(backward_demodulation,[status(thm)],[f431,f432]) ).
fof(f468,plain,
ssList(sk1),
inference(forward_demodulation,[status(thm)],[f431,f428]) ).
fof(f472,plain,
ssList(sk2),
inference(backward_demodulation,[status(thm)],[f430,f429]) ).
fof(f473,plain,
frontsegP(sk2,sk1),
inference(backward_demodulation,[status(thm)],[f430,f462]) ).
fof(f497,plain,
( ~ ssList(sk2)
| ~ ssList(sk1)
| sk2 = app(sk1,skaf45(sk2,sk1)) ),
inference(resolution,[status(thm)],[f340,f473]) ).
fof(f498,definition,
( sQ2_spl
<=> sk2 = app(sk1,skaf45(sk2,sk1)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f499,plain,
( ~ sQ2_spl
| sk2 = app(sk1,skaf45(sk2,sk1)) ),
inference(component_clause,[status(thm)],[f498]) ).
fof(f501,definition,
( sQ3_spl
<=> ssList(sk1) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f503,plain,
( sQ3_spl
| ~ ssList(sk1) ),
inference(component_clause,[status(thm)],[f501]) ).
fof(f504,definition,
( sQ4_spl
<=> ssList(sk2) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f506,plain,
( sQ4_spl
| ~ ssList(sk2) ),
inference(component_clause,[status(thm)],[f504]) ).
fof(f507,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f497,f498,f501,f504]) ).
fof(f519,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f503,f468]) ).
fof(f520,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f519]) ).
fof(f523,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f506,f472]) ).
fof(f524,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f523]) ).
fof(f532,plain,
! [X0] :
( ~ sQ2_spl
| ~ ssList(skaf45(sk2,sk1))
| ~ ssList(X0)
| sk1 != app(sk1,X0)
| sk2 != app(sk2,X0)
| ~ ssList(sk1) ),
inference(paramodulation,[status(thm)],[f499,f435]) ).
fof(f534,definition,
( sQ9_spl
<=> ssList(skaf45(sk2,sk1)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f536,plain,
( sQ9_spl
| ~ ssList(skaf45(sk2,sk1)) ),
inference(component_clause,[status(thm)],[f534]) ).
fof(f538,definition,
! [X0] :
( sQ10_spl
<=> ( ~ ssList(X0)
| sk1 != app(sk1,X0)
| sk2 != app(sk2,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f539,plain,
! [X0] :
( ~ sQ10_spl
| ~ ssList(X0)
| app(sk1,X0) != sk1
| sk2 != app(sk2,X0) ),
inference(component_clause,[status(thm)],[f538]) ).
fof(f541,plain,
( ~ sQ2_spl
| ~ sQ9_spl
| sQ10_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f532,f501,f538,f534,f498]) ).
fof(f694,plain,
( ~ sQ10_spl
| app(sk1,nil) != sk1
| sk2 != app(sk2,nil) ),
inference(resolution,[status(thm)],[f539,f203]) ).
fof(f703,definition,
( sQ27_spl
<=> sk2 = app(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f705,plain,
( sQ27_spl
| sk2 != app(sk2,nil) ),
inference(component_clause,[status(thm)],[f703]) ).
fof(f706,definition,
( sQ28_spl
<=> app(sk1,nil) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f708,plain,
( sQ28_spl
| app(sk1,nil) != sk1 ),
inference(component_clause,[status(thm)],[f706]) ).
fof(f709,plain,
( ~ sQ10_spl
| ~ sQ28_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f694,f703,f706,f538]) ).
fof(f1135,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f536,f246]) ).
fof(f1136,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f1135]) ).
fof(f3437,plain,
sk2 = app(sk2,nil),
inference(resolution,[status(thm)],[f269,f472]) ).
fof(f3463,plain,
app(sk1,nil) = sk1,
inference(resolution,[status(thm)],[f269,f468]) ).
fof(f3464,plain,
( sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3437,f705]) ).
fof(f3465,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f3464]) ).
fof(f3467,plain,
( sQ28_spl
| sk1 != sk1 ),
inference(forward_demodulation,[status(thm)],[f3463,f708]) ).
fof(f3468,plain,
( sQ28_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3467]) ).
fof(f3469,plain,
sQ28_spl,
inference(contradiction_clause,[status(thm)],[f3468]) ).
fof(f3470,plain,
$false,
inference(sat_refutation,[status(thm)],[f507,f520,f524,f541,f709,f1136,f3465,f3469]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC008-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 07:46:51 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 57.03/7.61 % Refutation found
% 57.03/7.61 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 57.03/7.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 57.03/7.67 % Elapsed time: 7.290893 seconds
% 57.03/7.67 % CPU time: 57.452882 seconds
% 57.03/7.67 % Total memory used: 431.715 MB
% 57.03/7.67 % Net memory used: 402.283 MB
%------------------------------------------------------------------------------