%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HWV052-1.001.001 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 12:46:15 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.38s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 13 unt; 2 def)
% Number of atoms : 59 ( 41 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 13 ~; 23 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] :
( X = i
| X = o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : inv(X) != X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X1] : unpack1(X1,pack1(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X1] : unpack1(inv(X1),pack1(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X1] : unpack1(X1,inv(pack1(X1))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0] :
( X0 = i
| X0 = o ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0] : inv(X0) != X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0] : unpack1(X0,pack1(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f9,plain,
! [X0] : unpack1(inv(X0),pack1(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f10,plain,
! [X0] : unpack1(X0,inv(pack1(X0))) = X0,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,plain,
inv(i) = o,
inference(resolution,[status(thm)],[f6,f7]) ).
fof(f22,plain,
! [X0] :
( pack1(X0) = o
| unpack1(X0,i) = X0 ),
inference(paramodulation,[status(thm)],[f6,f8]) ).
fof(f28,plain,
! [X0] :
( pack1(X0) = o
| unpack1(inv(X0),i) = X0 ),
inference(paramodulation,[status(thm)],[f6,f9]) ).
fof(f31,plain,
! [X0] :
( inv(pack1(X0)) = o
| unpack1(X0,i) = X0 ),
inference(paramodulation,[status(thm)],[f6,f10]) ).
fof(f32,plain,
! [X0] :
( pack1(X0) = o
| unpack1(X0,inv(i)) = X0 ),
inference(paramodulation,[status(thm)],[f6,f10]) ).
fof(f128,definition,
( sQ14_spl
<=> inv(o) = o ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f129,plain,
( ~ sQ14_spl
| inv(o) = o ),
inference(component_clause,[status(thm)],[f128]) ).
fof(f153,plain,
( ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f129,f7]) ).
fof(f154,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f153]) ).
fof(f167,plain,
! [X0] :
( pack1(X0) = o
| unpack1(X0,o) = X0 ),
inference(backward_demodulation,[status(thm)],[f11,f32]) ).
fof(f193,plain,
! [X0] :
( unpack1(X0,i) = X0
| inv(o) = o
| unpack1(X0,i) = X0 ),
inference(paramodulation,[status(thm)],[f22,f31]) ).
fof(f201,definition,
! [X0] :
( sQ21_spl
<=> ( unpack1(X0,i) = X0
| unpack1(X0,i) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f202,plain,
! [X0] :
( ~ sQ21_spl
| unpack1(X0,i) = X0
| unpack1(X0,i) = X0 ),
inference(component_clause,[status(thm)],[f201]) ).
fof(f204,plain,
( sQ14_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f193,f201,f128]) ).
fof(f206,plain,
! [X0] :
( ~ sQ21_spl
| unpack1(X0,i) = X0 ),
inference(duplicate_literals_removal,[status(thm)],[f202]) ).
fof(f207,plain,
! [X0] :
( ~ sQ21_spl
| pack1(X0) = o
| inv(X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f206,f28]) ).
fof(f214,plain,
! [X0] :
( ~ sQ21_spl
| pack1(X0) = o ),
inference(forward_subsumption_resolution,[status(thm)],[f207,f7]) ).
fof(f225,plain,
! [X0] :
( unpack1(X0,o) = X0
| unpack1(X0,o) = X0 ),
inference(paramodulation,[status(thm)],[f167,f8]) ).
fof(f234,plain,
! [X0] : unpack1(X0,o) = X0,
inference(duplicate_literals_removal,[status(thm)],[f225]) ).
fof(f238,plain,
! [X0] :
( ~ sQ21_spl
| unpack1(inv(X0),o) = X0 ),
inference(backward_demodulation,[status(thm)],[f214,f9]) ).
fof(f274,plain,
! [X0] :
( ~ sQ21_spl
| inv(X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f234,f238]) ).
fof(f278,plain,
( ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f274,f7]) ).
fof(f279,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f278]) ).
fof(f280,plain,
$false,
inference(sat_refutation,[status(thm)],[f154,f204,f279]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWV052-1.001.001 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n003.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 21:05:15 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.15/0.37 % Drodi V4.1.1
% 0.15/0.38 % Refutation found
% 0.15/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.39 % Elapsed time: 0.025603 seconds
% 0.15/0.39 % CPU time: 0.087332 seconds
% 0.15/0.39 % Total memory used: 1.384 MB
% 0.15/0.39 % Net memory used: 1.297 MB
%------------------------------------------------------------------------------