%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN009-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 12:45:22 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.45s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 51 ( 15 unt; 6 def)
% Number of atoms : 93 ( 51 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 78 ( 36 ~; 36 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 7 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Z,Y] : divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : divide(zero,X) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] :
( X = Y
| divide(Y,X) != zero
| divide(X,Y) != zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : divide(X,identity) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,Z] :
( divide(divide(X,Z),Y) = zero
| divide(divide(X,Y),Z) != zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y,Z] :
( divide(divide(Z,Y),divide(Z,X)) = zero
| divide(X,Y) != zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,plain,
! [X0,X1,X2] : divide(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)) = zero,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
! [X0] : divide(zero,X0) = zero,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f13,plain,
! [X0,X1] :
( X0 = X1
| divide(X1,X0) != zero
| divide(X0,X1) != zero ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
! [X0] : divide(X0,identity) = zero,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f17,plain,
! [X0,X1,X2] :
( divide(divide(X0,X2),X1) = zero
| divide(divide(X0,X1),X2) != zero ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f18,plain,
! [X,Y] :
( ! [Z] : divide(divide(Z,Y),divide(Z,X)) = zero
| divide(X,Y) != zero ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f19,plain,
! [X0,X1,X2] :
( divide(divide(X2,X1),divide(X2,X0)) = zero
| divide(X0,X1) != zero ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f43,plain,
! [X0,X1] : divide(divide(divide(X0,X1),divide(identity,X1)),divide(zero,X1)) = zero,
inference(paramodulation,[status(thm)],[f14,f11]) ).
fof(f54,plain,
! [X0,X1] : divide(divide(divide(X0,X1),divide(identity,X1)),zero) = zero,
inference(forward_demodulation,[status(thm)],[f12,f43]) ).
fof(f71,plain,
( divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,a)) != zero
| divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))) != zero ),
inference(resolution,[status(thm)],[f13,f20]) ).
fof(f73,definition,
( sQ0_spl
<=> divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))) = zero ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( sQ0_spl
| divide(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))) != zero ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,definition,
( sQ1_spl
<=> divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,a)) = zero ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( sQ1_spl
| divide(divide(identity,divide(identity,divide(identity,a))),divide(identity,a)) != zero ),
inference(component_clause,[status(thm)],[f76]) ).
fof(f79,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f71,f73,f76]) ).
fof(f228,plain,
( sQ0_spl
| divide(divide(identity,divide(identity,a)),a) != zero ),
inference(resolution,[status(thm)],[f75,f19]) ).
fof(f245,plain,
( sQ1_spl
| divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))) != zero ),
inference(resolution,[status(thm)],[f78,f17]) ).
fof(f260,plain,
( sQ0_spl
| divide(divide(identity,a),divide(identity,a)) != zero ),
inference(resolution,[status(thm)],[f228,f17]) ).
fof(f275,plain,
( sQ0_spl
| divide(zero,divide(divide(identity,a),divide(identity,a))) != zero
| divide(divide(divide(identity,a),divide(identity,a)),zero) != zero ),
inference(resolution,[status(thm)],[f260,f13]) ).
fof(f277,definition,
( sQ23_spl
<=> divide(divide(divide(identity,a),divide(identity,a)),zero) = zero ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f279,plain,
( sQ23_spl
| divide(divide(divide(identity,a),divide(identity,a)),zero) != zero ),
inference(component_clause,[status(thm)],[f277]) ).
fof(f280,definition,
( sQ24_spl
<=> divide(zero,divide(divide(identity,a),divide(identity,a))) = zero ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f282,plain,
( sQ24_spl
| divide(zero,divide(divide(identity,a),divide(identity,a))) != zero ),
inference(component_clause,[status(thm)],[f280]) ).
fof(f283,plain,
( sQ0_spl
| ~ sQ24_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f275,f277,f280,f73]) ).
fof(f832,plain,
( sQ1_spl
| divide(zero,divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))) != zero
| divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),zero) != zero ),
inference(resolution,[status(thm)],[f245,f13]) ).
fof(f834,definition,
( sQ67_spl
<=> divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),zero) = zero ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f836,plain,
( sQ67_spl
| divide(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a))),zero) != zero ),
inference(component_clause,[status(thm)],[f834]) ).
fof(f837,definition,
( sQ68_spl
<=> divide(zero,divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))) = zero ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f839,plain,
( sQ68_spl
| divide(zero,divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))) != zero ),
inference(component_clause,[status(thm)],[f837]) ).
fof(f840,plain,
( sQ1_spl
| ~ sQ68_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f832,f834,f837,f76]) ).
fof(f842,plain,
( sQ67_spl
| zero != zero ),
inference(forward_demodulation,[status(thm)],[f54,f836]) ).
fof(f843,plain,
( sQ67_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f842]) ).
fof(f844,plain,
sQ67_spl,
inference(contradiction_clause,[status(thm)],[f843]) ).
fof(f845,plain,
( sQ68_spl
| zero != zero ),
inference(forward_demodulation,[status(thm)],[f12,f839]) ).
fof(f846,plain,
( sQ68_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f845]) ).
fof(f847,plain,
sQ68_spl,
inference(contradiction_clause,[status(thm)],[f846]) ).
fof(f848,plain,
( sQ23_spl
| zero != zero ),
inference(forward_demodulation,[status(thm)],[f54,f279]) ).
fof(f849,plain,
( sQ23_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f848]) ).
fof(f850,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f849]) ).
fof(f852,plain,
( sQ24_spl
| zero != zero ),
inference(forward_demodulation,[status(thm)],[f12,f282]) ).
fof(f853,plain,
( sQ24_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f852]) ).
fof(f854,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f853]) ).
fof(f855,plain,
$false,
inference(sat_refutation,[status(thm)],[f79,f283,f840,f844,f847,f850,f854]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN009-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n011.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sun Sep 20 20:46:26 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.08/0.45 % Refutation found
% 0.08/0.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.49 % Elapsed time: 0.100171 seconds
% 0.08/0.49 % CPU time: 0.519486 seconds
% 0.08/0.49 % Total memory used: 80.131 MB
% 0.08/0.49 % Net memory used: 79.365 MB
%------------------------------------------------------------------------------