%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COM003-2 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 12:10:15 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 43 ( 4 unt; 4 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 88 ( 47 ~; 37 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 5 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 73 ( 73 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X,Y] :
( halts2(X,Y)
| ~ program_halts2(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Y] :
( ~ halts2(X,Y)
| ~ program_not_halts2(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y,Z,W] :
( program_halts2(Y,Z)
| ~ program_halts2_halts3_outputs(X,Y,Z,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [X,Y,Z,W] :
( program_not_halts2(Y,Z)
| ~ program_not_halts2_halts3_outputs(X,Y,Z,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,hypothesis,
! [X] :
( program_program_decides(c1)
| ~ algorithm_program_decides(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,hypothesis,
! [W,Y,Z] :
( program_halts2_halts3_outputs(W,Y,Z,good)
| ~ program_program_decides(W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,hypothesis,
! [W,Y,Z] :
( program_not_halts2_halts3_outputs(W,Y,Z,bad)
| ~ program_program_decides(W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
algorithm_program_decides(c4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,plain,
! [X0,X1] :
( halts2(X0,X1)
| ~ program_halts2(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f66,plain,
! [X0,X1] :
( ~ halts2(X0,X1)
| ~ program_not_halts2(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f74,plain,
! [Y,Z] :
( program_halts2(Y,Z)
| ! [X,W] : ~ program_halts2_halts3_outputs(X,Y,Z,W) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f75,plain,
! [X0,X1,X2,X3] :
( program_halts2(X1,X2)
| ~ program_halts2_halts3_outputs(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f78,plain,
! [Y,Z] :
( program_not_halts2(Y,Z)
| ! [X,W] : ~ program_not_halts2_halts3_outputs(X,Y,Z,W) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f79,plain,
! [X0,X1,X2,X3] :
( program_not_halts2(X1,X2)
| ~ program_not_halts2_halts3_outputs(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f90,plain,
( program_program_decides(c1)
| ! [X] : ~ algorithm_program_decides(X) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f91,plain,
! [X0] :
( program_program_decides(c1)
| ~ algorithm_program_decides(X0) ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f92,plain,
! [W] :
( ! [Y,Z] : program_halts2_halts3_outputs(W,Y,Z,good)
| ~ program_program_decides(W) ),
inference(miniscoping,[status(thm)],[f35]) ).
fof(f93,plain,
! [X0,X1,X2] :
( program_halts2_halts3_outputs(X0,X1,X2,good)
| ~ program_program_decides(X0) ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f94,plain,
! [W] :
( ! [Y,Z] : program_not_halts2_halts3_outputs(W,Y,Z,bad)
| ~ program_program_decides(W) ),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f95,plain,
! [X0,X1,X2] :
( program_not_halts2_halts3_outputs(X0,X1,X2,bad)
| ~ program_program_decides(X0) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f108,plain,
algorithm_program_decides(c4),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f109,definition,
! [X0] :
( sQ0_spl
<=> ~ algorithm_program_decides(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f110,plain,
! [X0] :
( ~ sQ0_spl
| ~ algorithm_program_decides(X0) ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,definition,
( sQ1_spl
<=> program_program_decides(c1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f113,plain,
( ~ sQ1_spl
| program_program_decides(c1) ),
inference(component_clause,[status(thm)],[f112]) ).
fof(f115,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f91,f109,f112]) ).
fof(f146,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f108,f110]) ).
fof(f147,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f146]) ).
fof(f152,plain,
! [X0,X1,X2] :
( program_halts2(X1,X2)
| ~ program_program_decides(X0) ),
inference(resolution,[status(thm)],[f93,f75]) ).
fof(f153,definition,
! [X0] :
( sQ10_spl
<=> ~ program_program_decides(X0) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f154,plain,
! [X0] :
( ~ sQ10_spl
| ~ program_program_decides(X0) ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,definition,
! [X1,X2] :
( sQ11_spl
<=> program_halts2(X1,X2) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f157,plain,
! [X0,X1] :
( ~ sQ11_spl
| program_halts2(X0,X1) ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f159,plain,
( sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f152,f153,f156]) ).
fof(f160,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f113,f154]) ).
fof(f162,plain,
( ~ sQ1_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f160]) ).
fof(f163,plain,
! [X0,X1] :
( ~ sQ11_spl
| halts2(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f56,f157]) ).
fof(f166,plain,
! [X0,X1] :
( ~ sQ11_spl
| ~ program_not_halts2(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f66,f163]) ).
fof(f167,plain,
! [X0,X1,X2,X3] :
( ~ sQ11_spl
| ~ program_not_halts2_halts3_outputs(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f79,f166]) ).
fof(f172,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f113,f174]) ).
fof(f174,plain,
! [X0] :
( ~ sQ11_spl
| ~ program_program_decides(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f95,f167]) ).
fof(f175,plain,
( ~ sQ1_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f172]) ).
fof(f176,plain,
$false,
inference(sat_refutation,[status(thm)],[f115,f147,f159,f162,f175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM003-2 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 14:17:06 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.44 % Elapsed time: 0.053623 seconds
% 0.10/0.44 % CPU time: 0.131905 seconds
% 0.10/0.44 % Total memory used: 17.780 MB
% 0.10/0.44 % Net memory used: 17.696 MB
%------------------------------------------------------------------------------