%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COM003+2 : TPTP v9.3.1. Bugfixed v2.2.0.
% 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 12:10:15 PM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 26
% Syntax : Number of formulae : 116 ( 6 unt; 16 def)
% Number of atoms : 366 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 439 ( 189 ~; 175 |; 47 &)
% ( 22 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 30 ( 29 usr; 17 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-1 aty)
% Number of variables : 161 ( 142 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X] :
( program_program_decides(X)
<=> ( program_decides(X)
& program(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] :
( program_halts2(X,Y)
<=> ( halts2(X,Y)
& program(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] :
( program_not_halts2(X,Y)
<=> ( ~ halts2(X,Y)
& program(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,W] :
( halts2_outputs(X,Y,W)
<=> ( outputs(X,W)
& halts2(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y,W] :
( program_not_halts2_halts2_outputs(X,Y,W)
<=> ( program_not_halts2(Y,Y)
=> halts2_outputs(X,Y,W) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
( ? [X] : algorithm_program_decides(X)
=> ? [W] : program_program_decides(W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [W] :
( program_program_decides(W)
=> ! [Y,Z] :
( program_not_halts2_halts3_outputs(W,Y,Z,bad)
& program_halts2_halts3_outputs(W,Y,Z,good) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
( ? [W] :
( ! [Y] :
( program_not_halts2_halts3_outputs(W,Y,Y,bad)
& program_halts2_halts3_outputs(W,Y,Y,good) )
& program(W) )
=> ? [V] :
( ! [Y] :
( program_not_halts2_halts2_outputs(V,Y,bad)
& program_halts2_halts2_outputs(V,Y,good) )
& program(V) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
( ? [V] :
( ! [Y] :
( program_not_halts2_halts2_outputs(V,Y,bad)
& program_halts2_halts2_outputs(V,Y,good) )
& program(V) )
=> ? [U] :
( ! [Y] :
( program_not_halts2_halts2_outputs(U,Y,good)
& ( program_halts2(Y,Y)
=> ~ halts2(U,Y) ) )
& program(U) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,conjecture,
~ ? [X] : algorithm_program_decides(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
~ ~ ? [X] : algorithm_program_decides(X),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f25,plain,
! [X] :
( ( ~ program_decides(X)
| ~ program(X)
| program_program_decides(X) )
& ( ( program_decides(X)
& program(X) )
| ~ program_program_decides(X) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f26,plain,
( ! [X] :
( ~ program_decides(X)
| ~ program(X)
| program_program_decides(X) )
& ! [X] :
( ( program_decides(X)
& program(X) )
| ~ program_program_decides(X) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0] :
( program(X0)
| ~ program_program_decides(X0) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f35,plain,
! [X,Y] :
( ( ~ halts2(X,Y)
| ~ program(X)
| program_halts2(X,Y) )
& ( ( halts2(X,Y)
& program(X) )
| ~ program_halts2(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f36,plain,
( ! [X,Y] :
( ~ halts2(X,Y)
| ~ program(X)
| program_halts2(X,Y) )
& ! [X,Y] :
( ( halts2(X,Y)
& program(X) )
| ~ program_halts2(X,Y) ) ),
inference(miniscoping,[status(thm)],[f35]) ).
fof(f38,plain,
! [X0,X1] :
( halts2(X0,X1)
| ~ program_halts2(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f39,plain,
! [X0,X1] :
( ~ halts2(X0,X1)
| ~ program(X0)
| program_halts2(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f45,plain,
! [X,Y] :
( ( halts2(X,Y)
| ~ program(X)
| program_not_halts2(X,Y) )
& ( ( ~ halts2(X,Y)
& program(X) )
| ~ program_not_halts2(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f46,plain,
( ! [X,Y] :
( halts2(X,Y)
| ~ program(X)
| program_not_halts2(X,Y) )
& ! [X,Y] :
( ( ~ halts2(X,Y)
& program(X) )
| ~ program_not_halts2(X,Y) ) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f49,plain,
! [X0,X1] :
( halts2(X0,X1)
| ~ program(X0)
| program_not_halts2(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f50,plain,
! [X,Y,W] :
( ( ~ outputs(X,W)
| ~ halts2(X,Y)
| halts2_outputs(X,Y,W) )
& ( ( outputs(X,W)
& halts2(X,Y) )
| ~ halts2_outputs(X,Y,W) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f51,plain,
( ! [X,Y,W] :
( ~ outputs(X,W)
| ~ halts2(X,Y)
| halts2_outputs(X,Y,W) )
& ! [X,Y,W] :
( ( outputs(X,W)
& halts2(X,Y) )
| ~ halts2_outputs(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( halts2(X0,X1)
| ~ halts2_outputs(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f73,plain,
! [X,Y,W] :
( program_not_halts2_halts2_outputs(X,Y,W)
<=> ( halts2_outputs(X,Y,W)
| ~ program_not_halts2(Y,Y) ) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f74,plain,
! [X,Y,W] :
( ( ( ~ halts2_outputs(X,Y,W)
& program_not_halts2(Y,Y) )
| program_not_halts2_halts2_outputs(X,Y,W) )
& ( halts2_outputs(X,Y,W)
| ~ program_not_halts2(Y,Y)
| ~ program_not_halts2_halts2_outputs(X,Y,W) ) ),
inference(NNF_transformation,[status(thm)],[f73]) ).
fof(f75,plain,
( ! [X,Y,W] :
( ( ~ halts2_outputs(X,Y,W)
& program_not_halts2(Y,Y) )
| program_not_halts2_halts2_outputs(X,Y,W) )
& ! [X,Y,W] :
( halts2_outputs(X,Y,W)
| ~ program_not_halts2(Y,Y)
| ~ program_not_halts2_halts2_outputs(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f74]) ).
fof(f76,plain,
! [X0,X1,X2] :
( halts2_outputs(X0,X1,X2)
| ~ program_not_halts2(X1,X1)
| ~ program_not_halts2_halts2_outputs(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f79,plain,
( ? [W] : program_program_decides(W)
| ! [X] : ~ algorithm_program_decides(X) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f80,plain,
( program_program_decides(sK2_skl)
| ! [X] : ~ algorithm_program_decides(X) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(W,sK2_skl)],[f79]) ).
fof(f81,plain,
! [X0] :
( program_program_decides(sK2_skl)
| ~ algorithm_program_decides(X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f82,plain,
! [W] :
( ! [Y,Z] :
( program_not_halts2_halts3_outputs(W,Y,Z,bad)
& program_halts2_halts3_outputs(W,Y,Z,good) )
| ~ program_program_decides(W) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f83,plain,
! [W] :
( ( ! [Y,Z] : program_not_halts2_halts3_outputs(W,Y,Z,bad)
& ! [Y,Z] : program_halts2_halts3_outputs(W,Y,Z,good) )
| ~ program_program_decides(W) ),
inference(miniscoping,[status(thm)],[f82]) ).
fof(f84,plain,
! [X0,X1,X2] :
( program_halts2_halts3_outputs(X0,X1,X2,good)
| ~ program_program_decides(X0) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f85,plain,
! [X0,X1,X2] :
( program_not_halts2_halts3_outputs(X0,X1,X2,bad)
| ~ program_program_decides(X0) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f86,plain,
( ? [V] :
( ! [Y] :
( program_not_halts2_halts2_outputs(V,Y,bad)
& program_halts2_halts2_outputs(V,Y,good) )
& program(V) )
| ! [W] :
( ? [Y] :
( ~ program_not_halts2_halts3_outputs(W,Y,Y,bad)
| ~ program_halts2_halts3_outputs(W,Y,Y,good) )
| ~ program(W) ) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f87,plain,
( ? [V] :
( ! [Y] : program_not_halts2_halts2_outputs(V,Y,bad)
& ! [Y] : program_halts2_halts2_outputs(V,Y,good)
& program(V) )
| ! [W] :
( ? [Y] : ~ program_not_halts2_halts3_outputs(W,Y,Y,bad)
| ? [Y] : ~ program_halts2_halts3_outputs(W,Y,Y,good)
| ~ program(W) ) ),
inference(miniscoping,[status(thm)],[f86]) ).
fof(f88,plain,
( ( ! [Y] : program_not_halts2_halts2_outputs(sK5_skl,Y,bad)
& ! [Y] : program_halts2_halts2_outputs(sK5_skl,Y,good)
& program(sK5_skl) )
| ! [W] :
( ~ program_not_halts2_halts3_outputs(W,sK4_skl(W),sK4_skl(W),bad)
| ~ program_halts2_halts3_outputs(W,sK3_skl(W),sK3_skl(W),good)
| ~ program(W) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(Y,sK3_skl(W)),skolemize(Y,sK4_skl(W)),skolemize(V,sK5_skl)],[f87]) ).
fof(f89,plain,
! [X0] :
( program(sK5_skl)
| ~ program_not_halts2_halts3_outputs(X0,sK4_skl(X0),sK4_skl(X0),bad)
| ~ program_halts2_halts3_outputs(X0,sK3_skl(X0),sK3_skl(X0),good)
| ~ program(X0) ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f90,plain,
! [X0,X1] :
( program_halts2_halts2_outputs(sK5_skl,X1,good)
| ~ program_not_halts2_halts3_outputs(X0,sK4_skl(X0),sK4_skl(X0),bad)
| ~ program_halts2_halts3_outputs(X0,sK3_skl(X0),sK3_skl(X0),good)
| ~ program(X0) ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f91,plain,
! [X0,X1] :
( program_not_halts2_halts2_outputs(sK5_skl,X1,bad)
| ~ program_not_halts2_halts3_outputs(X0,sK4_skl(X0),sK4_skl(X0),bad)
| ~ program_halts2_halts3_outputs(X0,sK3_skl(X0),sK3_skl(X0),good)
| ~ program(X0) ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f92,plain,
( ? [U] :
( ! [Y] :
( program_not_halts2_halts2_outputs(U,Y,good)
& ( ~ halts2(U,Y)
| ~ program_halts2(Y,Y) ) )
& program(U) )
| ! [V] :
( ? [Y] :
( ~ program_not_halts2_halts2_outputs(V,Y,bad)
| ~ program_halts2_halts2_outputs(V,Y,good) )
| ~ program(V) ) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f93,plain,
( ? [U] :
( ! [Y] : program_not_halts2_halts2_outputs(U,Y,good)
& ! [Y] :
( ~ halts2(U,Y)
| ~ program_halts2(Y,Y) )
& program(U) )
| ! [V] :
( ? [Y] : ~ program_not_halts2_halts2_outputs(V,Y,bad)
| ? [Y] : ~ program_halts2_halts2_outputs(V,Y,good)
| ~ program(V) ) ),
inference(miniscoping,[status(thm)],[f92]) ).
fof(f94,plain,
( ( ! [Y] : program_not_halts2_halts2_outputs(sK8_skl,Y,good)
& ! [Y] :
( ~ halts2(sK8_skl,Y)
| ~ program_halts2(Y,Y) )
& program(sK8_skl) )
| ! [V] :
( ~ program_not_halts2_halts2_outputs(V,sK7_skl(V),bad)
| ~ program_halts2_halts2_outputs(V,sK6_skl(V),good)
| ~ program(V) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl,sK8_skl]),skolemize(Y,sK6_skl(V)),skolemize(Y,sK7_skl(V)),skolemize(U,sK8_skl)],[f93]) ).
fof(f95,plain,
! [X0] :
( program(sK8_skl)
| ~ program_not_halts2_halts2_outputs(X0,sK7_skl(X0),bad)
| ~ program_halts2_halts2_outputs(X0,sK6_skl(X0),good)
| ~ program(X0) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f96,plain,
! [X0,X1] :
( ~ halts2(sK8_skl,X1)
| ~ program_halts2(X1,X1)
| ~ program_not_halts2_halts2_outputs(X0,sK7_skl(X0),bad)
| ~ program_halts2_halts2_outputs(X0,sK6_skl(X0),good)
| ~ program(X0) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f97,plain,
! [X0,X1] :
( program_not_halts2_halts2_outputs(sK8_skl,X1,good)
| ~ program_not_halts2_halts2_outputs(X0,sK7_skl(X0),bad)
| ~ program_halts2_halts2_outputs(X0,sK6_skl(X0),good)
| ~ program(X0) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f98,plain,
algorithm_program_decides(sK9_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(X,sK9_skl)],[f17]) ).
fof(f99,plain,
algorithm_program_decides(sK9_skl),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f100,definition,
! [X0] :
( sQ0_spl
<=> ~ algorithm_program_decides(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f101,plain,
! [X0] :
( ~ sQ0_spl
| ~ algorithm_program_decides(X0) ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f103,definition,
( sQ1_spl
<=> program_program_decides(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f104,plain,
( ~ sQ1_spl
| program_program_decides(sK2_skl) ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f81,f100,f103]) ).
fof(f107,definition,
! [X0] :
( sQ2_spl
<=> ( ~ program_not_halts2_halts3_outputs(X0,sK4_skl(X0),sK4_skl(X0),bad)
| ~ program_halts2_halts3_outputs(X0,sK3_skl(X0),sK3_skl(X0),good)
| ~ program(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f108,plain,
! [X0] :
( ~ sQ2_spl
| ~ program_not_halts2_halts3_outputs(X0,sK4_skl(X0),sK4_skl(X0),bad)
| ~ program_halts2_halts3_outputs(X0,sK3_skl(X0),sK3_skl(X0),good)
| ~ program(X0) ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,definition,
( sQ3_spl
<=> program(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f111,plain,
( ~ sQ3_spl
| program(sK5_skl) ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f113,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f89,f107,f110]) ).
fof(f114,definition,
! [X1] :
( sQ4_spl
<=> program_halts2_halts2_outputs(sK5_skl,X1,good) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f115,plain,
! [X0] :
( ~ sQ4_spl
| program_halts2_halts2_outputs(sK5_skl,X0,good) ),
inference(component_clause,[status(thm)],[f114]) ).
fof(f117,plain,
( sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f90,f107,f114]) ).
fof(f118,definition,
! [X1] :
( sQ5_spl
<=> program_not_halts2_halts2_outputs(sK5_skl,X1,bad) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f119,plain,
! [X0] :
( ~ sQ5_spl
| program_not_halts2_halts2_outputs(sK5_skl,X0,bad) ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,plain,
( sQ5_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f91,f107,f118]) ).
fof(f122,definition,
! [X0] :
( sQ6_spl
<=> ( ~ program_not_halts2_halts2_outputs(X0,sK7_skl(X0),bad)
| ~ program_halts2_halts2_outputs(X0,sK6_skl(X0),good)
| ~ program(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f123,plain,
! [X0] :
( ~ sQ6_spl
| ~ program_not_halts2_halts2_outputs(X0,sK7_skl(X0),bad)
| ~ program_halts2_halts2_outputs(X0,sK6_skl(X0),good)
| ~ program(X0) ),
inference(component_clause,[status(thm)],[f122]) ).
fof(f125,definition,
( sQ7_spl
<=> program(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ7_spl
| program(sK8_skl) ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f95,f122,f125]) ).
fof(f129,definition,
! [X1] :
( sQ8_spl
<=> ( ~ halts2(sK8_skl,X1)
| ~ program_halts2(X1,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f130,plain,
! [X0] :
( ~ sQ8_spl
| ~ halts2(sK8_skl,X0)
| ~ program_halts2(X0,X0) ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,plain,
( sQ8_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f96,f122,f129]) ).
fof(f133,definition,
! [X1] :
( sQ9_spl
<=> program_not_halts2_halts2_outputs(sK8_skl,X1,good) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f134,plain,
! [X0] :
( ~ sQ9_spl
| program_not_halts2_halts2_outputs(sK8_skl,X0,good) ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( sQ9_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f97,f122,f133]) ).
fof(f137,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f99,f101]) ).
fof(f138,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f137]) ).
fof(f199,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ program_not_halts2_halts2_outputs(sK5_skl,sK7_skl(sK5_skl),bad)
| ~ program_halts2_halts2_outputs(sK5_skl,sK6_skl(sK5_skl),good) ),
inference(resolution,[status(thm)],[f111,f123]) ).
fof(f202,definition,
( sQ19_spl
<=> program_halts2_halts2_outputs(sK5_skl,sK6_skl(sK5_skl),good) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f204,plain,
( sQ19_spl
| ~ program_halts2_halts2_outputs(sK5_skl,sK6_skl(sK5_skl),good) ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,definition,
( sQ20_spl
<=> program_not_halts2_halts2_outputs(sK5_skl,sK7_skl(sK5_skl),bad) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f207,plain,
( sQ20_spl
| ~ program_not_halts2_halts2_outputs(sK5_skl,sK7_skl(sK5_skl),bad) ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f199,f202,f205,f110,f122]) ).
fof(f222,plain,
( sQ20_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f207,f119]) ).
fof(f223,plain,
( sQ20_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f222]) ).
fof(f224,plain,
! [X0] :
( ~ sQ7_spl
| ~ halts2(sK8_skl,X0)
| program_halts2(sK8_skl,X0) ),
inference(resolution,[status(thm)],[f126,f39]) ).
fof(f233,plain,
( sQ19_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f204,f115]) ).
fof(f234,plain,
( sQ19_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f233]) ).
fof(f235,plain,
! [X0] :
( ~ sQ7_spl
| ~ program(sK8_skl)
| program_not_halts2(sK8_skl,X0)
| program_halts2(sK8_skl,X0) ),
inference(resolution,[status(thm)],[f224,f49]) ).
fof(f236,plain,
! [X0,X1] :
( ~ sQ7_spl
| ~ halts2_outputs(sK8_skl,X0,X1)
| program_halts2(sK8_skl,X0) ),
inference(resolution,[status(thm)],[f224,f52]) ).
fof(f238,definition,
! [X0] :
( sQ24_spl
<=> ( program_not_halts2(sK8_skl,X0)
| program_halts2(sK8_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f239,plain,
! [X0] :
( ~ sQ24_spl
| program_not_halts2(sK8_skl,X0)
| program_halts2(sK8_skl,X0) ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f241,plain,
( ~ sQ7_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f235,f238,f125]) ).
fof(f288,plain,
! [X0,X1] :
( ~ sQ24_spl
| halts2_outputs(X0,sK8_skl,X1)
| ~ program_not_halts2_halts2_outputs(X0,sK8_skl,X1)
| program_halts2(sK8_skl,sK8_skl) ),
inference(resolution,[status(thm)],[f239,f76]) ).
fof(f291,definition,
( sQ36_spl
<=> program_halts2(sK8_skl,sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f292,plain,
( ~ sQ36_spl
| program_halts2(sK8_skl,sK8_skl) ),
inference(component_clause,[status(thm)],[f291]) ).
fof(f294,definition,
! [X0,X1] :
( sQ37_spl
<=> ( halts2_outputs(X0,sK8_skl,X1)
| ~ program_not_halts2_halts2_outputs(X0,sK8_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f295,plain,
! [X0,X1] :
( ~ sQ37_spl
| halts2_outputs(X0,sK8_skl,X1)
| ~ program_not_halts2_halts2_outputs(X0,sK8_skl,X1) ),
inference(component_clause,[status(thm)],[f294]) ).
fof(f297,plain,
( ~ sQ24_spl
| sQ37_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f288,f291,f294,f238]) ).
fof(f310,plain,
( ~ sQ8_spl
| ~ sQ36_spl
| ~ halts2(sK8_skl,sK8_skl) ),
inference(resolution,[status(thm)],[f292,f130]) ).
fof(f346,plain,
( ~ sQ8_spl
| ~ sQ36_spl
| ~ program_halts2(sK8_skl,sK8_skl) ),
inference(resolution,[status(thm)],[f310,f38]) ).
fof(f351,plain,
( ~ sQ8_spl
| ~ sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f346,f292]) ).
fof(f352,plain,
( ~ sQ8_spl
| ~ sQ36_spl ),
inference(contradiction_clause,[status(thm)],[f351]) ).
fof(f362,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ37_spl
| program_halts2(sK8_skl,sK8_skl)
| ~ program_not_halts2_halts2_outputs(sK8_skl,sK8_skl,X0) ),
inference(resolution,[status(thm)],[f295,f236]) ).
fof(f366,definition,
! [X0] :
( sQ44_spl
<=> ~ program_not_halts2_halts2_outputs(sK8_skl,sK8_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f367,plain,
! [X0] :
( ~ sQ44_spl
| ~ program_not_halts2_halts2_outputs(sK8_skl,sK8_skl,X0) ),
inference(component_clause,[status(thm)],[f366]) ).
fof(f369,plain,
( ~ sQ7_spl
| ~ sQ37_spl
| sQ36_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f362,f366,f291,f294,f125]) ).
fof(f401,plain,
( ~ sQ9_spl
| ~ sQ44_spl
| $false ),
inference(resolution,[status(thm)],[f367,f134]) ).
fof(f404,plain,
( ~ sQ9_spl
| ~ sQ44_spl ),
inference(contradiction_clause,[status(thm)],[f401]) ).
fof(f432,plain,
! [X0] :
( ~ sQ2_spl
| ~ program_program_decides(X0)
| ~ program_halts2_halts3_outputs(X0,sK3_skl(X0),sK3_skl(X0),good)
| ~ program(X0) ),
inference(resolution,[status(thm)],[f108,f85]) ).
fof(f435,plain,
! [X0] :
( ~ sQ2_spl
| ~ program_program_decides(X0)
| ~ program_halts2_halts3_outputs(X0,sK3_skl(X0),sK3_skl(X0),good) ),
inference(forward_subsumption_resolution,[status(thm)],[f432,f27]) ).
fof(f465,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f104,f467]) ).
fof(f467,plain,
! [X0] :
( ~ sQ2_spl
| ~ program_program_decides(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f435,f84]) ).
fof(f468,plain,
( ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f465]) ).
fof(f469,plain,
$false,
inference(sat_refutation,[status(thm)],[f106,f113,f117,f121,f128,f132,f136,f138,f208,f223,f234,f241,f297,f352,f369,f404,f468]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM003+2 : TPTP v9.3.1. Bugfixed v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 14:18:38 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.43 % Elapsed time: 0.047097 seconds
% 0.09/0.43 % CPU time: 0.162539 seconds
% 0.09/0.43 % Total memory used: 13.416 MB
% 0.09/0.43 % Net memory used: 13.315 MB
%------------------------------------------------------------------------------