%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COM003+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 12:10:14 PM UTC 2026
% Result : Theorem 0.12s 0.43s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 11
% Syntax : Number of formulae : 138 ( 13 unt; 6 def)
% Number of atoms : 642 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 834 ( 330 ~; 323 |; 154 &)
% ( 8 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 302 ( 266 !; 36 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( ? [X] :
( ! [Y] :
( program(Y)
=> ! [Z] : decides(X,Y,Z) )
& algorithm(X) )
=> ? [W] :
( ! [Y] :
( program(Y)
=> ! [Z] : decides(W,Y,Z) )
& program(W) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [W] :
( ( ! [Y] :
( program(Y)
=> ! [Z] : decides(W,Y,Z) )
& program(W) )
=> ! [Y,Z] :
( ( ( ~ halts2(Y,Z)
& program(Y) )
=> ( outputs(W,bad)
& halts3(W,Y,Z) ) )
& ( ( halts2(Y,Z)
& program(Y) )
=> ( outputs(W,good)
& halts3(W,Y,Z) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
( ? [W] :
( ! [Y] :
( ( ( ~ halts2(Y,Y)
& program(Y) )
=> ( outputs(W,bad)
& halts3(W,Y,Y) ) )
& ( ( halts2(Y,Y)
& program(Y) )
=> ( outputs(W,good)
& halts3(W,Y,Y) ) ) )
& program(W) )
=> ? [V] :
( ! [Y] :
( ( ( ~ halts2(Y,Y)
& program(Y) )
=> ( outputs(V,bad)
& halts2(V,Y) ) )
& ( ( halts2(Y,Y)
& program(Y) )
=> ( outputs(V,good)
& halts2(V,Y) ) ) )
& program(V) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
( ? [V] :
( ! [Y] :
( ( ( ~ halts2(Y,Y)
& program(Y) )
=> ( outputs(V,bad)
& halts2(V,Y) ) )
& ( ( halts2(Y,Y)
& program(Y) )
=> ( outputs(V,good)
& halts2(V,Y) ) ) )
& program(V) )
=> ? [U] :
( ! [Y] :
( ( ( ~ halts2(Y,Y)
& program(Y) )
=> ( outputs(U,bad)
& halts2(U,Y) ) )
& ( ( halts2(Y,Y)
& program(Y) )
=> ~ halts2(U,Y) ) )
& program(U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,conjecture,
~ ? [X1] :
( ! [Y1] :
( program(Y1)
=> ! [Z1] : decides(X1,Y1,Z1) )
& algorithm(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
~ ~ ? [X1] :
( ! [Y1] :
( program(Y1)
=> ! [Z1] : decides(X1,Y1,Z1) )
& algorithm(X1) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,plain,
( ? [W] :
( ! [Y] :
( ! [Z] : decides(W,Y,Z)
| ~ program(Y) )
& program(W) )
| ! [X] :
( ? [Y] :
( ? [Z] : ~ decides(X,Y,Z)
& program(Y) )
| ~ algorithm(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f8,definition,
! [X,Y] :
( sP0_prd(Y,X)
<=> ( ? [Z] : ~ decides(X,Y,Z)
& program(Y) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f9,plain,
( ? [W] :
( ! [Y] :
( ! [Z] : decides(W,Y,Z)
| ~ program(Y) )
& program(W) )
| ! [X] :
( ? [Y] : sP0_prd(Y,X)
| ~ algorithm(X) ) ),
inference(formula_renaming,[status(thm)],[f7,f8]) ).
fof(f10,plain,
( ( ! [Y] :
( ! [Z] : decides(sK1_skl,Y,Z)
| ~ program(Y) )
& program(sK1_skl) )
| ! [X] :
( sP0_prd(sK0_skl(X),X)
| ~ algorithm(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl(X)),skolemize(W,sK1_skl)],[f9]) ).
fof(f11,plain,
! [X0] :
( program(sK1_skl)
| sP0_prd(sK0_skl(X0),X0)
| ~ algorithm(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f12,plain,
! [X0,X1,X2] :
( decides(sK1_skl,X1,X2)
| ~ program(X1)
| sP0_prd(sK0_skl(X0),X0)
| ~ algorithm(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f13,plain,
! [W] :
( ! [Y,Z] :
( ( ( outputs(W,bad)
& halts3(W,Y,Z) )
| halts2(Y,Z)
| ~ program(Y) )
& ( ( outputs(W,good)
& halts3(W,Y,Z) )
| ~ halts2(Y,Z)
| ~ program(Y) ) )
| ? [Y] :
( ? [Z] : ~ decides(W,Y,Z)
& program(Y) )
| ~ program(W) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f14,definition,
! [W,Y] :
( sP1_prd(Y,W)
<=> ( ? [Z] : ~ decides(W,Y,Z)
& program(Y) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f15,plain,
! [W] :
( ! [Y,Z] :
( ( ( outputs(W,bad)
& halts3(W,Y,Z) )
| halts2(Y,Z)
| ~ program(Y) )
& ( ( outputs(W,good)
& halts3(W,Y,Z) )
| ~ halts2(Y,Z)
| ~ program(Y) ) )
| ? [Y] : sP1_prd(Y,W)
| ~ program(W) ),
inference(formula_renaming,[status(thm)],[f13,f14]) ).
fof(f16,plain,
! [W] :
( ( ! [Y,Z] :
( ( outputs(W,bad)
& halts3(W,Y,Z) )
| halts2(Y,Z)
| ~ program(Y) )
& ! [Y,Z] :
( ( outputs(W,good)
& halts3(W,Y,Z) )
| ~ halts2(Y,Z)
| ~ program(Y) ) )
| ? [Y] : sP1_prd(Y,W)
| ~ program(W) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f17,plain,
! [W] :
( ( ! [Y,Z] :
( ( outputs(W,bad)
& halts3(W,Y,Z) )
| halts2(Y,Z)
| ~ program(Y) )
& ! [Y,Z] :
( ( outputs(W,good)
& halts3(W,Y,Z) )
| ~ halts2(Y,Z)
| ~ program(Y) ) )
| sP1_prd(sK2_skl(W),W)
| ~ program(W) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y,sK2_skl(W))],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( halts3(X0,X1,X2)
| ~ halts2(X1,X2)
| ~ program(X1)
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( outputs(X0,good)
| ~ halts2(X1,X2)
| ~ program(X1)
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
! [X0,X1,X2] :
( halts3(X0,X1,X2)
| halts2(X1,X2)
| ~ program(X1)
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f21,plain,
! [X0,X1,X2] :
( outputs(X0,bad)
| halts2(X1,X2)
| ~ program(X1)
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f22,plain,
( ? [V] :
( ! [Y] :
( ( ( outputs(V,bad)
& halts2(V,Y) )
| halts2(Y,Y)
| ~ program(Y) )
& ( ( outputs(V,good)
& halts2(V,Y) )
| ~ halts2(Y,Y)
| ~ program(Y) ) )
& program(V) )
| ! [W] :
( ? [Y] :
( ( ( ~ outputs(W,bad)
| ~ halts3(W,Y,Y) )
& ~ halts2(Y,Y)
& program(Y) )
| ( ( ~ outputs(W,good)
| ~ halts3(W,Y,Y) )
& halts2(Y,Y)
& program(Y) ) )
| ~ program(W) ) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f23,definition,
! [W,Y] :
( sP2_prd(Y,W)
<=> ( ( ( ~ outputs(W,bad)
| ~ halts3(W,Y,Y) )
& ~ halts2(Y,Y)
& program(Y) )
| ( ( ~ outputs(W,good)
| ~ halts3(W,Y,Y) )
& halts2(Y,Y)
& program(Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f24,plain,
( ? [V] :
( ! [Y] :
( ( ( outputs(V,bad)
& halts2(V,Y) )
| halts2(Y,Y)
| ~ program(Y) )
& ( ( outputs(V,good)
& halts2(V,Y) )
| ~ halts2(Y,Y)
| ~ program(Y) ) )
& program(V) )
| ! [W] :
( ? [Y] : sP2_prd(Y,W)
| ~ program(W) ) ),
inference(formula_renaming,[status(thm)],[f22,f23]) ).
fof(f25,plain,
( ? [V] :
( ! [Y] :
( ( outputs(V,bad)
& halts2(V,Y) )
| halts2(Y,Y)
| ~ program(Y) )
& ! [Y] :
( ( outputs(V,good)
& halts2(V,Y) )
| ~ halts2(Y,Y)
| ~ program(Y) )
& program(V) )
| ! [W] :
( ? [Y] : sP2_prd(Y,W)
| ~ program(W) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f26,plain,
( ( ! [Y] :
( ( outputs(sK4_skl,bad)
& halts2(sK4_skl,Y) )
| halts2(Y,Y)
| ~ program(Y) )
& ! [Y] :
( ( outputs(sK4_skl,good)
& halts2(sK4_skl,Y) )
| ~ halts2(Y,Y)
| ~ program(Y) )
& program(sK4_skl) )
| ! [W] :
( sP2_prd(sK3_skl(W),W)
| ~ program(W) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(Y,sK3_skl(W)),skolemize(V,sK4_skl)],[f25]) ).
fof(f27,plain,
! [X0] :
( program(sK4_skl)
| sP2_prd(sK3_skl(X0),X0)
| ~ program(X0) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( halts2(sK4_skl,X1)
| ~ halts2(X1,X1)
| ~ program(X1)
| sP2_prd(sK3_skl(X0),X0)
| ~ program(X0) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f29,plain,
! [X0,X1] :
( outputs(sK4_skl,good)
| ~ halts2(X1,X1)
| ~ program(X1)
| sP2_prd(sK3_skl(X0),X0)
| ~ program(X0) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f30,plain,
! [X0,X1] :
( halts2(sK4_skl,X1)
| halts2(X1,X1)
| ~ program(X1)
| sP2_prd(sK3_skl(X0),X0)
| ~ program(X0) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f31,plain,
! [X0,X1] :
( outputs(sK4_skl,bad)
| halts2(X1,X1)
| ~ program(X1)
| sP2_prd(sK3_skl(X0),X0)
| ~ program(X0) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f32,plain,
( ? [U] :
( ! [Y] :
( ( ( outputs(U,bad)
& halts2(U,Y) )
| halts2(Y,Y)
| ~ program(Y) )
& ( ~ halts2(U,Y)
| ~ halts2(Y,Y)
| ~ program(Y) ) )
& program(U) )
| ! [V] :
( ? [Y] :
( ( ( ~ outputs(V,bad)
| ~ halts2(V,Y) )
& ~ halts2(Y,Y)
& program(Y) )
| ( ( ~ outputs(V,good)
| ~ halts2(V,Y) )
& halts2(Y,Y)
& program(Y) ) )
| ~ program(V) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f33,definition,
! [V,Y] :
( sP3_prd(Y,V)
<=> ( ( ( ~ outputs(V,bad)
| ~ halts2(V,Y) )
& ~ halts2(Y,Y)
& program(Y) )
| ( ( ~ outputs(V,good)
| ~ halts2(V,Y) )
& halts2(Y,Y)
& program(Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f34,plain,
( ? [U] :
( ! [Y] :
( ( ( outputs(U,bad)
& halts2(U,Y) )
| halts2(Y,Y)
| ~ program(Y) )
& ( ~ halts2(U,Y)
| ~ halts2(Y,Y)
| ~ program(Y) ) )
& program(U) )
| ! [V] :
( ? [Y] : sP3_prd(Y,V)
| ~ program(V) ) ),
inference(formula_renaming,[status(thm)],[f32,f33]) ).
fof(f35,plain,
( ? [U] :
( ! [Y] :
( ( outputs(U,bad)
& halts2(U,Y) )
| halts2(Y,Y)
| ~ program(Y) )
& ! [Y] :
( ~ halts2(U,Y)
| ~ halts2(Y,Y)
| ~ program(Y) )
& program(U) )
| ! [V] :
( ? [Y] : sP3_prd(Y,V)
| ~ program(V) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f36,plain,
( ( ! [Y] :
( ( outputs(sK6_skl,bad)
& halts2(sK6_skl,Y) )
| halts2(Y,Y)
| ~ program(Y) )
& ! [Y] :
( ~ halts2(sK6_skl,Y)
| ~ halts2(Y,Y)
| ~ program(Y) )
& program(sK6_skl) )
| ! [V] :
( sP3_prd(sK5_skl(V),V)
| ~ program(V) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl]),skolemize(Y,sK5_skl(V)),skolemize(U,sK6_skl)],[f35]) ).
fof(f37,plain,
! [X0] :
( program(sK6_skl)
| sP3_prd(sK5_skl(X0),X0)
| ~ program(X0) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ~ halts2(sK6_skl,X1)
| ~ halts2(X1,X1)
| ~ program(X1)
| sP3_prd(sK5_skl(X0),X0)
| ~ program(X0) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f39,plain,
! [X0,X1] :
( halts2(sK6_skl,X1)
| halts2(X1,X1)
| ~ program(X1)
| sP3_prd(sK5_skl(X0),X0)
| ~ program(X0) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f41,plain,
? [X1] :
( ! [Y1] :
( ! [Z1] : decides(X1,Y1,Z1)
| ~ program(Y1) )
& algorithm(X1) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f42,plain,
( ! [Y1] :
( ! [Z1] : decides(sK7_skl,Y1,Z1)
| ~ program(Y1) )
& algorithm(sK7_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(X1,sK7_skl)],[f41]) ).
fof(f43,plain,
algorithm(sK7_skl),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( decides(sK7_skl,X0,X1)
| ~ program(X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f45,plain,
! [X,Y] :
( ( ! [Z] : decides(X,Y,Z)
| ~ program(Y)
| sP0_prd(Y,X) )
& ( ( ? [Z] : ~ decides(X,Y,Z)
& program(Y) )
| ~ sP0_prd(Y,X) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f46,plain,
( ! [X,Y] :
( ! [Z] : decides(X,Y,Z)
| ~ program(Y)
| sP0_prd(Y,X) )
& ! [X,Y] :
( ( ? [Z] : ~ decides(X,Y,Z)
& program(Y) )
| ~ sP0_prd(Y,X) ) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f47,plain,
( ! [X,Y] :
( ! [Z] : decides(X,Y,Z)
| ~ program(Y)
| sP0_prd(Y,X) )
& ! [X,Y] :
( ( ~ decides(X,Y,sK8_skl(Y,X))
& program(Y) )
| ~ sP0_prd(Y,X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(Z,sK8_skl(Y,X))],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( program(X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( ~ decides(X1,X0,sK8_skl(X0,X1))
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f51,plain,
! [W,Y] :
( ( ! [Z] : decides(W,Y,Z)
| ~ program(Y)
| sP1_prd(Y,W) )
& ( ( ? [Z] : ~ decides(W,Y,Z)
& program(Y) )
| ~ sP1_prd(Y,W) ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f52,plain,
( ! [W,Y] :
( ! [Z] : decides(W,Y,Z)
| ~ program(Y)
| sP1_prd(Y,W) )
& ! [W,Y] :
( ( ? [Z] : ~ decides(W,Y,Z)
& program(Y) )
| ~ sP1_prd(Y,W) ) ),
inference(miniscoping,[status(thm)],[f51]) ).
fof(f53,plain,
( ! [W,Y] :
( ! [Z] : decides(W,Y,Z)
| ~ program(Y)
| sP1_prd(Y,W) )
& ! [W,Y] :
( ( ~ decides(W,Y,sK9_skl(Y,W))
& program(Y) )
| ~ sP1_prd(Y,W) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(Z,sK9_skl(Y,W))],[f52]) ).
fof(f54,plain,
! [X0,X1] :
( program(X0)
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f55,plain,
! [X0,X1] :
( ~ decides(X1,X0,sK9_skl(X0,X1))
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f57,definition,
! [W,Y] :
( sP4_prd(Y,W)
<=> ( ( ~ outputs(W,good)
| ~ halts3(W,Y,Y) )
& halts2(Y,Y)
& program(Y) ) ),
introduced(definition,[new_symbols(definition,[sP4_prd])],[]) ).
fof(f58,plain,
! [W,Y] :
( sP2_prd(Y,W)
<=> ( ( ( ~ outputs(W,bad)
| ~ halts3(W,Y,Y) )
& ~ halts2(Y,Y)
& program(Y) )
| sP4_prd(Y,W) ) ),
inference(formula_renaming,[status(thm)],[f23,f57]) ).
fof(f59,plain,
! [W,Y] :
( ( ( ( ( outputs(W,bad)
& halts3(W,Y,Y) )
| halts2(Y,Y)
| ~ program(Y) )
& ~ sP4_prd(Y,W) )
| sP2_prd(Y,W) )
& ( ( ( ~ outputs(W,bad)
| ~ halts3(W,Y,Y) )
& ~ halts2(Y,Y)
& program(Y) )
| sP4_prd(Y,W)
| ~ sP2_prd(Y,W) ) ),
inference(NNF_transformation,[status(thm)],[f58]) ).
fof(f60,plain,
( ! [W,Y] :
( ( ( ( outputs(W,bad)
& halts3(W,Y,Y) )
| halts2(Y,Y)
| ~ program(Y) )
& ~ sP4_prd(Y,W) )
| sP2_prd(Y,W) )
& ! [W,Y] :
( ( ( ~ outputs(W,bad)
| ~ halts3(W,Y,Y) )
& ~ halts2(Y,Y)
& program(Y) )
| sP4_prd(Y,W)
| ~ sP2_prd(Y,W) ) ),
inference(miniscoping,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0,X1] :
( program(X0)
| sP4_prd(X0,X1)
| ~ sP2_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f62,plain,
! [X0,X1] :
( ~ halts2(X0,X0)
| sP4_prd(X0,X1)
| ~ sP2_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f63,plain,
! [X0,X1] :
( ~ outputs(X1,bad)
| ~ halts3(X1,X0,X0)
| sP4_prd(X0,X1)
| ~ sP2_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f67,definition,
! [V,Y] :
( sP5_prd(Y,V)
<=> ( ( ~ outputs(V,good)
| ~ halts2(V,Y) )
& halts2(Y,Y)
& program(Y) ) ),
introduced(definition,[new_symbols(definition,[sP5_prd])],[]) ).
fof(f68,plain,
! [V,Y] :
( sP3_prd(Y,V)
<=> ( ( ( ~ outputs(V,bad)
| ~ halts2(V,Y) )
& ~ halts2(Y,Y)
& program(Y) )
| sP5_prd(Y,V) ) ),
inference(formula_renaming,[status(thm)],[f33,f67]) ).
fof(f69,plain,
! [V,Y] :
( ( ( ( ( outputs(V,bad)
& halts2(V,Y) )
| halts2(Y,Y)
| ~ program(Y) )
& ~ sP5_prd(Y,V) )
| sP3_prd(Y,V) )
& ( ( ( ~ outputs(V,bad)
| ~ halts2(V,Y) )
& ~ halts2(Y,Y)
& program(Y) )
| sP5_prd(Y,V)
| ~ sP3_prd(Y,V) ) ),
inference(NNF_transformation,[status(thm)],[f68]) ).
fof(f70,plain,
( ! [V,Y] :
( ( ( ( outputs(V,bad)
& halts2(V,Y) )
| halts2(Y,Y)
| ~ program(Y) )
& ~ sP5_prd(Y,V) )
| sP3_prd(Y,V) )
& ! [V,Y] :
( ( ( ~ outputs(V,bad)
| ~ halts2(V,Y) )
& ~ halts2(Y,Y)
& program(Y) )
| sP5_prd(Y,V)
| ~ sP3_prd(Y,V) ) ),
inference(miniscoping,[status(thm)],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( program(X0)
| sP5_prd(X0,X1)
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( ~ halts2(X0,X0)
| sP5_prd(X0,X1)
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f73,plain,
! [X0,X1] :
( ~ outputs(X1,bad)
| ~ halts2(X1,X0)
| sP5_prd(X0,X1)
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f77,plain,
! [W,Y] :
( ( ( outputs(W,good)
& halts3(W,Y,Y) )
| ~ halts2(Y,Y)
| ~ program(Y)
| sP4_prd(Y,W) )
& ( ( ( ~ outputs(W,good)
| ~ halts3(W,Y,Y) )
& halts2(Y,Y)
& program(Y) )
| ~ sP4_prd(Y,W) ) ),
inference(NNF_transformation,[status(thm)],[f57]) ).
fof(f78,plain,
( ! [W,Y] :
( ( outputs(W,good)
& halts3(W,Y,Y) )
| ~ halts2(Y,Y)
| ~ program(Y)
| sP4_prd(Y,W) )
& ! [W,Y] :
( ( ( ~ outputs(W,good)
| ~ halts3(W,Y,Y) )
& halts2(Y,Y)
& program(Y) )
| ~ sP4_prd(Y,W) ) ),
inference(miniscoping,[status(thm)],[f77]) ).
fof(f79,plain,
! [X0,X1] :
( program(X0)
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f80,plain,
! [X0,X1] :
( halts2(X0,X0)
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f81,plain,
! [X0,X1] :
( ~ outputs(X1,good)
| ~ halts3(X1,X0,X0)
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f84,plain,
! [V,Y] :
( ( ( outputs(V,good)
& halts2(V,Y) )
| ~ halts2(Y,Y)
| ~ program(Y)
| sP5_prd(Y,V) )
& ( ( ( ~ outputs(V,good)
| ~ halts2(V,Y) )
& halts2(Y,Y)
& program(Y) )
| ~ sP5_prd(Y,V) ) ),
inference(NNF_transformation,[status(thm)],[f67]) ).
fof(f85,plain,
( ! [V,Y] :
( ( outputs(V,good)
& halts2(V,Y) )
| ~ halts2(Y,Y)
| ~ program(Y)
| sP5_prd(Y,V) )
& ! [V,Y] :
( ( ( ~ outputs(V,good)
| ~ halts2(V,Y) )
& halts2(Y,Y)
& program(Y) )
| ~ sP5_prd(Y,V) ) ),
inference(miniscoping,[status(thm)],[f84]) ).
fof(f86,plain,
! [X0,X1] :
( program(X0)
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f88,plain,
! [X0,X1] :
( ~ outputs(X1,good)
| ~ halts2(X1,X0)
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f91,plain,
! [X0,X1] :
( program(X0)
| ~ sP2_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f61,f79]) ).
fof(f92,plain,
! [X0,X1] :
( program(X0)
| ~ sP3_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f71,f86]) ).
fof(f94,plain,
! [X0] :
( ~ program(X0)
| ~ sP0_prd(X0,sK7_skl) ),
inference(resolution,[status(thm)],[f49,f44]) ).
fof(f97,plain,
! [X0] : ~ sP0_prd(X0,sK7_skl),
inference(forward_subsumption_resolution,[status(thm)],[f94,f48]) ).
fof(f99,plain,
! [X0,X1] :
( decides(sK1_skl,X0,X1)
| ~ program(X0)
| ~ algorithm(sK7_skl) ),
inference(resolution,[status(thm)],[f97,f12]) ).
fof(f100,plain,
( program(sK1_skl)
| ~ algorithm(sK7_skl) ),
inference(resolution,[status(thm)],[f97,f11]) ).
fof(f101,plain,
! [X0,X1] :
( decides(sK1_skl,X0,X1)
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f99,f43]) ).
fof(f102,plain,
program(sK1_skl),
inference(forward_subsumption_resolution,[status(thm)],[f100,f43]) ).
fof(f106,plain,
! [X0] :
( ~ program(X0)
| ~ sP1_prd(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f55,f101]) ).
fof(f110,plain,
! [X0] : ~ sP1_prd(X0,sK1_skl),
inference(forward_subsumption_resolution,[status(thm)],[f106,f54]) ).
fof(f121,plain,
! [X0,X1] :
( outputs(sK1_skl,good)
| ~ halts2(X0,X1)
| ~ program(X0)
| ~ program(sK1_skl) ),
inference(resolution,[status(thm)],[f19,f110]) ).
fof(f122,plain,
! [X0,X1] :
( outputs(sK1_skl,good)
| ~ halts2(X0,X1)
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f121,f102]) ).
fof(f123,plain,
! [X0,X1,X2] :
( halts3(X0,X1,X2)
| ~ program(X1)
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f20,f18]) ).
fof(f125,plain,
! [X0,X1] :
( halts3(sK1_skl,X0,X1)
| ~ program(X0)
| ~ program(sK1_skl) ),
inference(resolution,[status(thm)],[f123,f110]) ).
fof(f126,plain,
! [X0,X1] :
( halts3(sK1_skl,X0,X1)
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f125,f102]) ).
fof(f128,plain,
! [X0,X1] :
( outputs(sK1_skl,bad)
| halts2(X0,X1)
| ~ program(X0)
| ~ program(sK1_skl) ),
inference(resolution,[status(thm)],[f21,f110]) ).
fof(f129,plain,
! [X0,X1] :
( outputs(sK1_skl,bad)
| halts2(X0,X1)
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f128,f102]) ).
fof(f190,plain,
! [X0,X1] :
( halts2(sK4_skl,X1)
| ~ program(X1)
| sP2_prd(sK3_skl(X0),X0)
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f30,f28]) ).
fof(f231,plain,
! [X0] :
( ~ program(X0)
| ~ outputs(sK1_skl,good)
| ~ sP4_prd(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f81,f126]) ).
fof(f234,plain,
! [X0] :
( ~ outputs(sK1_skl,good)
| ~ sP4_prd(X0,sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f231,f79]) ).
fof(f237,plain,
! [X0,X1,X2] :
( ~ halts2(X1,X2)
| ~ program(X1)
| ~ sP4_prd(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f234,f122]) ).
fof(f244,plain,
! [X0,X1,X2] :
( ~ sP4_prd(X1,X2)
| ~ program(X1)
| ~ sP4_prd(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f237,f80]) ).
fof(f250,plain,
! [X0,X1,X2] :
( ~ sP4_prd(X1,X2)
| ~ sP4_prd(X0,sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f244,f79]) ).
fof(f253,plain,
! [X0] :
( ~ halts2(X0,X0)
| ~ sP2_prd(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f250,f62]) ).
fof(f256,plain,
! [X0] : ~ sP4_prd(X0,sK1_skl),
inference(factoring,[status(thm)],[f250]) ).
fof(f260,plain,
! [X0] :
( outputs(sK1_skl,bad)
| ~ program(X0)
| ~ sP2_prd(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f253,f129]) ).
fof(f266,plain,
! [X0] :
( outputs(sK1_skl,bad)
| ~ sP2_prd(X0,sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f260,f91]) ).
fof(f383,plain,
! [X0] :
( ~ outputs(sK1_skl,bad)
| ~ halts3(sK1_skl,X0,X0)
| ~ sP2_prd(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f63,f256]) ).
fof(f386,plain,
! [X0] :
( ~ halts3(sK1_skl,X0,X0)
| ~ sP2_prd(X0,sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f383,f266]) ).
fof(f388,plain,
! [X0] :
( ~ program(X0)
| ~ sP2_prd(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f386,f126]) ).
fof(f391,plain,
! [X0] : ~ sP2_prd(X0,sK1_skl),
inference(forward_subsumption_resolution,[status(thm)],[f388,f91]) ).
fof(f393,plain,
! [X0] :
( outputs(sK4_skl,bad)
| halts2(X0,X0)
| ~ program(X0)
| ~ program(sK1_skl) ),
inference(resolution,[status(thm)],[f391,f31]) ).
fof(f394,plain,
! [X0] :
( halts2(sK4_skl,X0)
| ~ program(X0)
| ~ program(sK1_skl) ),
inference(resolution,[status(thm)],[f391,f190]) ).
fof(f395,plain,
! [X0] :
( outputs(sK4_skl,good)
| ~ halts2(X0,X0)
| ~ program(X0)
| ~ program(sK1_skl) ),
inference(resolution,[status(thm)],[f391,f29]) ).
fof(f396,plain,
( program(sK4_skl)
| ~ program(sK1_skl) ),
inference(resolution,[status(thm)],[f391,f27]) ).
fof(f398,plain,
! [X0] :
( outputs(sK4_skl,bad)
| halts2(X0,X0)
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f393,f102]) ).
fof(f399,plain,
! [X0] :
( halts2(sK4_skl,X0)
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f394,f102]) ).
fof(f400,plain,
! [X0] :
( outputs(sK4_skl,good)
| ~ halts2(X0,X0)
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f395,f102]) ).
fof(f401,plain,
program(sK4_skl),
inference(forward_subsumption_resolution,[status(thm)],[f396,f102]) ).
fof(f403,plain,
! [X0] :
( ~ outputs(sK4_skl,good)
| ~ sP5_prd(X0,sK4_skl)
| ~ program(X0) ),
inference(resolution,[status(thm)],[f399,f88]) ).
fof(f405,plain,
! [X0] :
( ~ outputs(sK4_skl,good)
| ~ sP5_prd(X0,sK4_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f403,f86]) ).
fof(f450,plain,
! [X0,X1] :
( ~ sP5_prd(X1,sK4_skl)
| ~ halts2(X0,X0)
| ~ program(X0) ),
inference(resolution,[status(thm)],[f400,f405]) ).
fof(f456,plain,
! [X0] :
( ~ program(sK4_skl)
| ~ sP5_prd(X0,sK4_skl)
| ~ program(sK4_skl) ),
inference(resolution,[status(thm)],[f450,f399]) ).
fof(f477,plain,
! [X0] :
( ~ sP5_prd(X0,sK4_skl)
| ~ program(sK4_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f456]) ).
fof(f478,plain,
! [X0] : ~ sP5_prd(X0,sK4_skl),
inference(forward_subsumption_resolution,[status(thm)],[f477,f401]) ).
fof(f541,plain,
! [X0] :
( ~ halts2(X0,X0)
| ~ sP3_prd(X0,sK4_skl) ),
inference(resolution,[status(thm)],[f478,f72]) ).
fof(f545,plain,
! [X0] :
( outputs(sK4_skl,bad)
| ~ program(X0)
| ~ sP3_prd(X0,sK4_skl) ),
inference(resolution,[status(thm)],[f541,f398]) ).
fof(f563,plain,
! [X0] :
( outputs(sK4_skl,bad)
| ~ sP3_prd(X0,sK4_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f545,f92]) ).
fof(f623,plain,
! [X0] :
( ~ outputs(sK4_skl,bad)
| ~ halts2(sK4_skl,X0)
| ~ sP3_prd(X0,sK4_skl) ),
inference(resolution,[status(thm)],[f73,f478]) ).
fof(f627,plain,
! [X0] :
( ~ halts2(sK4_skl,X0)
| ~ sP3_prd(X0,sK4_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f623,f563]) ).
fof(f650,plain,
! [X0] :
( ~ program(X0)
| ~ sP3_prd(X0,sK4_skl) ),
inference(resolution,[status(thm)],[f627,f399]) ).
fof(f667,plain,
! [X0] : ~ sP3_prd(X0,sK4_skl),
inference(forward_subsumption_resolution,[status(thm)],[f650,f92]) ).
fof(f671,plain,
! [X0] :
( halts2(sK6_skl,X0)
| halts2(X0,X0)
| ~ program(X0)
| ~ program(sK4_skl) ),
inference(resolution,[status(thm)],[f667,f39]) ).
fof(f672,plain,
! [X0] :
( ~ halts2(sK6_skl,X0)
| ~ halts2(X0,X0)
| ~ program(X0)
| ~ program(sK4_skl) ),
inference(resolution,[status(thm)],[f667,f38]) ).
fof(f673,plain,
( program(sK6_skl)
| ~ program(sK4_skl) ),
inference(resolution,[status(thm)],[f667,f37]) ).
fof(f677,plain,
! [X0] :
( halts2(sK6_skl,X0)
| halts2(X0,X0)
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f671,f401]) ).
fof(f678,plain,
! [X0] :
( ~ halts2(sK6_skl,X0)
| ~ halts2(X0,X0)
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f672,f401]) ).
fof(f679,plain,
program(sK6_skl),
inference(forward_subsumption_resolution,[status(thm)],[f673,f401]) ).
fof(f704,plain,
( halts2(sK6_skl,sK6_skl)
| ~ program(sK6_skl) ),
inference(factoring,[status(thm)],[f677]) ).
fof(f713,plain,
halts2(sK6_skl,sK6_skl),
inference(forward_subsumption_resolution,[status(thm)],[f704,f679]) ).
fof(f717,plain,
~ program(sK6_skl),
inference(resolution,[status(thm)],[f678,f713]) ).
fof(f771,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f717,f679]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM003+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 14:14:32 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.38 % Drodi V4.1.1
% 0.12/0.43 % Refutation found
% 0.12/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.45 % Elapsed time: 0.074510 seconds
% 0.12/0.45 % CPU time: 0.371409 seconds
% 0.12/0.45 % Total memory used: 22.417 MB
% 0.12/0.45 % Net memory used: 22.029 MB
%------------------------------------------------------------------------------