%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COM003+3 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 0.14s 10.46s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 20
% Syntax : Number of formulae : 177 ( 4 unt; 16 def)
% Number of atoms : 912 ( 0 equ)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 1290 ( 555 ~; 606 |; 98 &)
% ( 17 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 23 ( 22 usr; 13 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 355 ( 325 !; 30 ?)
% 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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [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) ) ) )
& program(W) )
=> ? [V] :
( ! [Y] :
( ( ( outputs(W,bad)
& halts3(W,Y,Y)
& program(Y) )
=> ( outputs(V,bad)
& halts2(V,Y) ) )
& ( ( outputs(W,good)
& halts3(W,Y,Y)
& program(Y) )
=> ~ halts2(V,Y) ) )
& program(V) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,conjecture,
~ ? [X1] :
( ! [Y1] :
( program(Y1)
=> ! [Z1] : decides(X1,Y1,Z1) )
& algorithm(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ ~ ? [X1] :
( ! [Y1] :
( program(Y1)
=> ! [Z1] : decides(X1,Y1,Z1) )
& algorithm(X1) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,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(f7,definition,
! [X,Y] :
( sP0_prd(Y,X)
<=> ( ? [Z] : ~ decides(X,Y,Z)
& program(Y) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f8,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)],[f6,f7]) ).
fof(f9,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)],[f8]) ).
fof(f10,plain,
! [X0] :
( program(sK1_skl)
| sP0_prd(sK0_skl(X0),X0)
| ~ algorithm(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f11,plain,
! [X0,X1,X2] :
( decides(sK1_skl,X1,X2)
| ~ program(X1)
| sP0_prd(sK0_skl(X0),X0)
| ~ algorithm(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f12,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(f13,definition,
! [W,Y] :
( sP1_prd(Y,W)
<=> ( ? [Z] : ~ decides(W,Y,Z)
& program(Y) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f14,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)],[f12,f13]) ).
fof(f15,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)],[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) ) )
| sP1_prd(sK2_skl(W),W)
| ~ program(W) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y,sK2_skl(W))],[f15]) ).
fof(f17,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)],[f16]) ).
fof(f18,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)],[f16]) ).
fof(f19,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)],[f16]) ).
fof(f20,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)],[f16]) ).
fof(f21,plain,
! [W] :
( ? [V] :
( ! [Y] :
( ( ( outputs(V,bad)
& halts2(V,Y) )
| ~ outputs(W,bad)
| ~ halts3(W,Y,Y)
| ~ program(Y) )
& ( ~ halts2(V,Y)
| ~ outputs(W,good)
| ~ halts3(W,Y,Y)
| ~ program(Y) ) )
& program(V) )
| ? [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) ) )
| ~ program(W) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f22,definition,
! [W,Y,Z] :
( sP2_prd(Z,Y,W)
<=> ( ( ( ~ outputs(W,bad)
| ~ halts3(W,Y,Z) )
& ~ halts2(Y,Z)
& program(Y) )
| ( ( ~ outputs(W,good)
| ~ halts3(W,Y,Z) )
& halts2(Y,Z)
& program(Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f23,plain,
! [W] :
( ? [V] :
( ! [Y] :
( ( ( outputs(V,bad)
& halts2(V,Y) )
| ~ outputs(W,bad)
| ~ halts3(W,Y,Y)
| ~ program(Y) )
& ( ~ halts2(V,Y)
| ~ outputs(W,good)
| ~ halts3(W,Y,Y)
| ~ program(Y) ) )
& program(V) )
| ? [Y,Z] : sP2_prd(Z,Y,W)
| ~ program(W) ),
inference(formula_renaming,[status(thm)],[f21,f22]) ).
fof(f24,plain,
! [W] :
( ? [V] :
( ! [Y] :
( ( outputs(V,bad)
& halts2(V,Y) )
| ~ outputs(W,bad)
| ~ halts3(W,Y,Y)
| ~ program(Y) )
& ! [Y] :
( ~ halts2(V,Y)
| ~ outputs(W,good)
| ~ halts3(W,Y,Y)
| ~ program(Y) )
& program(V) )
| ? [Y,Z] : sP2_prd(Z,Y,W)
| ~ program(W) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f25,plain,
! [W] :
( ( ! [Y] :
( ( outputs(sK5_skl(W),bad)
& halts2(sK5_skl(W),Y) )
| ~ outputs(W,bad)
| ~ halts3(W,Y,Y)
| ~ program(Y) )
& ! [Y] :
( ~ halts2(sK5_skl(W),Y)
| ~ outputs(W,good)
| ~ halts3(W,Y,Y)
| ~ program(Y) )
& program(sK5_skl(W)) )
| sP2_prd(sK4_skl(W),sK3_skl(W),W)
| ~ program(W) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(Y,sK3_skl(W)),skolemize(Z,sK4_skl(W)),skolemize(V,sK5_skl(W))],[f24]) ).
fof(f26,plain,
! [X0] :
( program(sK5_skl(X0))
| sP2_prd(sK4_skl(X0),sK3_skl(X0),X0)
| ~ program(X0) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( ~ halts2(sK5_skl(X0),X1)
| ~ outputs(X0,good)
| ~ halts3(X0,X1,X1)
| ~ program(X1)
| sP2_prd(sK4_skl(X0),sK3_skl(X0),X0)
| ~ program(X0) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f28,plain,
! [X0,X1] :
( halts2(sK5_skl(X0),X1)
| ~ outputs(X0,bad)
| ~ halts3(X0,X1,X1)
| ~ program(X1)
| sP2_prd(sK4_skl(X0),sK3_skl(X0),X0)
| ~ program(X0) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f30,plain,
? [X1] :
( ! [Y1] :
( ! [Z1] : decides(X1,Y1,Z1)
| ~ program(Y1) )
& algorithm(X1) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f31,plain,
( ! [Y1] :
( ! [Z1] : decides(sK6_skl,Y1,Z1)
| ~ program(Y1) )
& algorithm(sK6_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(X1,sK6_skl)],[f30]) ).
fof(f32,plain,
algorithm(sK6_skl),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( decides(sK6_skl,X0,X1)
| ~ program(X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f34,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)],[f7]) ).
fof(f35,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)],[f34]) ).
fof(f36,plain,
( ! [X,Y] :
( ! [Z] : decides(X,Y,Z)
| ~ program(Y)
| sP0_prd(Y,X) )
& ! [X,Y] :
( ( ~ decides(X,Y,sK7_skl(Y,X))
& program(Y) )
| ~ sP0_prd(Y,X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(Z,sK7_skl(Y,X))],[f35]) ).
fof(f37,plain,
! [X0,X1] :
( program(X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ~ decides(X1,X0,sK7_skl(X0,X1))
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f39,plain,
! [X0,X1,X2] :
( decides(X1,X0,X2)
| ~ program(X0)
| sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f40,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)],[f13]) ).
fof(f41,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)],[f40]) ).
fof(f42,plain,
( ! [W,Y] :
( ! [Z] : decides(W,Y,Z)
| ~ program(Y)
| sP1_prd(Y,W) )
& ! [W,Y] :
( ( ~ decides(W,Y,sK8_skl(Y,W))
& program(Y) )
| ~ sP1_prd(Y,W) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(Z,sK8_skl(Y,W))],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( program(X0)
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( ~ decides(X1,X0,sK8_skl(X0,X1))
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f45,plain,
! [X0,X1,X2] :
( decides(X1,X0,X2)
| ~ program(X0)
| sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f46,definition,
! [W,Y,Z] :
( sP3_prd(Z,Y,W)
<=> ( ( ~ outputs(W,good)
| ~ halts3(W,Y,Z) )
& halts2(Y,Z)
& program(Y) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f47,plain,
! [W,Y,Z] :
( sP2_prd(Z,Y,W)
<=> ( ( ( ~ outputs(W,bad)
| ~ halts3(W,Y,Z) )
& ~ halts2(Y,Z)
& program(Y) )
| sP3_prd(Z,Y,W) ) ),
inference(formula_renaming,[status(thm)],[f22,f46]) ).
fof(f48,plain,
! [W,Y,Z] :
( ( ( ( ( outputs(W,bad)
& halts3(W,Y,Z) )
| halts2(Y,Z)
| ~ program(Y) )
& ~ sP3_prd(Z,Y,W) )
| sP2_prd(Z,Y,W) )
& ( ( ( ~ outputs(W,bad)
| ~ halts3(W,Y,Z) )
& ~ halts2(Y,Z)
& program(Y) )
| sP3_prd(Z,Y,W)
| ~ sP2_prd(Z,Y,W) ) ),
inference(NNF_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
( ! [W,Y,Z] :
( ( ( ( outputs(W,bad)
& halts3(W,Y,Z) )
| halts2(Y,Z)
| ~ program(Y) )
& ~ sP3_prd(Z,Y,W) )
| sP2_prd(Z,Y,W) )
& ! [W,Y,Z] :
( ( ( ~ outputs(W,bad)
| ~ halts3(W,Y,Z) )
& ~ halts2(Y,Z)
& program(Y) )
| sP3_prd(Z,Y,W)
| ~ sP2_prd(Z,Y,W) ) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f50,plain,
! [X0,X1,X2] :
( program(X1)
| sP3_prd(X0,X1,X2)
| ~ sP2_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ halts2(X1,X0)
| sP3_prd(X0,X1,X2)
| ~ sP2_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ~ outputs(X2,bad)
| ~ halts3(X2,X1,X0)
| sP3_prd(X0,X1,X2)
| ~ sP2_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f56,plain,
! [W,Y,Z] :
( ( ( outputs(W,good)
& halts3(W,Y,Z) )
| ~ halts2(Y,Z)
| ~ program(Y)
| sP3_prd(Z,Y,W) )
& ( ( ( ~ outputs(W,good)
| ~ halts3(W,Y,Z) )
& halts2(Y,Z)
& program(Y) )
| ~ sP3_prd(Z,Y,W) ) ),
inference(NNF_transformation,[status(thm)],[f46]) ).
fof(f57,plain,
( ! [W,Y,Z] :
( ( outputs(W,good)
& halts3(W,Y,Z) )
| ~ halts2(Y,Z)
| ~ program(Y)
| sP3_prd(Z,Y,W) )
& ! [W,Y,Z] :
( ( ( ~ outputs(W,good)
| ~ halts3(W,Y,Z) )
& halts2(Y,Z)
& program(Y) )
| ~ sP3_prd(Z,Y,W) ) ),
inference(miniscoping,[status(thm)],[f56]) ).
fof(f58,plain,
! [X0,X1,X2] :
( program(X1)
| ~ sP3_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f59,plain,
! [X0,X1,X2] :
( halts2(X1,X0)
| ~ sP3_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ~ outputs(X2,good)
| ~ halts3(X2,X1,X0)
| ~ sP3_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f63,definition,
! [X0] :
( sQ0_spl
<=> ( sP0_prd(sK0_skl(X0),X0)
| ~ algorithm(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f64,plain,
! [X0] :
( ~ sQ0_spl
| sP0_prd(sK0_skl(X0),X0)
| ~ algorithm(X0) ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,definition,
( sQ1_spl
<=> program(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f67,plain,
( ~ sQ1_spl
| program(sK1_skl) ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f69,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f10,f63,f66]) ).
fof(f70,definition,
! [X1,X2] :
( sQ2_spl
<=> ( decides(sK1_skl,X1,X2)
| ~ program(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f71,plain,
! [X0,X1] :
( ~ sQ2_spl
| decides(sK1_skl,X0,X1)
| ~ program(X0) ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f11,f63,f70]) ).
fof(f74,definition,
! [X0] :
( sQ3_spl
<=> ( outputs(X0,good)
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f75,plain,
! [X0] :
( ~ sQ3_spl
| outputs(X0,good)
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0) ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,definition,
! [X1,X2] :
( sQ4_spl
<=> ( ~ halts2(X1,X2)
| ~ program(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f78,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ halts2(X0,X1)
| ~ program(X0) ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f18,f74,f77]) ).
fof(f81,definition,
! [X0] :
( sQ5_spl
<=> ( outputs(X0,bad)
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f82,plain,
! [X0] :
( ~ sQ5_spl
| outputs(X0,bad)
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0) ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,definition,
! [X1,X2] :
( sQ6_spl
<=> ( halts2(X1,X2)
| ~ program(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f85,plain,
! [X0,X1] :
( ~ sQ6_spl
| halts2(X0,X1)
| ~ program(X0) ),
inference(component_clause,[status(thm)],[f84]) ).
fof(f87,plain,
( sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f20,f81,f84]) ).
fof(f89,plain,
! [X0] :
( ~ program(X0)
| ~ sP0_prd(X0,sK6_skl) ),
inference(resolution,[status(thm)],[f38,f33]) ).
fof(f90,plain,
! [X0,X1] :
( ~ program(X0)
| sP1_prd(X0,X1)
| ~ sP0_prd(X0,X1) ),
inference(resolution,[status(thm)],[f38,f45]) ).
fof(f91,plain,
! [X0] : ~ sP0_prd(X0,sK6_skl),
inference(forward_subsumption_resolution,[status(thm)],[f89,f37]) ).
fof(f92,plain,
! [X0,X1] :
( sP1_prd(X0,X1)
| ~ sP0_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f90,f37]) ).
fof(f93,plain,
( ~ sQ0_spl
| ~ algorithm(sK6_skl) ),
inference(resolution,[status(thm)],[f91,f64]) ).
fof(f94,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f93,f32]) ).
fof(f95,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f94]) ).
fof(f99,plain,
! [X0] :
( ~ sQ2_spl
| ~ program(X0)
| ~ sP1_prd(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f44,f71]) ).
fof(f101,plain,
! [X0,X1] :
( ~ program(X0)
| sP0_prd(X0,X1)
| ~ sP1_prd(X0,X1) ),
inference(resolution,[status(thm)],[f44,f39]) ).
fof(f103,plain,
! [X0] :
( ~ sQ2_spl
| ~ sP1_prd(X0,sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f99,f43]) ).
fof(f105,plain,
! [X0,X1] :
( sP0_prd(X0,X1)
| ~ sP1_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f101,f43]) ).
fof(f106,plain,
! [X0,X1,X2] :
( halts3(X0,X1,X2)
| ~ program(X1)
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f19,f17]) ).
fof(f107,plain,
! [X0,X1,X2] :
( program(X1)
| ~ sP2_prd(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f50,f58]) ).
fof(f108,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| outputs(sK1_skl,bad)
| ~ program(sK1_skl) ),
inference(resolution,[status(thm)],[f82,f103]) ).
fof(f112,definition,
( sQ7_spl
<=> outputs(sK1_skl,bad) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f115,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| sQ7_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f108,f66,f112,f81,f70]) ).
fof(f125,plain,
! [X0] :
( ~ sQ3_spl
| sP0_prd(sK2_skl(X0),X0)
| outputs(X0,good)
| ~ program(X0) ),
inference(resolution,[status(thm)],[f75,f105]) ).
fof(f147,plain,
! [X0,X1,X2] :
( ~ program(X1)
| sP1_prd(sK2_skl(X2),X2)
| ~ program(X2)
| ~ outputs(X2,good)
| ~ sP3_prd(X0,X1,X2) ),
inference(resolution,[status(thm)],[f60,f106]) ).
fof(f148,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ program(X1)
| sP1_prd(sK2_skl(X2),X2)
| ~ program(X2)
| ~ sP3_prd(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f147,f75]) ).
fof(f149,plain,
! [X0] :
( ~ halts2(sK3_skl(X0),sK4_skl(X0))
| sP3_prd(sK4_skl(X0),sK3_skl(X0),X0)
| program(sK5_skl(X0))
| ~ program(X0) ),
inference(resolution,[status(thm)],[f26,f51]) ).
fof(f150,plain,
! [X0] :
( program(sK3_skl(X0))
| program(sK5_skl(X0))
| ~ program(X0) ),
inference(resolution,[status(thm)],[f26,f107]) ).
fof(f161,plain,
! [X0,X1] :
( ~ halts2(sK3_skl(X0),sK4_skl(X0))
| sP3_prd(sK4_skl(X0),sK3_skl(X0),X0)
| ~ halts2(sK5_skl(X0),X1)
| ~ outputs(X0,good)
| ~ halts3(X0,X1,X1)
| ~ program(X1)
| ~ program(X0) ),
inference(resolution,[status(thm)],[f27,f51]) ).
fof(f162,plain,
! [X0,X1] :
( program(sK3_skl(X0))
| ~ halts2(sK5_skl(X0),X1)
| ~ outputs(X0,good)
| ~ halts3(X0,X1,X1)
| ~ program(X1)
| ~ program(X0) ),
inference(resolution,[status(thm)],[f27,f107]) ).
fof(f216,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| sP1_prd(sK2_skl(X2),X2)
| ~ program(X2)
| ~ sP3_prd(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f148,f58]) ).
fof(f220,plain,
! [X0] :
( ~ sQ3_spl
| sP1_prd(sK2_skl(X0),X0)
| outputs(X0,good)
| ~ program(X0) ),
inference(resolution,[status(thm)],[f125,f92]) ).
fof(f233,plain,
! [X0,X1,X2] :
( ~ program(X1)
| sP1_prd(sK2_skl(X2),X2)
| ~ program(X2)
| ~ outputs(X2,bad)
| sP3_prd(X0,X1,X2)
| ~ sP2_prd(X0,X1,X2) ),
inference(resolution,[status(thm)],[f52,f106]) ).
fof(f236,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ program(X1)
| sP1_prd(sK2_skl(X2),X2)
| ~ program(X2)
| ~ outputs(X2,bad)
| ~ sP2_prd(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f233,f216]) ).
fof(f242,definition,
! [X0] :
( sQ19_spl
<=> ~ program(X0) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f243,plain,
! [X0] :
( ~ sQ19_spl
| ~ program(X0) ),
inference(component_clause,[status(thm)],[f242]) ).
fof(f260,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| sP1_prd(sK2_skl(X2),X2)
| ~ program(X2)
| ~ outputs(X2,bad)
| ~ sP2_prd(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f236,f107]) ).
fof(f262,plain,
! [X0,X1] :
( ~ sQ3_spl
| halts2(sK5_skl(X0),X1)
| ~ outputs(X0,bad)
| ~ halts3(X0,X1,X1)
| ~ program(X1)
| ~ program(X0)
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0)
| ~ outputs(X0,bad) ),
inference(resolution,[status(thm)],[f260,f28]) ).
fof(f267,plain,
! [X0,X1] :
( ~ sQ3_spl
| halts2(sK5_skl(X0),X1)
| ~ halts3(X0,X1,X1)
| ~ program(X1)
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0)
| ~ outputs(X0,bad) ),
inference(duplicate_literals_removal,[status(thm)],[f262]) ).
fof(f268,plain,
! [X0,X1] :
( ~ sQ3_spl
| halts2(sK5_skl(X0),X1)
| ~ program(X1)
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0)
| ~ outputs(X0,bad) ),
inference(forward_subsumption_resolution,[status(thm)],[f267,f106]) ).
fof(f274,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ6_spl
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f78,f85]) ).
fof(f281,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ6_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f67,f274]) ).
fof(f282,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f281]) ).
fof(f287,plain,
( ~ sQ1_spl
| ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f67,f243]) ).
fof(f288,plain,
( ~ sQ1_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f287]) ).
fof(f334,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ halts2(sK5_skl(X0),X1)
| ~ outputs(X0,good)
| ~ halts3(X0,X1,X1)
| ~ program(X1)
| ~ program(X0)
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0)
| ~ outputs(X0,bad) ),
inference(resolution,[status(thm)],[f260,f27]) ).
fof(f339,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ halts2(sK5_skl(X0),X1)
| ~ outputs(X0,good)
| ~ halts3(X0,X1,X1)
| ~ program(X1)
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0)
| ~ outputs(X0,bad) ),
inference(duplicate_literals_removal,[status(thm)],[f334]) ).
fof(f340,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ halts2(sK5_skl(X0),X1)
| ~ outputs(X0,good)
| ~ program(X1)
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0)
| ~ outputs(X0,bad) ),
inference(forward_subsumption_resolution,[status(thm)],[f339,f106]) ).
fof(f349,plain,
! [X0,X1] :
( program(sK3_skl(X0))
| halts2(sK5_skl(X0),X1)
| ~ outputs(X0,bad)
| ~ halts3(X0,X1,X1)
| ~ program(X1)
| ~ program(X0) ),
inference(resolution,[status(thm)],[f28,f107]) ).
fof(f355,plain,
! [X0] :
( ~ sQ3_spl
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0)
| ~ halts2(sK3_skl(X0),sK4_skl(X0))
| program(sK5_skl(X0))
| ~ program(X0) ),
inference(resolution,[status(thm)],[f149,f216]) ).
fof(f359,plain,
! [X0] :
( ~ sQ3_spl
| sP1_prd(sK2_skl(X0),X0)
| ~ halts2(sK3_skl(X0),sK4_skl(X0))
| program(sK5_skl(X0))
| ~ program(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f355]) ).
fof(f374,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ3_spl
| ~ program(sK3_skl(X0))
| sP1_prd(sK2_skl(X0),X0)
| program(sK5_skl(X0))
| ~ program(X0) ),
inference(resolution,[status(thm)],[f359,f85]) ).
fof(f376,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ3_spl
| sP1_prd(sK2_skl(X0),X0)
| program(sK5_skl(X0))
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f374,f150]) ).
fof(f389,plain,
! [X0,X1] :
( ~ program(X1)
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0)
| program(sK3_skl(X0))
| ~ halts2(sK5_skl(X0),X1)
| ~ outputs(X0,good)
| ~ program(X1)
| ~ program(X0) ),
inference(resolution,[status(thm)],[f162,f106]) ).
fof(f391,plain,
! [X0,X1] :
( sP1_prd(sK2_skl(X0),X0)
| program(sK3_skl(X0))
| ~ halts2(sK5_skl(X0),X1)
| ~ outputs(X0,good)
| ~ program(X1)
| ~ program(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f389]) ).
fof(f392,plain,
! [X0,X1] :
( ~ sQ3_spl
| sP1_prd(sK2_skl(X0),X0)
| program(sK3_skl(X0))
| ~ halts2(sK5_skl(X0),X1)
| ~ program(X1)
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f391,f220]) ).
fof(f400,plain,
! [X0,X1] :
( ~ sQ3_spl
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0)
| ~ halts2(sK3_skl(X0),sK4_skl(X0))
| ~ halts2(sK5_skl(X0),X1)
| ~ outputs(X0,good)
| ~ halts3(X0,X1,X1)
| ~ program(X1)
| ~ program(X0) ),
inference(resolution,[status(thm)],[f161,f216]) ).
fof(f404,plain,
! [X0,X1] :
( ~ sQ3_spl
| sP1_prd(sK2_skl(X0),X0)
| ~ halts2(sK3_skl(X0),sK4_skl(X0))
| ~ halts2(sK5_skl(X0),X1)
| ~ outputs(X0,good)
| ~ halts3(X0,X1,X1)
| ~ program(X1)
| ~ program(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f400]) ).
fof(f405,plain,
! [X0,X1] :
( ~ sQ3_spl
| sP1_prd(sK2_skl(X0),X0)
| ~ halts2(sK3_skl(X0),sK4_skl(X0))
| ~ halts2(sK5_skl(X0),X1)
| ~ outputs(X0,good)
| ~ program(X1)
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f404,f106]) ).
fof(f417,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ sQ3_spl
| ~ program(sK5_skl(X0))
| sP1_prd(sK2_skl(X0),X0)
| program(sK3_skl(X0))
| ~ program(X1)
| ~ program(X0) ),
inference(resolution,[status(thm)],[f392,f85]) ).
fof(f425,definition,
! [X0] :
( sQ25_spl
<=> ( ~ program(sK5_skl(X0))
| sP1_prd(sK2_skl(X0),X0)
| program(sK3_skl(X0))
| ~ program(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f426,plain,
! [X0] :
( ~ sQ25_spl
| ~ program(sK5_skl(X0))
| sP1_prd(sK2_skl(X0),X0)
| program(sK3_skl(X0))
| ~ program(X0) ),
inference(component_clause,[status(thm)],[f425]) ).
fof(f428,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| sQ19_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f417,f425,f242,f74,f84]) ).
fof(f429,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ6_spl
| ~ sQ3_spl
| sP1_prd(sK2_skl(X0),X0)
| program(sK3_skl(X0))
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f426,f376]) ).
fof(f471,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ program(X1)
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0)
| ~ outputs(X0,bad) ),
inference(backward_subsumption_resolution,[status(thm)],[f268,f472]) ).
fof(f472,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ halts2(sK5_skl(X0),X1)
| ~ program(X1)
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0)
| ~ outputs(X0,bad) ),
inference(forward_subsumption_resolution,[status(thm)],[f340,f220]) ).
fof(f474,definition,
! [X0] :
( sQ31_spl
<=> ( sP1_prd(sK2_skl(X0),X0)
| ~ program(X0)
| ~ outputs(X0,bad) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f475,plain,
! [X0] :
( ~ sQ31_spl
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0)
| ~ outputs(X0,bad) ),
inference(component_clause,[status(thm)],[f474]) ).
fof(f477,plain,
( ~ sQ3_spl
| sQ19_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f471,f474,f242,f74]) ).
fof(f483,plain,
( ~ sQ2_spl
| ~ sQ31_spl
| ~ program(sK1_skl)
| ~ outputs(sK1_skl,bad) ),
inference(resolution,[status(thm)],[f475,f103]) ).
fof(f487,plain,
( ~ sQ2_spl
| ~ sQ31_spl
| ~ sQ1_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f483,f112,f66,f474,f70]) ).
fof(f500,plain,
! [X0,X1] :
( ~ sQ3_spl
| sP1_prd(sK2_skl(X0),X0)
| ~ halts2(sK3_skl(X0),sK4_skl(X0))
| ~ halts2(sK5_skl(X0),X1)
| ~ program(X1)
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f405,f220]) ).
fof(f503,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ sQ3_spl
| ~ program(sK3_skl(X0))
| sP1_prd(sK2_skl(X0),X0)
| ~ halts2(sK5_skl(X0),X1)
| ~ program(X1)
| ~ program(X0) ),
inference(resolution,[status(thm)],[f500,f85]) ).
fof(f508,definition,
! [X0] :
( sQ33_spl
<=> ( ~ program(sK5_skl(X0))
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f509,plain,
! [X0] :
( ~ sQ33_spl
| ~ program(sK5_skl(X0))
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0) ),
inference(component_clause,[status(thm)],[f508]) ).
fof(f512,plain,
! [X0] :
( ~ sQ33_spl
| ~ sQ6_spl
| ~ sQ3_spl
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f509,f376]) ).
fof(f513,plain,
( ~ sQ2_spl
| ~ sQ33_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ program(sK1_skl) ),
inference(resolution,[status(thm)],[f512,f103]) ).
fof(f517,plain,
( ~ sQ2_spl
| ~ sQ33_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f513,f67]) ).
fof(f518,plain,
( ~ sQ2_spl
| ~ sQ33_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f517]) ).
fof(f571,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ25_spl
| sP1_prd(sK2_skl(X0),X0)
| ~ halts2(sK5_skl(X0),X1)
| ~ program(X1)
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f503,f429]) ).
fof(f572,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ25_spl
| ~ program(sK5_skl(X0))
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X1)
| ~ program(X0) ),
inference(resolution,[status(thm)],[f571,f85]) ).
fof(f573,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ25_spl
| sQ19_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f572,f508,f242,f425,f74,f84]) ).
fof(f589,plain,
! [X0,X1,X2] :
( ~ program(X1)
| sP1_prd(sK2_skl(X2),X2)
| ~ program(X2)
| ~ outputs(X2,bad)
| sP3_prd(X0,X1,X2)
| ~ sP2_prd(X0,X1,X2) ),
inference(resolution,[status(thm)],[f52,f106]) ).
fof(f590,plain,
! [X0,X1,X2] :
( ~ sQ5_spl
| ~ program(X1)
| sP1_prd(sK2_skl(X2),X2)
| ~ program(X2)
| sP3_prd(X0,X1,X2)
| ~ sP2_prd(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f589,f82]) ).
fof(f683,plain,
! [X0,X1,X2] :
( ~ sQ5_spl
| sP1_prd(sK2_skl(X2),X2)
| ~ program(X2)
| sP3_prd(X0,X1,X2)
| ~ sP2_prd(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f590,f107]) ).
fof(f684,plain,
! [X0] :
( ~ sQ5_spl
| program(sK5_skl(X0))
| ~ program(X0)
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0)
| sP3_prd(sK4_skl(X0),sK3_skl(X0),X0) ),
inference(resolution,[status(thm)],[f683,f26]) ).
fof(f688,plain,
! [X0] :
( ~ sQ5_spl
| program(sK5_skl(X0))
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0)
| sP3_prd(sK4_skl(X0),sK3_skl(X0),X0) ),
inference(duplicate_literals_removal,[status(thm)],[f684]) ).
fof(f696,plain,
! [X0] :
( ~ sQ5_spl
| halts2(sK3_skl(X0),sK4_skl(X0))
| program(sK5_skl(X0))
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0) ),
inference(resolution,[status(thm)],[f688,f59]) ).
fof(f710,plain,
! [X0,X1] :
( ~ sQ5_spl
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0)
| sP3_prd(sK4_skl(X0),sK3_skl(X0),X0)
| halts2(sK5_skl(X0),X1)
| ~ outputs(X0,bad)
| ~ halts3(X0,X1,X1)
| ~ program(X1)
| ~ program(X0) ),
inference(resolution,[status(thm)],[f28,f683]) ).
fof(f713,plain,
! [X0,X1] :
( ~ sQ5_spl
| sP1_prd(sK2_skl(X0),X0)
| sP3_prd(sK4_skl(X0),sK3_skl(X0),X0)
| halts2(sK5_skl(X0),X1)
| ~ outputs(X0,bad)
| ~ halts3(X0,X1,X1)
| ~ program(X1)
| ~ program(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f710]) ).
fof(f714,plain,
! [X0,X1] :
( ~ sQ5_spl
| sP1_prd(sK2_skl(X0),X0)
| sP3_prd(sK4_skl(X0),sK3_skl(X0),X0)
| halts2(sK5_skl(X0),X1)
| ~ outputs(X0,bad)
| ~ program(X1)
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f713,f106]) ).
fof(f722,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ program(sK3_skl(X0))
| program(sK5_skl(X0))
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0) ),
inference(resolution,[status(thm)],[f696,f78]) ).
fof(f723,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| program(sK5_skl(X0))
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f722,f150]) ).
fof(f741,plain,
! [X0,X1] :
( ~ program(X1)
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0)
| program(sK3_skl(X0))
| halts2(sK5_skl(X0),X1)
| ~ outputs(X0,bad)
| ~ program(X1)
| ~ program(X0) ),
inference(resolution,[status(thm)],[f349,f106]) ).
fof(f743,plain,
! [X0,X1] :
( sP1_prd(sK2_skl(X0),X0)
| program(sK3_skl(X0))
| halts2(sK5_skl(X0),X1)
| ~ outputs(X0,bad)
| ~ program(X1)
| ~ program(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f741]) ).
fof(f744,plain,
! [X0,X1] :
( ~ sQ5_spl
| sP1_prd(sK2_skl(X0),X0)
| program(sK3_skl(X0))
| halts2(sK5_skl(X0),X1)
| ~ program(X1)
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f743,f82]) ).
fof(f786,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ program(sK5_skl(X0))
| sP1_prd(sK2_skl(X0),X0)
| program(sK3_skl(X0))
| ~ program(X1)
| ~ program(X0) ),
inference(resolution,[status(thm)],[f744,f78]) ).
fof(f787,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sQ19_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f786,f425,f242,f81,f77]) ).
fof(f788,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sP1_prd(sK2_skl(X0),X0)
| program(sK3_skl(X0))
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f426,f723]) ).
fof(f814,plain,
! [X0,X1] :
( ~ sQ5_spl
| sP1_prd(sK2_skl(X0),X0)
| sP3_prd(sK4_skl(X0),sK3_skl(X0),X0)
| halts2(sK5_skl(X0),X1)
| ~ program(X1)
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f714,f82]) ).
fof(f818,plain,
! [X0,X1] :
( ~ sQ5_spl
| halts2(sK3_skl(X0),sK4_skl(X0))
| sP1_prd(sK2_skl(X0),X0)
| halts2(sK5_skl(X0),X1)
| ~ program(X1)
| ~ program(X0) ),
inference(resolution,[status(thm)],[f814,f59]) ).
fof(f848,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ program(sK3_skl(X0))
| sP1_prd(sK2_skl(X0),X0)
| halts2(sK5_skl(X0),X1)
| ~ program(X1)
| ~ program(X0) ),
inference(resolution,[status(thm)],[f818,f78]) ).
fof(f851,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ25_spl
| sP1_prd(sK2_skl(X0),X0)
| halts2(sK5_skl(X0),X1)
| ~ program(X1)
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f848,f788]) ).
fof(f852,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ25_spl
| ~ program(sK5_skl(X0))
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X1)
| ~ program(X0) ),
inference(resolution,[status(thm)],[f851,f78]) ).
fof(f853,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ25_spl
| sQ19_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f852,f508,f242,f425,f81,f77]) ).
fof(f854,plain,
! [X0] :
( ~ sQ33_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sP1_prd(sK2_skl(X0),X0)
| ~ program(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f509,f723]) ).
fof(f855,plain,
( ~ sQ2_spl
| ~ sQ33_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ program(sK1_skl) ),
inference(resolution,[status(thm)],[f854,f103]) ).
fof(f859,plain,
( ~ sQ2_spl
| ~ sQ33_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f855,f67]) ).
fof(f860,plain,
( ~ sQ2_spl
| ~ sQ33_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f859]) ).
fof(f861,plain,
$false,
inference(sat_refutation,[status(thm)],[f69,f73,f80,f87,f95,f115,f282,f288,f428,f477,f487,f518,f573,f787,f853,f860]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM003+3 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/10.39 % Computer : n019.cluster.edu
% 0.10/10.39 % Model : x86_64 x86_64
% 0.10/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.39 % Memory : 8046.5625MB
% 0.10/10.39 % OS : Linux 6.8.0-71-generic
% 0.10/10.39 % CPULimit : 300
% 0.10/10.39 % WCLimit : 300
% 0.10/10.39 % DateTime : Mon Sep 21 14:14:14 UTC 2026
% 0.10/10.39 % CPUTime :
% 0.14/10.40 % Drodi V4.1.1
% 0.14/10.46 % Refutation found
% 0.14/10.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/10.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/10.48 % Elapsed time: 0.080979 seconds
% 0.14/10.48 % CPU time: 0.424750 seconds
% 0.14/10.48 % Total memory used: 22.599 MB
% 0.14/10.48 % Net memory used: 21.978 MB
%------------------------------------------------------------------------------