TSTP Solution File: COM003+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COM003+2 : TPTP v8.1.0. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Fri Jul 15 01:32:26 EDT 2022
% Result : Theorem 0.46s 0.64s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of formulae : 118 ( 24 unt; 0 def)
% Number of atoms : 352 ( 0 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 438 ( 204 ~; 177 |; 36 &)
% ( 15 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-1 aty)
% Number of variables : 177 ( 30 sgn 105 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(program_program_decides_def,axiom,
! [X] :
( program_program_decides(X)
<=> ( program(X)
& program_decides(X) ) ) ).
fof(program_halts2_def,axiom,
! [X,Y] :
( program_halts2(X,Y)
<=> ( program(X)
& halts2(X,Y) ) ) ).
fof(program_not_halts2_def,axiom,
! [X,Y] :
( program_not_halts2(X,Y)
<=> ( program(X)
& ~ halts2(X,Y) ) ) ).
fof(halts2_outputs_def,axiom,
! [X,Y,W] :
( halts2_outputs(X,Y,W)
<=> ( halts2(X,Y)
& outputs(X,W) ) ) ).
fof(program_not_halts2_halts2_outputs_def,axiom,
! [X,Y,W] :
( program_not_halts2_halts2_outputs(X,Y,W)
<=> ( program_not_halts2(Y,Y)
=> halts2_outputs(X,Y,W) ) ) ).
fof(p1,axiom,
( ? [X] : algorithm_program_decides(X)
=> ? [W] : program_program_decides(W) ) ).
fof(p2,axiom,
! [W] :
( program_program_decides(W)
=> ! [Y,Z] :
( program_halts2_halts3_outputs(W,Y,Z,good)
& program_not_halts2_halts3_outputs(W,Y,Z,bad) ) ) ).
fof(p3,axiom,
( ? [W] :
( program(W)
& ! [Y] :
( program_halts2_halts3_outputs(W,Y,Y,good)
& program_not_halts2_halts3_outputs(W,Y,Y,bad) ) )
=> ? [V] :
( program(V)
& ! [Y] :
( program_halts2_halts2_outputs(V,Y,good)
& program_not_halts2_halts2_outputs(V,Y,bad) ) ) ) ).
fof(p4,axiom,
( ? [V] :
( program(V)
& ! [Y] :
( program_halts2_halts2_outputs(V,Y,good)
& program_not_halts2_halts2_outputs(V,Y,bad) ) )
=> ? [U] :
( program(U)
& ! [Y] :
( ( program_halts2(Y,Y)
=> ~ halts2(U,Y) )
& program_not_halts2_halts2_outputs(U,Y,good) ) ) ) ).
fof(prove_this,conjecture,
~ ? [X] : algorithm_program_decides(X) ).
fof(subgoal_0,plain,
! [X] : ~ algorithm_program_decides(X),
inference(strip,[],[prove_this]) ).
fof(negate_0_0,plain,
~ ! [X] : ~ algorithm_program_decides(X),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] :
( ~ program_halts2(X,Y)
<=> ( ~ halts2(X,Y)
| ~ program(X) ) ),
inference(canonicalize,[],[program_halts2_def]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ program_halts2(X,Y)
<=> ( ~ halts2(X,Y)
| ~ program(X) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ( ~ program_halts2(X,Y)
| halts2(X,Y) )
& ( ~ program_halts2(X,Y)
| program(X) )
& ( ~ halts2(X,Y)
| ~ program(X)
| program_halts2(X,Y) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ halts2(X,Y)
| ~ program(X)
| program_halts2(X,Y) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [W,X,Y] :
( ~ halts2_outputs(X,Y,W)
<=> ( ~ halts2(X,Y)
| ~ outputs(X,W) ) ),
inference(canonicalize,[],[halts2_outputs_def]) ).
fof(normalize_0_5,plain,
! [W,X,Y] :
( ~ halts2_outputs(X,Y,W)
<=> ( ~ halts2(X,Y)
| ~ outputs(X,W) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [W,X,Y] :
( ( ~ halts2_outputs(X,Y,W)
| halts2(X,Y) )
& ( ~ halts2_outputs(X,Y,W)
| outputs(X,W) )
& ( ~ halts2(X,Y)
| ~ outputs(X,W)
| halts2_outputs(X,Y,W) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [W,X,Y] :
( ~ halts2_outputs(X,Y,W)
| halts2(X,Y) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [W,X,Y] :
( ~ program_not_halts2_halts2_outputs(X,Y,W)
<=> ( ~ halts2_outputs(X,Y,W)
& program_not_halts2(Y,Y) ) ),
inference(canonicalize,[],[program_not_halts2_halts2_outputs_def]) ).
fof(normalize_0_9,plain,
! [W,X,Y] :
( ~ program_not_halts2_halts2_outputs(X,Y,W)
<=> ( ~ halts2_outputs(X,Y,W)
& program_not_halts2(Y,Y) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [W,X,Y] :
( ( ~ halts2_outputs(X,Y,W)
| program_not_halts2_halts2_outputs(X,Y,W) )
& ( program_not_halts2(Y,Y)
| program_not_halts2_halts2_outputs(X,Y,W) )
& ( ~ program_not_halts2(Y,Y)
| ~ program_not_halts2_halts2_outputs(X,Y,W)
| halts2_outputs(X,Y,W) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [W,X,Y] :
( ~ program_not_halts2(Y,Y)
| ~ program_not_halts2_halts2_outputs(X,Y,W)
| halts2_outputs(X,Y,W) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
( ? [U] :
( program(U)
& ! [Y] : program_not_halts2_halts2_outputs(U,Y,good)
& ! [Y] :
( ~ halts2(U,Y)
| ~ program_halts2(Y,Y) ) )
| ! [V] :
( ~ program(V)
| ? [Y] : ~ program_halts2_halts2_outputs(V,Y,good)
| ? [Y] : ~ program_not_halts2_halts2_outputs(V,Y,bad) ) ),
inference(canonicalize,[],[p4]) ).
fof(normalize_0_13,plain,
! [V,Y] :
( ( ~ program(V)
| ~ program_halts2_halts2_outputs(V,skolemFOFtoCNF_Y_3(V),good)
| ~ program_not_halts2_halts2_outputs(V,skolemFOFtoCNF_Y_4(V),bad)
| program(skolemFOFtoCNF_U) )
& ( ~ program(V)
| ~ program_halts2_halts2_outputs(V,skolemFOFtoCNF_Y_3(V),good)
| ~ program_not_halts2_halts2_outputs(V,skolemFOFtoCNF_Y_4(V),bad)
| program_not_halts2_halts2_outputs(skolemFOFtoCNF_U,Y,good) )
& ( ~ halts2(skolemFOFtoCNF_U,Y)
| ~ program(V)
| ~ program_halts2(Y,Y)
| ~ program_halts2_halts2_outputs(V,skolemFOFtoCNF_Y_3(V),good)
| ~ program_not_halts2_halts2_outputs(V,skolemFOFtoCNF_Y_4(V),bad) ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [V,Y] :
( ~ program(V)
| ~ program_halts2_halts2_outputs(V,skolemFOFtoCNF_Y_3(V),good)
| ~ program_not_halts2_halts2_outputs(V,skolemFOFtoCNF_Y_4(V),bad)
| program_not_halts2_halts2_outputs(skolemFOFtoCNF_U,Y,good) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
? [X] : algorithm_program_decides(X),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_16,plain,
algorithm_program_decides(skolemFOFtoCNF_X),
inference(skolemize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
( ? [W] : program_program_decides(W)
| ! [X] : ~ algorithm_program_decides(X) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_0_18,plain,
! [X] :
( ~ algorithm_program_decides(X)
| program_program_decides(skolemFOFtoCNF_W) ),
inference(clausify,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [W] :
( ~ program_program_decides(W)
| ( ! [Y,Z] : program_halts2_halts3_outputs(W,Y,Z,good)
& ! [Y,Z] : program_not_halts2_halts3_outputs(W,Y,Z,bad) ) ),
inference(canonicalize,[],[p2]) ).
fof(normalize_0_20,plain,
! [W] :
( ~ program_program_decides(W)
| ( ! [Y,Z] : program_halts2_halts3_outputs(W,Y,Z,good)
& ! [Y,Z] : program_not_halts2_halts3_outputs(W,Y,Z,bad) ) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [W,Y,Z] :
( ( ~ program_program_decides(W)
| program_halts2_halts3_outputs(W,Y,Z,good) )
& ( ~ program_program_decides(W)
| program_not_halts2_halts3_outputs(W,Y,Z,bad) ) ),
inference(clausify,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [W,Y,Z] :
( ~ program_program_decides(W)
| program_not_halts2_halts3_outputs(W,Y,Z,bad) ),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
( ? [V] :
( program(V)
& ! [Y] : program_halts2_halts2_outputs(V,Y,good)
& ! [Y] : program_not_halts2_halts2_outputs(V,Y,bad) )
| ! [W] :
( ~ program(W)
| ? [Y] : ~ program_halts2_halts3_outputs(W,Y,Y,good)
| ? [Y] : ~ program_not_halts2_halts3_outputs(W,Y,Y,bad) ) ),
inference(canonicalize,[],[p3]) ).
fof(normalize_0_24,plain,
! [W,Y] :
( ( ~ program(W)
| ~ program_halts2_halts3_outputs(W,skolemFOFtoCNF_Y_1(W),skolemFOFtoCNF_Y_1(W),good)
| ~ program_not_halts2_halts3_outputs(W,skolemFOFtoCNF_Y_2(W),skolemFOFtoCNF_Y_2(W),bad)
| program(skolemFOFtoCNF_V) )
& ( ~ program(W)
| ~ program_halts2_halts3_outputs(W,skolemFOFtoCNF_Y_1(W),skolemFOFtoCNF_Y_1(W),good)
| ~ program_not_halts2_halts3_outputs(W,skolemFOFtoCNF_Y_2(W),skolemFOFtoCNF_Y_2(W),bad)
| program_halts2_halts2_outputs(skolemFOFtoCNF_V,Y,good) )
& ( ~ program(W)
| ~ program_halts2_halts3_outputs(W,skolemFOFtoCNF_Y_1(W),skolemFOFtoCNF_Y_1(W),good)
| ~ program_not_halts2_halts3_outputs(W,skolemFOFtoCNF_Y_2(W),skolemFOFtoCNF_Y_2(W),bad)
| program_not_halts2_halts2_outputs(skolemFOFtoCNF_V,Y,bad) ) ),
inference(clausify,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [W,Y] :
( ~ program(W)
| ~ program_halts2_halts3_outputs(W,skolemFOFtoCNF_Y_1(W),skolemFOFtoCNF_Y_1(W),good)
| ~ program_not_halts2_halts3_outputs(W,skolemFOFtoCNF_Y_2(W),skolemFOFtoCNF_Y_2(W),bad)
| program_not_halts2_halts2_outputs(skolemFOFtoCNF_V,Y,bad) ),
inference(conjunct,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [X] :
( ~ program_program_decides(X)
<=> ( ~ program(X)
| ~ program_decides(X) ) ),
inference(canonicalize,[],[program_program_decides_def]) ).
fof(normalize_0_27,plain,
! [X] :
( ~ program_program_decides(X)
<=> ( ~ program(X)
| ~ program_decides(X) ) ),
inference(specialize,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [X] :
( ( ~ program_program_decides(X)
| program(X) )
& ( ~ program_program_decides(X)
| program_decides(X) )
& ( ~ program(X)
| ~ program_decides(X)
| program_program_decides(X) ) ),
inference(clausify,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
! [X] :
( ~ program_program_decides(X)
| program(X) ),
inference(conjunct,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [W,Y,Z] :
( ~ program_program_decides(W)
| program_halts2_halts3_outputs(W,Y,Z,good) ),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_31,plain,
! [W] :
( ~ program(W)
| ~ program_halts2_halts3_outputs(W,skolemFOFtoCNF_Y_1(W),skolemFOFtoCNF_Y_1(W),good)
| ~ program_not_halts2_halts3_outputs(W,skolemFOFtoCNF_Y_2(W),skolemFOFtoCNF_Y_2(W),bad)
| program(skolemFOFtoCNF_V) ),
inference(conjunct,[],[normalize_0_24]) ).
fof(normalize_0_32,plain,
! [W,Y] :
( ~ program(W)
| ~ program_halts2_halts3_outputs(W,skolemFOFtoCNF_Y_1(W),skolemFOFtoCNF_Y_1(W),good)
| ~ program_not_halts2_halts3_outputs(W,skolemFOFtoCNF_Y_2(W),skolemFOFtoCNF_Y_2(W),bad)
| program_halts2_halts2_outputs(skolemFOFtoCNF_V,Y,good) ),
inference(conjunct,[],[normalize_0_24]) ).
fof(normalize_0_33,plain,
! [X,Y] :
( ~ program_not_halts2(X,Y)
<=> ( ~ program(X)
| halts2(X,Y) ) ),
inference(canonicalize,[],[program_not_halts2_def]) ).
fof(normalize_0_34,plain,
! [X,Y] :
( ~ program_not_halts2(X,Y)
<=> ( ~ program(X)
| halts2(X,Y) ) ),
inference(specialize,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
! [X,Y] :
( ( ~ halts2(X,Y)
| ~ program_not_halts2(X,Y) )
& ( ~ program_not_halts2(X,Y)
| program(X) )
& ( ~ program(X)
| halts2(X,Y)
| program_not_halts2(X,Y) ) ),
inference(clausify,[],[normalize_0_34]) ).
fof(normalize_0_36,plain,
! [X,Y] :
( ~ program(X)
| halts2(X,Y)
| program_not_halts2(X,Y) ),
inference(conjunct,[],[normalize_0_35]) ).
fof(normalize_0_37,plain,
! [V] :
( ~ program(V)
| ~ program_halts2_halts2_outputs(V,skolemFOFtoCNF_Y_3(V),good)
| ~ program_not_halts2_halts2_outputs(V,skolemFOFtoCNF_Y_4(V),bad)
| program(skolemFOFtoCNF_U) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_38,plain,
! [V,Y] :
( ~ halts2(skolemFOFtoCNF_U,Y)
| ~ program(V)
| ~ program_halts2(Y,Y)
| ~ program_halts2_halts2_outputs(V,skolemFOFtoCNF_Y_3(V),good)
| ~ program_not_halts2_halts2_outputs(V,skolemFOFtoCNF_Y_4(V),bad) ),
inference(conjunct,[],[normalize_0_13]) ).
cnf(refute_0_0,plain,
( ~ halts2(X,Y)
| ~ program(X)
| program_halts2(X,Y) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ halts2(skolemFOFtoCNF_U,skolemFOFtoCNF_U)
| ~ program(skolemFOFtoCNF_U)
| program_halts2(skolemFOFtoCNF_U,skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_2,plain,
( ~ halts2_outputs(X,Y,W)
| halts2(X,Y) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ halts2_outputs(skolemFOFtoCNF_U,skolemFOFtoCNF_U,good)
| halts2(skolemFOFtoCNF_U,skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_2:[bind(W,$fot(good)),bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_4,plain,
( ~ program_not_halts2(Y,Y)
| ~ program_not_halts2_halts2_outputs(X,Y,W)
| halts2_outputs(X,Y,W) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_5,plain,
( ~ program_not_halts2(X_340,X_340)
| ~ program_not_halts2_halts2_outputs(skolemFOFtoCNF_U,X_340,good)
| halts2_outputs(skolemFOFtoCNF_U,X_340,good) ),
inference(subst,[],[refute_0_4:[bind(W,$fot(good)),bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(X_340))]]) ).
cnf(refute_0_6,plain,
( ~ program(V)
| ~ program_halts2_halts2_outputs(V,skolemFOFtoCNF_Y_3(V),good)
| ~ program_not_halts2_halts2_outputs(V,skolemFOFtoCNF_Y_4(V),bad)
| program_not_halts2_halts2_outputs(skolemFOFtoCNF_U,Y,good) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_7,plain,
( ~ program(skolemFOFtoCNF_V)
| ~ program_halts2_halts2_outputs(skolemFOFtoCNF_V,skolemFOFtoCNF_Y_3(skolemFOFtoCNF_V),good)
| ~ program_not_halts2_halts2_outputs(skolemFOFtoCNF_V,skolemFOFtoCNF_Y_4(skolemFOFtoCNF_V),bad)
| program_not_halts2_halts2_outputs(skolemFOFtoCNF_U,Y,good) ),
inference(subst,[],[refute_0_6:[bind(V,$fot(skolemFOFtoCNF_V))]]) ).
cnf(refute_0_8,plain,
algorithm_program_decides(skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_9,plain,
( ~ algorithm_program_decides(X)
| program_program_decides(skolemFOFtoCNF_W) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_10,plain,
( ~ algorithm_program_decides(skolemFOFtoCNF_X)
| program_program_decides(skolemFOFtoCNF_W) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_11,plain,
program_program_decides(skolemFOFtoCNF_W),
inference(resolve,[$cnf( algorithm_program_decides(skolemFOFtoCNF_X) )],[refute_0_8,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ program_program_decides(W)
| program_not_halts2_halts3_outputs(W,Y,Z,bad) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_13,plain,
( ~ program_program_decides(skolemFOFtoCNF_W)
| program_not_halts2_halts3_outputs(skolemFOFtoCNF_W,X_49,X_50,bad) ),
inference(subst,[],[refute_0_12:[bind(W,$fot(skolemFOFtoCNF_W)),bind(Y,$fot(X_49)),bind(Z,$fot(X_50))]]) ).
cnf(refute_0_14,plain,
program_not_halts2_halts3_outputs(skolemFOFtoCNF_W,X_49,X_50,bad),
inference(resolve,[$cnf( program_program_decides(skolemFOFtoCNF_W) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
program_not_halts2_halts3_outputs(skolemFOFtoCNF_W,skolemFOFtoCNF_Y_2(skolemFOFtoCNF_W),skolemFOFtoCNF_Y_2(skolemFOFtoCNF_W),bad),
inference(subst,[],[refute_0_14:[bind(X_49,$fot(skolemFOFtoCNF_Y_2(skolemFOFtoCNF_W))),bind(X_50,$fot(skolemFOFtoCNF_Y_2(skolemFOFtoCNF_W)))]]) ).
cnf(refute_0_16,plain,
( ~ program(W)
| ~ program_halts2_halts3_outputs(W,skolemFOFtoCNF_Y_1(W),skolemFOFtoCNF_Y_1(W),good)
| ~ program_not_halts2_halts3_outputs(W,skolemFOFtoCNF_Y_2(W),skolemFOFtoCNF_Y_2(W),bad)
| program_not_halts2_halts2_outputs(skolemFOFtoCNF_V,Y,bad) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_17,plain,
( ~ program(skolemFOFtoCNF_W)
| ~ program_halts2_halts3_outputs(skolemFOFtoCNF_W,skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W),skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W),good)
| ~ program_not_halts2_halts3_outputs(skolemFOFtoCNF_W,skolemFOFtoCNF_Y_2(skolemFOFtoCNF_W),skolemFOFtoCNF_Y_2(skolemFOFtoCNF_W),bad)
| program_not_halts2_halts2_outputs(skolemFOFtoCNF_V,X_338,bad) ),
inference(subst,[],[refute_0_16:[bind(W,$fot(skolemFOFtoCNF_W)),bind(Y,$fot(X_338))]]) ).
cnf(refute_0_18,plain,
( ~ program(skolemFOFtoCNF_W)
| ~ program_halts2_halts3_outputs(skolemFOFtoCNF_W,skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W),skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W),good)
| program_not_halts2_halts2_outputs(skolemFOFtoCNF_V,X_338,bad) ),
inference(resolve,[$cnf( program_not_halts2_halts3_outputs(skolemFOFtoCNF_W,skolemFOFtoCNF_Y_2(skolemFOFtoCNF_W),skolemFOFtoCNF_Y_2(skolemFOFtoCNF_W),bad) )],[refute_0_15,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ program_program_decides(X)
| program(X) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_20,plain,
( ~ program_program_decides(skolemFOFtoCNF_W)
| program(skolemFOFtoCNF_W) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(skolemFOFtoCNF_W))]]) ).
cnf(refute_0_21,plain,
program(skolemFOFtoCNF_W),
inference(resolve,[$cnf( program_program_decides(skolemFOFtoCNF_W) )],[refute_0_11,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ program_halts2_halts3_outputs(skolemFOFtoCNF_W,skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W),skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W),good)
| program_not_halts2_halts2_outputs(skolemFOFtoCNF_V,X_338,bad) ),
inference(resolve,[$cnf( program(skolemFOFtoCNF_W) )],[refute_0_21,refute_0_18]) ).
cnf(refute_0_23,plain,
( ~ program_program_decides(W)
| program_halts2_halts3_outputs(W,Y,Z,good) ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_24,plain,
( ~ program_program_decides(skolemFOFtoCNF_W)
| program_halts2_halts3_outputs(skolemFOFtoCNF_W,X_44,X_45,good) ),
inference(subst,[],[refute_0_23:[bind(W,$fot(skolemFOFtoCNF_W)),bind(Y,$fot(X_44)),bind(Z,$fot(X_45))]]) ).
cnf(refute_0_25,plain,
program_halts2_halts3_outputs(skolemFOFtoCNF_W,X_44,X_45,good),
inference(resolve,[$cnf( program_program_decides(skolemFOFtoCNF_W) )],[refute_0_11,refute_0_24]) ).
cnf(refute_0_26,plain,
program_halts2_halts3_outputs(skolemFOFtoCNF_W,skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W),skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W),good),
inference(subst,[],[refute_0_25:[bind(X_44,$fot(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W))),bind(X_45,$fot(skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W)))]]) ).
cnf(refute_0_27,plain,
program_not_halts2_halts2_outputs(skolemFOFtoCNF_V,X_338,bad),
inference(resolve,[$cnf( program_halts2_halts3_outputs(skolemFOFtoCNF_W,skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W),skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W),good) )],[refute_0_26,refute_0_22]) ).
cnf(refute_0_28,plain,
program_not_halts2_halts2_outputs(skolemFOFtoCNF_V,skolemFOFtoCNF_Y_4(skolemFOFtoCNF_V),bad),
inference(subst,[],[refute_0_27:[bind(X_338,$fot(skolemFOFtoCNF_Y_4(skolemFOFtoCNF_V)))]]) ).
cnf(refute_0_29,plain,
( ~ program(skolemFOFtoCNF_V)
| ~ program_halts2_halts2_outputs(skolemFOFtoCNF_V,skolemFOFtoCNF_Y_3(skolemFOFtoCNF_V),good)
| program_not_halts2_halts2_outputs(skolemFOFtoCNF_U,Y,good) ),
inference(resolve,[$cnf( program_not_halts2_halts2_outputs(skolemFOFtoCNF_V,skolemFOFtoCNF_Y_4(skolemFOFtoCNF_V),bad) )],[refute_0_28,refute_0_7]) ).
cnf(refute_0_30,plain,
( ~ program(W)
| ~ program_halts2_halts3_outputs(W,skolemFOFtoCNF_Y_1(W),skolemFOFtoCNF_Y_1(W),good)
| ~ program_not_halts2_halts3_outputs(W,skolemFOFtoCNF_Y_2(W),skolemFOFtoCNF_Y_2(W),bad)
| program(skolemFOFtoCNF_V) ),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_31,plain,
( ~ program(skolemFOFtoCNF_W)
| ~ program_halts2_halts3_outputs(skolemFOFtoCNF_W,skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W),skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W),good)
| ~ program_not_halts2_halts3_outputs(skolemFOFtoCNF_W,skolemFOFtoCNF_Y_2(skolemFOFtoCNF_W),skolemFOFtoCNF_Y_2(skolemFOFtoCNF_W),bad)
| program(skolemFOFtoCNF_V) ),
inference(subst,[],[refute_0_30:[bind(W,$fot(skolemFOFtoCNF_W))]]) ).
cnf(refute_0_32,plain,
( ~ program(skolemFOFtoCNF_W)
| ~ program_halts2_halts3_outputs(skolemFOFtoCNF_W,skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W),skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W),good)
| program(skolemFOFtoCNF_V) ),
inference(resolve,[$cnf( program_not_halts2_halts3_outputs(skolemFOFtoCNF_W,skolemFOFtoCNF_Y_2(skolemFOFtoCNF_W),skolemFOFtoCNF_Y_2(skolemFOFtoCNF_W),bad) )],[refute_0_15,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ program_halts2_halts3_outputs(skolemFOFtoCNF_W,skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W),skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W),good)
| program(skolemFOFtoCNF_V) ),
inference(resolve,[$cnf( program(skolemFOFtoCNF_W) )],[refute_0_21,refute_0_32]) ).
cnf(refute_0_34,plain,
program(skolemFOFtoCNF_V),
inference(resolve,[$cnf( program_halts2_halts3_outputs(skolemFOFtoCNF_W,skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W),skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W),good) )],[refute_0_26,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ program_halts2_halts2_outputs(skolemFOFtoCNF_V,skolemFOFtoCNF_Y_3(skolemFOFtoCNF_V),good)
| program_not_halts2_halts2_outputs(skolemFOFtoCNF_U,Y,good) ),
inference(resolve,[$cnf( program(skolemFOFtoCNF_V) )],[refute_0_34,refute_0_29]) ).
cnf(refute_0_36,plain,
( ~ program(W)
| ~ program_halts2_halts3_outputs(W,skolemFOFtoCNF_Y_1(W),skolemFOFtoCNF_Y_1(W),good)
| ~ program_not_halts2_halts3_outputs(W,skolemFOFtoCNF_Y_2(W),skolemFOFtoCNF_Y_2(W),bad)
| program_halts2_halts2_outputs(skolemFOFtoCNF_V,Y,good) ),
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_37,plain,
( ~ program(skolemFOFtoCNF_W)
| ~ program_halts2_halts3_outputs(skolemFOFtoCNF_W,skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W),skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W),good)
| ~ program_not_halts2_halts3_outputs(skolemFOFtoCNF_W,skolemFOFtoCNF_Y_2(skolemFOFtoCNF_W),skolemFOFtoCNF_Y_2(skolemFOFtoCNF_W),bad)
| program_halts2_halts2_outputs(skolemFOFtoCNF_V,X_283,good) ),
inference(subst,[],[refute_0_36:[bind(W,$fot(skolemFOFtoCNF_W)),bind(Y,$fot(X_283))]]) ).
cnf(refute_0_38,plain,
( ~ program(skolemFOFtoCNF_W)
| ~ program_halts2_halts3_outputs(skolemFOFtoCNF_W,skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W),skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W),good)
| program_halts2_halts2_outputs(skolemFOFtoCNF_V,X_283,good) ),
inference(resolve,[$cnf( program_not_halts2_halts3_outputs(skolemFOFtoCNF_W,skolemFOFtoCNF_Y_2(skolemFOFtoCNF_W),skolemFOFtoCNF_Y_2(skolemFOFtoCNF_W),bad) )],[refute_0_15,refute_0_37]) ).
cnf(refute_0_39,plain,
( ~ program_halts2_halts3_outputs(skolemFOFtoCNF_W,skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W),skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W),good)
| program_halts2_halts2_outputs(skolemFOFtoCNF_V,X_283,good) ),
inference(resolve,[$cnf( program(skolemFOFtoCNF_W) )],[refute_0_21,refute_0_38]) ).
cnf(refute_0_40,plain,
program_halts2_halts2_outputs(skolemFOFtoCNF_V,X_283,good),
inference(resolve,[$cnf( program_halts2_halts3_outputs(skolemFOFtoCNF_W,skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W),skolemFOFtoCNF_Y_1(skolemFOFtoCNF_W),good) )],[refute_0_26,refute_0_39]) ).
cnf(refute_0_41,plain,
program_halts2_halts2_outputs(skolemFOFtoCNF_V,skolemFOFtoCNF_Y_3(skolemFOFtoCNF_V),good),
inference(subst,[],[refute_0_40:[bind(X_283,$fot(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_V)))]]) ).
cnf(refute_0_42,plain,
program_not_halts2_halts2_outputs(skolemFOFtoCNF_U,Y,good),
inference(resolve,[$cnf( program_halts2_halts2_outputs(skolemFOFtoCNF_V,skolemFOFtoCNF_Y_3(skolemFOFtoCNF_V),good) )],[refute_0_41,refute_0_35]) ).
cnf(refute_0_43,plain,
program_not_halts2_halts2_outputs(skolemFOFtoCNF_U,X_340,good),
inference(subst,[],[refute_0_42:[bind(Y,$fot(X_340))]]) ).
cnf(refute_0_44,plain,
( ~ program_not_halts2(X_340,X_340)
| halts2_outputs(skolemFOFtoCNF_U,X_340,good) ),
inference(resolve,[$cnf( program_not_halts2_halts2_outputs(skolemFOFtoCNF_U,X_340,good) )],[refute_0_43,refute_0_5]) ).
cnf(refute_0_45,plain,
( ~ program_not_halts2(skolemFOFtoCNF_U,skolemFOFtoCNF_U)
| halts2_outputs(skolemFOFtoCNF_U,skolemFOFtoCNF_U,good) ),
inference(subst,[],[refute_0_44:[bind(X_340,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_46,plain,
( ~ program(X)
| halts2(X,Y)
| program_not_halts2(X,Y) ),
inference(canonicalize,[],[normalize_0_36]) ).
cnf(refute_0_47,plain,
( ~ program(skolemFOFtoCNF_U)
| halts2(skolemFOFtoCNF_U,Y)
| program_not_halts2(skolemFOFtoCNF_U,Y) ),
inference(subst,[],[refute_0_46:[bind(X,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_48,plain,
( ~ program(V)
| ~ program_halts2_halts2_outputs(V,skolemFOFtoCNF_Y_3(V),good)
| ~ program_not_halts2_halts2_outputs(V,skolemFOFtoCNF_Y_4(V),bad)
| program(skolemFOFtoCNF_U) ),
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_49,plain,
( ~ program(skolemFOFtoCNF_V)
| ~ program_halts2_halts2_outputs(skolemFOFtoCNF_V,skolemFOFtoCNF_Y_3(skolemFOFtoCNF_V),good)
| ~ program_not_halts2_halts2_outputs(skolemFOFtoCNF_V,skolemFOFtoCNF_Y_4(skolemFOFtoCNF_V),bad)
| program(skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_48:[bind(V,$fot(skolemFOFtoCNF_V))]]) ).
cnf(refute_0_50,plain,
( ~ program(skolemFOFtoCNF_V)
| ~ program_halts2_halts2_outputs(skolemFOFtoCNF_V,skolemFOFtoCNF_Y_3(skolemFOFtoCNF_V),good)
| program(skolemFOFtoCNF_U) ),
inference(resolve,[$cnf( program_not_halts2_halts2_outputs(skolemFOFtoCNF_V,skolemFOFtoCNF_Y_4(skolemFOFtoCNF_V),bad) )],[refute_0_28,refute_0_49]) ).
cnf(refute_0_51,plain,
( ~ program_halts2_halts2_outputs(skolemFOFtoCNF_V,skolemFOFtoCNF_Y_3(skolemFOFtoCNF_V),good)
| program(skolemFOFtoCNF_U) ),
inference(resolve,[$cnf( program(skolemFOFtoCNF_V) )],[refute_0_34,refute_0_50]) ).
cnf(refute_0_52,plain,
program(skolemFOFtoCNF_U),
inference(resolve,[$cnf( program_halts2_halts2_outputs(skolemFOFtoCNF_V,skolemFOFtoCNF_Y_3(skolemFOFtoCNF_V),good) )],[refute_0_41,refute_0_51]) ).
cnf(refute_0_53,plain,
( halts2(skolemFOFtoCNF_U,Y)
| program_not_halts2(skolemFOFtoCNF_U,Y) ),
inference(resolve,[$cnf( program(skolemFOFtoCNF_U) )],[refute_0_52,refute_0_47]) ).
cnf(refute_0_54,plain,
( halts2(skolemFOFtoCNF_U,skolemFOFtoCNF_U)
| program_not_halts2(skolemFOFtoCNF_U,skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_53:[bind(Y,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_55,plain,
( halts2(skolemFOFtoCNF_U,skolemFOFtoCNF_U)
| halts2_outputs(skolemFOFtoCNF_U,skolemFOFtoCNF_U,good) ),
inference(resolve,[$cnf( program_not_halts2(skolemFOFtoCNF_U,skolemFOFtoCNF_U) )],[refute_0_54,refute_0_45]) ).
cnf(refute_0_56,plain,
halts2(skolemFOFtoCNF_U,skolemFOFtoCNF_U),
inference(resolve,[$cnf( halts2_outputs(skolemFOFtoCNF_U,skolemFOFtoCNF_U,good) )],[refute_0_55,refute_0_3]) ).
cnf(refute_0_57,plain,
( ~ program(skolemFOFtoCNF_U)
| program_halts2(skolemFOFtoCNF_U,skolemFOFtoCNF_U) ),
inference(resolve,[$cnf( halts2(skolemFOFtoCNF_U,skolemFOFtoCNF_U) )],[refute_0_56,refute_0_1]) ).
cnf(refute_0_58,plain,
program_halts2(skolemFOFtoCNF_U,skolemFOFtoCNF_U),
inference(resolve,[$cnf( program(skolemFOFtoCNF_U) )],[refute_0_52,refute_0_57]) ).
cnf(refute_0_59,plain,
( ~ halts2(skolemFOFtoCNF_U,Y)
| ~ program(V)
| ~ program_halts2(Y,Y)
| ~ program_halts2_halts2_outputs(V,skolemFOFtoCNF_Y_3(V),good)
| ~ program_not_halts2_halts2_outputs(V,skolemFOFtoCNF_Y_4(V),bad) ),
inference(canonicalize,[],[normalize_0_38]) ).
cnf(refute_0_60,plain,
( ~ halts2(skolemFOFtoCNF_U,X_662)
| ~ program(skolemFOFtoCNF_V)
| ~ program_halts2(X_662,X_662)
| ~ program_halts2_halts2_outputs(skolemFOFtoCNF_V,skolemFOFtoCNF_Y_3(skolemFOFtoCNF_V),good)
| ~ program_not_halts2_halts2_outputs(skolemFOFtoCNF_V,skolemFOFtoCNF_Y_4(skolemFOFtoCNF_V),bad) ),
inference(subst,[],[refute_0_59:[bind(V,$fot(skolemFOFtoCNF_V)),bind(Y,$fot(X_662))]]) ).
cnf(refute_0_61,plain,
( ~ halts2(skolemFOFtoCNF_U,X_662)
| ~ program(skolemFOFtoCNF_V)
| ~ program_halts2(X_662,X_662)
| ~ program_halts2_halts2_outputs(skolemFOFtoCNF_V,skolemFOFtoCNF_Y_3(skolemFOFtoCNF_V),good) ),
inference(resolve,[$cnf( program_not_halts2_halts2_outputs(skolemFOFtoCNF_V,skolemFOFtoCNF_Y_4(skolemFOFtoCNF_V),bad) )],[refute_0_28,refute_0_60]) ).
cnf(refute_0_62,plain,
( ~ halts2(skolemFOFtoCNF_U,X_662)
| ~ program_halts2(X_662,X_662)
| ~ program_halts2_halts2_outputs(skolemFOFtoCNF_V,skolemFOFtoCNF_Y_3(skolemFOFtoCNF_V),good) ),
inference(resolve,[$cnf( program(skolemFOFtoCNF_V) )],[refute_0_34,refute_0_61]) ).
cnf(refute_0_63,plain,
( ~ halts2(skolemFOFtoCNF_U,X_662)
| ~ program_halts2(X_662,X_662) ),
inference(resolve,[$cnf( program_halts2_halts2_outputs(skolemFOFtoCNF_V,skolemFOFtoCNF_Y_3(skolemFOFtoCNF_V),good) )],[refute_0_41,refute_0_62]) ).
cnf(refute_0_64,plain,
( ~ halts2(skolemFOFtoCNF_U,skolemFOFtoCNF_U)
| ~ program_halts2(skolemFOFtoCNF_U,skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_63:[bind(X_662,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_65,plain,
~ halts2(skolemFOFtoCNF_U,skolemFOFtoCNF_U),
inference(resolve,[$cnf( program_halts2(skolemFOFtoCNF_U,skolemFOFtoCNF_U) )],[refute_0_58,refute_0_64]) ).
cnf(refute_0_66,plain,
$false,
inference(resolve,[$cnf( halts2(skolemFOFtoCNF_U,skolemFOFtoCNF_U) )],[refute_0_56,refute_0_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : COM003+2 : TPTP v8.1.0. Bugfixed v2.2.0.
% 0.00/0.10 % Command : metis --show proof --show saturation %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Thu Jun 16 20:08:45 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.09/0.29 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.46/0.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.46/0.64
% 0.46/0.64 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.46/0.65
%------------------------------------------------------------------------------