%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : COM003+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 08:14:42 AM UTC 2026
% Result : Theorem 38.45s 38.76s
% Output : Proof 38.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 216 ( 87 unt; 0 def)
% Number of atoms : 795 ( 0 equ)
% Maximal formula atoms : 36 ( 3 avg)
% Number of connectives : 955 ( 376 ~; 367 |; 193 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 22 ( 21 usr; 1 prp; 0-5 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-1 aty)
% Number of variables : 296 ( 39 sgn 167 !; 46 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
( ? [X] :
( ! [Y] :
( program(Y)
=> ! [Z] : decides(X,Y,Z) )
& algorithm(X) )
=> ? [W] :
( ! [Y] :
( program(Y)
=> ! [Z] : decides(W,Y,Z) )
& program(W) ) ),
file('theBenchmark.p',p1) ).
fof(p2,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('theBenchmark.p',p2) ).
fof(p3,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('theBenchmark.p',p3) ).
fof(p4,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('theBenchmark.p',p4) ).
fof(prove_this,conjecture,
~ ? [X1] :
( ! [Y1] :
( program(Y1)
=> ! [Z1] : decides(X1,Y1,Z1) )
& algorithm(X1) ),
file('theBenchmark.p',prove_this) ).
fof(f_1_1,plain,
( ? [W] :
( ! [Y] :
( ! [Z] : decides(W,Y,Z)
| ~ program(Y) )
& program(W) )
| ! [X] :
( ? [Y] :
( ? [Z] : ~ decides(X,Y,Z)
& program(Y) )
| ~ algorithm(X) ) ),
inference(fof_nnf,[status(thm)],[p1]) ).
fof(f_1_2,plain,
( ? [U_5] :
( ! [U_4] :
( ! [U_3] : decides(U_5,U_4,U_3)
| ~ program(U_4) )
& program(U_5) )
| ! [U_2] :
( ? [U_1] :
( ? [U_0] : ~ decides(U_2,U_1,U_0)
& program(U_1) )
| ~ algorithm(U_2) ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ? [U_5] :
( ! [U_4] :
( ! [U_3] : decides(U_5,U_4,U_3)
| ~ program(U_4) )
& program(U_5) )
| ! [U_2] :
( ( ? [U_0] : ~ decides(U_2,sK1(U_2),U_0)
& program(sK1(U_2)) )
| ~ algorithm(U_2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_1,sK1(U_2))],[f_1_2]) ).
fof(f_1_4,plain,
( ? [U_5] :
( ! [U_4] :
( ! [U_3] : decides(U_5,U_4,U_3)
| ~ program(U_4) )
& program(U_5) )
| ! [U_2] :
( ( ~ decides(U_2,sK1(U_2),sK2(U_2))
& program(sK1(U_2)) )
| ~ algorithm(U_2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_0,sK2(U_2))],[f_1_3]) ).
fof(f_1_5,plain,
( ( ! [U_4] :
( ! [U_3] : decides(sK3,U_4,U_3)
| ~ program(U_4) )
& program(sK3) )
| ! [U_2] :
( ( ~ decides(U_2,sK1(U_2),sK2(U_2))
& program(sK1(U_2)) )
| ~ algorithm(U_2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_5,sK3)],[f_1_4]) ).
fof(f_1_6,plain,
( ! [U_3,U_4] :
( decides(sK3,U_4,U_3)
| ~ program(U_4)
| ~ sP1(U_3,U_4) )
& ! [U_3,U_4] :
( program(sK3)
| ~ sP1(U_3,U_4) )
& ! [U_2] :
( ~ decides(U_2,sK1(U_2),sK2(U_2))
| ~ sP0(U_2) )
& ! [U_2] :
( program(sK1(U_2))
| ~ sP0(U_2) )
& ! [U_2,U_3,U_4] :
( sP1(U_3,U_4)
| sP0(U_2)
| ~ algorithm(U_2) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_1_5]) ).
cnf(f_1_7,plain,
( sP1(U_3,U_4)
| sP0(U_2)
| ~ algorithm(U_2) ),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_8,plain,
( program(sK1(U_2))
| ~ sP0(U_2) ),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_9,plain,
( ~ decides(U_2,sK1(U_2),sK2(U_2))
| ~ sP0(U_2) ),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_10,plain,
( program(sK3)
| ~ sP1(U_3,U_4) ),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_11,plain,
( decides(sK3,U_4,U_3)
| ~ program(U_4)
| ~ sP1(U_3,U_4) ),
inference(clausify,[status(thm)],[f_1_6]) ).
fof(f_2_1,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(fof_nnf,[status(thm)],[p2]) ).
fof(f_2_2,plain,
! [U_10] :
( ! [U_9,U_8] :
( ( ( outputs(U_10,bad)
& halts3(U_10,U_9,U_8) )
| halts2(U_9,U_8)
| ~ program(U_9) )
& ( ( outputs(U_10,good)
& halts3(U_10,U_9,U_8) )
| ~ halts2(U_9,U_8)
| ~ program(U_9) ) )
| ? [U_7] :
( ? [U_6] : ~ decides(U_10,U_7,U_6)
& program(U_7) )
| ~ program(U_10) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_10] :
( ( ! [U_14,U_12] :
( ( outputs(U_10,bad)
& halts3(U_10,U_14,U_12) )
| halts2(U_14,U_12)
| ~ program(U_14) )
& ! [U_13,U_11] :
( ( outputs(U_10,good)
& halts3(U_10,U_13,U_11) )
| ~ halts2(U_13,U_11)
| ~ program(U_13) ) )
| ? [U_7] :
( ? [U_6] : ~ decides(U_10,U_7,U_6)
& program(U_7) )
| ~ program(U_10) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
fof(f_2_4,plain,
! [U_10] :
( ( ! [U_14,U_12] :
( ( outputs(U_10,bad)
& halts3(U_10,U_14,U_12) )
| halts2(U_14,U_12)
| ~ program(U_14) )
& ! [U_13,U_11] :
( ( outputs(U_10,good)
& halts3(U_10,U_13,U_11) )
| ~ halts2(U_13,U_11)
| ~ program(U_13) ) )
| ( ? [U_6] : ~ decides(U_10,sK4(U_10),U_6)
& program(sK4(U_10)) )
| ~ program(U_10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_7,sK4(U_10))],[f_2_3]) ).
fof(f_2_5,plain,
! [U_10] :
( ( ! [U_14,U_12] :
( ( outputs(U_10,bad)
& halts3(U_10,U_14,U_12) )
| halts2(U_14,U_12)
| ~ program(U_14) )
& ! [U_13,U_11] :
( ( outputs(U_10,good)
& halts3(U_10,U_13,U_11) )
| ~ halts2(U_13,U_11)
| ~ program(U_13) ) )
| ( ~ decides(U_10,sK4(U_10),sK5(U_10))
& program(sK4(U_10)) )
| ~ program(U_10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_6,sK5(U_10))],[f_2_4]) ).
fof(f_2_6,plain,
( ! [U_14,U_10,U_12] :
( outputs(U_10,bad)
| ~ sP4(U_14,U_10,U_12) )
& ! [U_14,U_10,U_12] :
( halts3(U_10,U_14,U_12)
| ~ sP4(U_14,U_10,U_12) )
& ! [U_10,U_13,U_11] :
( outputs(U_10,good)
| ~ sP3(U_10,U_13,U_11) )
& ! [U_10,U_13,U_11] :
( halts3(U_10,U_13,U_11)
| ~ sP3(U_10,U_13,U_11) )
& ! [U_14,U_10,U_13,U_11,U_12] :
( sP4(U_14,U_10,U_12)
| halts2(U_14,U_12)
| ~ program(U_14)
| ~ sP5(U_14,U_10,U_13,U_11,U_12) )
& ! [U_14,U_10,U_13,U_11,U_12] :
( sP3(U_10,U_13,U_11)
| ~ halts2(U_13,U_11)
| ~ program(U_13)
| ~ sP5(U_14,U_10,U_13,U_11,U_12) )
& ! [U_10] :
( ~ decides(U_10,sK4(U_10),sK5(U_10))
| ~ sP2(U_10) )
& ! [U_10] :
( program(sK4(U_10))
| ~ sP2(U_10) )
& ! [U_14,U_10,U_13,U_11,U_12] :
( sP5(U_14,U_10,U_13,U_11,U_12)
| sP2(U_10)
| ~ program(U_10) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2,sP3,sP4,sP5])],[f_2_5]) ).
cnf(f_2_7,plain,
( sP5(U_14,U_10,U_13,U_11,U_12)
| sP2(U_10)
| ~ program(U_10) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_8,plain,
( program(sK4(U_10))
| ~ sP2(U_10) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_9,plain,
( ~ decides(U_10,sK4(U_10),sK5(U_10))
| ~ sP2(U_10) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_10,plain,
( sP3(U_10,U_13,U_11)
| ~ halts2(U_13,U_11)
| ~ program(U_13)
| ~ sP5(U_14,U_10,U_13,U_11,U_12) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_11,plain,
( sP4(U_14,U_10,U_12)
| halts2(U_14,U_12)
| ~ program(U_14)
| ~ sP5(U_14,U_10,U_13,U_11,U_12) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_12,plain,
( halts3(U_10,U_13,U_11)
| ~ sP3(U_10,U_13,U_11) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_13,plain,
( outputs(U_10,good)
| ~ sP3(U_10,U_13,U_11) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_14,plain,
( halts3(U_10,U_14,U_12)
| ~ sP4(U_14,U_10,U_12) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_15,plain,
( outputs(U_10,bad)
| ~ sP4(U_14,U_10,U_12) ),
inference(clausify,[status(thm)],[f_2_6]) ).
fof(f_3_1,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(fof_nnf,[status(thm)],[p3]) ).
fof(f_3_2,plain,
( ? [U_18] :
( ! [U_17] :
( ( ( outputs(U_18,bad)
& halts2(U_18,U_17) )
| halts2(U_17,U_17)
| ~ program(U_17) )
& ( ( outputs(U_18,good)
& halts2(U_18,U_17) )
| ~ halts2(U_17,U_17)
| ~ program(U_17) ) )
& program(U_18) )
| ! [U_16] :
( ? [U_15] :
( ( ( ~ outputs(U_16,bad)
| ~ halts3(U_16,U_15,U_15) )
& ~ halts2(U_15,U_15)
& program(U_15) )
| ( ( ~ outputs(U_16,good)
| ~ halts3(U_16,U_15,U_15) )
& halts2(U_15,U_15)
& program(U_15) ) )
| ~ program(U_16) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ? [U_18] :
( ! [U_22] :
( ( outputs(U_18,bad)
& halts2(U_18,U_22) )
| halts2(U_22,U_22)
| ~ program(U_22) )
& ! [U_21] :
( ( outputs(U_18,good)
& halts2(U_18,U_21) )
| ~ halts2(U_21,U_21)
| ~ program(U_21) )
& program(U_18) )
| ! [U_16] :
( ? [U_20] :
( ( ~ outputs(U_16,bad)
| ~ halts3(U_16,U_20,U_20) )
& ~ halts2(U_20,U_20)
& program(U_20) )
| ? [U_19] :
( ( ~ outputs(U_16,good)
| ~ halts3(U_16,U_19,U_19) )
& halts2(U_19,U_19)
& program(U_19) )
| ~ program(U_16) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ? [U_18] :
( ! [U_22] :
( ( outputs(U_18,bad)
& halts2(U_18,U_22) )
| halts2(U_22,U_22)
| ~ program(U_22) )
& ! [U_21] :
( ( outputs(U_18,good)
& halts2(U_18,U_21) )
| ~ halts2(U_21,U_21)
| ~ program(U_21) )
& program(U_18) )
| ! [U_16] :
( ? [U_20] :
( ( ~ outputs(U_16,bad)
| ~ halts3(U_16,U_20,U_20) )
& ~ halts2(U_20,U_20)
& program(U_20) )
| ( ( ~ outputs(U_16,good)
| ~ halts3(U_16,sK6(U_16),sK6(U_16)) )
& halts2(sK6(U_16),sK6(U_16))
& program(sK6(U_16)) )
| ~ program(U_16) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_19,sK6(U_16))],[f_3_3]) ).
fof(f_3_5,plain,
( ? [U_18] :
( ! [U_22] :
( ( outputs(U_18,bad)
& halts2(U_18,U_22) )
| halts2(U_22,U_22)
| ~ program(U_22) )
& ! [U_21] :
( ( outputs(U_18,good)
& halts2(U_18,U_21) )
| ~ halts2(U_21,U_21)
| ~ program(U_21) )
& program(U_18) )
| ! [U_16] :
( ( ( ~ outputs(U_16,bad)
| ~ halts3(U_16,sK7(U_16),sK7(U_16)) )
& ~ halts2(sK7(U_16),sK7(U_16))
& program(sK7(U_16)) )
| ( ( ~ outputs(U_16,good)
| ~ halts3(U_16,sK6(U_16),sK6(U_16)) )
& halts2(sK6(U_16),sK6(U_16))
& program(sK6(U_16)) )
| ~ program(U_16) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_20,sK7(U_16))],[f_3_4]) ).
fof(f_3_6,plain,
( ( ! [U_22] :
( ( outputs(sK8,bad)
& halts2(sK8,U_22) )
| halts2(U_22,U_22)
| ~ program(U_22) )
& ! [U_21] :
( ( outputs(sK8,good)
& halts2(sK8,U_21) )
| ~ halts2(U_21,U_21)
| ~ program(U_21) )
& program(sK8) )
| ! [U_16] :
( ( ( ~ outputs(U_16,bad)
| ~ halts3(U_16,sK7(U_16),sK7(U_16)) )
& ~ halts2(sK7(U_16),sK7(U_16))
& program(sK7(U_16)) )
| ( ( ~ outputs(U_16,good)
| ~ halts3(U_16,sK6(U_16),sK6(U_16)) )
& halts2(sK6(U_16),sK6(U_16))
& program(sK6(U_16)) )
| ~ program(U_16) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_18,sK8)],[f_3_5]) ).
fof(f_3_7,plain,
( ! [U_22] :
( outputs(sK8,bad)
| ~ sP9(U_22) )
& ! [U_22] :
( halts2(sK8,U_22)
| ~ sP9(U_22) )
& ! [U_21] :
( outputs(sK8,good)
| ~ sP8(U_21) )
& ! [U_21] :
( halts2(sK8,U_21)
| ~ sP8(U_21) )
& ! [U_22,U_21] :
( sP9(U_22)
| halts2(U_22,U_22)
| ~ program(U_22)
| ~ sP10(U_22,U_21) )
& ! [U_22,U_21] :
( sP8(U_21)
| ~ halts2(U_21,U_21)
| ~ program(U_21)
| ~ sP10(U_22,U_21) )
& ! [U_22,U_21] :
( program(sK8)
| ~ sP10(U_22,U_21) )
& ! [U_16] :
( ~ outputs(U_16,bad)
| ~ halts3(U_16,sK7(U_16),sK7(U_16))
| ~ sP7(U_16) )
& ! [U_16] :
( ~ halts2(sK7(U_16),sK7(U_16))
| ~ sP7(U_16) )
& ! [U_16] :
( program(sK7(U_16))
| ~ sP7(U_16) )
& ! [U_16] :
( ~ outputs(U_16,good)
| ~ halts3(U_16,sK6(U_16),sK6(U_16))
| ~ sP6(U_16) )
& ! [U_16] :
( halts2(sK6(U_16),sK6(U_16))
| ~ sP6(U_16) )
& ! [U_16] :
( program(sK6(U_16))
| ~ sP6(U_16) )
& ! [U_16,U_22,U_21] :
( sP10(U_22,U_21)
| sP7(U_16)
| sP6(U_16)
| ~ program(U_16) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6,sP7,sP8,sP9,sP10])],[f_3_6]) ).
cnf(f_3_8,plain,
( sP10(U_22,U_21)
| sP7(U_16)
| sP6(U_16)
| ~ program(U_16) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_9,plain,
( program(sK6(U_16))
| ~ sP6(U_16) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_10,plain,
( halts2(sK6(U_16),sK6(U_16))
| ~ sP6(U_16) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_11,plain,
( ~ outputs(U_16,good)
| ~ halts3(U_16,sK6(U_16),sK6(U_16))
| ~ sP6(U_16) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_12,plain,
( program(sK7(U_16))
| ~ sP7(U_16) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_13,plain,
( ~ halts2(sK7(U_16),sK7(U_16))
| ~ sP7(U_16) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_14,plain,
( ~ outputs(U_16,bad)
| ~ halts3(U_16,sK7(U_16),sK7(U_16))
| ~ sP7(U_16) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_15,plain,
( program(sK8)
| ~ sP10(U_22,U_21) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_16,plain,
( sP8(U_21)
| ~ halts2(U_21,U_21)
| ~ program(U_21)
| ~ sP10(U_22,U_21) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_17,plain,
( sP9(U_22)
| halts2(U_22,U_22)
| ~ program(U_22)
| ~ sP10(U_22,U_21) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_18,plain,
( halts2(sK8,U_21)
| ~ sP8(U_21) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_19,plain,
( outputs(sK8,good)
| ~ sP8(U_21) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_20,plain,
( halts2(sK8,U_22)
| ~ sP9(U_22) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_21,plain,
( outputs(sK8,bad)
| ~ sP9(U_22) ),
inference(clausify,[status(thm)],[f_3_7]) ).
fof(f_4_1,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(fof_nnf,[status(thm)],[p4]) ).
fof(f_4_2,plain,
( ? [U_26] :
( ! [U_25] :
( ( ( outputs(U_26,bad)
& halts2(U_26,U_25) )
| halts2(U_25,U_25)
| ~ program(U_25) )
& ( ~ halts2(U_26,U_25)
| ~ halts2(U_25,U_25)
| ~ program(U_25) ) )
& program(U_26) )
| ! [U_24] :
( ? [U_23] :
( ( ( ~ outputs(U_24,bad)
| ~ halts2(U_24,U_23) )
& ~ halts2(U_23,U_23)
& program(U_23) )
| ( ( ~ outputs(U_24,good)
| ~ halts2(U_24,U_23) )
& halts2(U_23,U_23)
& program(U_23) ) )
| ~ program(U_24) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ? [U_26] :
( ! [U_30] :
( ( outputs(U_26,bad)
& halts2(U_26,U_30) )
| halts2(U_30,U_30)
| ~ program(U_30) )
& ! [U_29] :
( ~ halts2(U_26,U_29)
| ~ halts2(U_29,U_29)
| ~ program(U_29) )
& program(U_26) )
| ! [U_24] :
( ? [U_28] :
( ( ~ outputs(U_24,bad)
| ~ halts2(U_24,U_28) )
& ~ halts2(U_28,U_28)
& program(U_28) )
| ? [U_27] :
( ( ~ outputs(U_24,good)
| ~ halts2(U_24,U_27) )
& halts2(U_27,U_27)
& program(U_27) )
| ~ program(U_24) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ? [U_26] :
( ! [U_30] :
( ( outputs(U_26,bad)
& halts2(U_26,U_30) )
| halts2(U_30,U_30)
| ~ program(U_30) )
& ! [U_29] :
( ~ halts2(U_26,U_29)
| ~ halts2(U_29,U_29)
| ~ program(U_29) )
& program(U_26) )
| ! [U_24] :
( ? [U_28] :
( ( ~ outputs(U_24,bad)
| ~ halts2(U_24,U_28) )
& ~ halts2(U_28,U_28)
& program(U_28) )
| ( ( ~ outputs(U_24,good)
| ~ halts2(U_24,sK9(U_24)) )
& halts2(sK9(U_24),sK9(U_24))
& program(sK9(U_24)) )
| ~ program(U_24) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_27,sK9(U_24))],[f_4_3]) ).
fof(f_4_5,plain,
( ? [U_26] :
( ! [U_30] :
( ( outputs(U_26,bad)
& halts2(U_26,U_30) )
| halts2(U_30,U_30)
| ~ program(U_30) )
& ! [U_29] :
( ~ halts2(U_26,U_29)
| ~ halts2(U_29,U_29)
| ~ program(U_29) )
& program(U_26) )
| ! [U_24] :
( ( ( ~ outputs(U_24,bad)
| ~ halts2(U_24,sK10(U_24)) )
& ~ halts2(sK10(U_24),sK10(U_24))
& program(sK10(U_24)) )
| ( ( ~ outputs(U_24,good)
| ~ halts2(U_24,sK9(U_24)) )
& halts2(sK9(U_24),sK9(U_24))
& program(sK9(U_24)) )
| ~ program(U_24) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_28,sK10(U_24))],[f_4_4]) ).
fof(f_4_6,plain,
( ( ! [U_30] :
( ( outputs(sK11,bad)
& halts2(sK11,U_30) )
| halts2(U_30,U_30)
| ~ program(U_30) )
& ! [U_29] :
( ~ halts2(sK11,U_29)
| ~ halts2(U_29,U_29)
| ~ program(U_29) )
& program(sK11) )
| ! [U_24] :
( ( ( ~ outputs(U_24,bad)
| ~ halts2(U_24,sK10(U_24)) )
& ~ halts2(sK10(U_24),sK10(U_24))
& program(sK10(U_24)) )
| ( ( ~ outputs(U_24,good)
| ~ halts2(U_24,sK9(U_24)) )
& halts2(sK9(U_24),sK9(U_24))
& program(sK9(U_24)) )
| ~ program(U_24) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_26,sK11)],[f_4_5]) ).
fof(f_4_7,plain,
( ! [U_30] :
( outputs(sK11,bad)
| ~ sP13(U_30) )
& ! [U_30] :
( halts2(sK11,U_30)
| ~ sP13(U_30) )
& ! [U_29,U_30] :
( sP13(U_30)
| halts2(U_30,U_30)
| ~ program(U_30)
| ~ sP14(U_29,U_30) )
& ! [U_29,U_30] :
( ~ halts2(sK11,U_29)
| ~ halts2(U_29,U_29)
| ~ program(U_29)
| ~ sP14(U_29,U_30) )
& ! [U_29,U_30] :
( program(sK11)
| ~ sP14(U_29,U_30) )
& ! [U_24] :
( ~ outputs(U_24,bad)
| ~ halts2(U_24,sK10(U_24))
| ~ sP12(U_24) )
& ! [U_24] :
( ~ halts2(sK10(U_24),sK10(U_24))
| ~ sP12(U_24) )
& ! [U_24] :
( program(sK10(U_24))
| ~ sP12(U_24) )
& ! [U_24] :
( ~ outputs(U_24,good)
| ~ halts2(U_24,sK9(U_24))
| ~ sP11(U_24) )
& ! [U_24] :
( halts2(sK9(U_24),sK9(U_24))
| ~ sP11(U_24) )
& ! [U_24] :
( program(sK9(U_24))
| ~ sP11(U_24) )
& ! [U_29,U_30,U_24] :
( sP14(U_29,U_30)
| sP12(U_24)
| sP11(U_24)
| ~ program(U_24) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11,sP12,sP13,sP14])],[f_4_6]) ).
cnf(f_4_8,plain,
( sP14(U_29,U_30)
| sP12(U_24)
| sP11(U_24)
| ~ program(U_24) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_9,plain,
( program(sK9(U_24))
| ~ sP11(U_24) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_10,plain,
( halts2(sK9(U_24),sK9(U_24))
| ~ sP11(U_24) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_11,plain,
( ~ outputs(U_24,good)
| ~ halts2(U_24,sK9(U_24))
| ~ sP11(U_24) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_12,plain,
( program(sK10(U_24))
| ~ sP12(U_24) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_13,plain,
( ~ halts2(sK10(U_24),sK10(U_24))
| ~ sP12(U_24) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_14,plain,
( ~ outputs(U_24,bad)
| ~ halts2(U_24,sK10(U_24))
| ~ sP12(U_24) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_15,plain,
( program(sK11)
| ~ sP14(U_29,U_30) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_16,plain,
( ~ halts2(sK11,U_29)
| ~ halts2(U_29,U_29)
| ~ program(U_29)
| ~ sP14(U_29,U_30) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_17,plain,
( sP13(U_30)
| halts2(U_30,U_30)
| ~ program(U_30)
| ~ sP14(U_29,U_30) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_18,plain,
( halts2(sK11,U_30)
| ~ sP13(U_30) ),
inference(clausify,[status(thm)],[f_4_7]) ).
fof(f_5_1,negated_conjecture,
? [X1] :
( ! [Y1] :
( program(Y1)
=> ! [Z1] : decides(X1,Y1,Z1) )
& algorithm(X1) ),
inference(negate,[status(cth)],[prove_this]) ).
fof(f_5_2,negated_conjecture,
? [X1] :
( ! [Y1] :
( ! [Z1] : decides(X1,Y1,Z1)
| ~ program(Y1) )
& algorithm(X1) ),
inference(fof_nnf,[status(thm)],[f_5_1]) ).
fof(f_5_3,negated_conjecture,
? [U_33] :
( ! [U_32] :
( ! [U_31] : decides(U_33,U_32,U_31)
| ~ program(U_32) )
& algorithm(U_33) ),
inference(variable_rename,[status(thm)],[f_5_2]) ).
fof(f_5_4,negated_conjecture,
( ! [U_32] :
( ! [U_31] : decides(sK12,U_32,U_31)
| ~ program(U_32) )
& algorithm(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_33,sK12)],[f_5_3]) ).
fof(f_5_5,negated_conjecture,
( ! [U_32,U_31] :
( decides(sK12,U_32,U_31)
| ~ program(U_32) )
& algorithm(sK12) ),
inference(definitional_conversion,[status(esa)],[f_5_4]) ).
cnf(f_5_6,negated_conjecture,
algorithm(sK12),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_7,negated_conjecture,
( decides(sK12,U_32,U_31)
| ~ program(U_32) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(t1,plain,
algorithm(sK12),
inference(start,[status(thm),parent(0:0)],[f_5_6]) ).
cnf(t2,plain,
( sP0(sK12)
| sP1(sK5(sK3),sK4(sK3))
| ~ algorithm(sK12) ),
inference(extension,[status(thm),parent(t1:1)],[f_1_7]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( program(sK3)
| ~ sP1(sK5(sK3),sK4(sK3)) ),
inference(extension,[status(thm),parent(t2:2)],[f_1_10]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( sP6(sK3)
| sP7(sK3)
| sP10(sK10(sK8),sK9(sK8))
| ~ program(sK3) ),
inference(extension,[status(thm),parent(t4:2)],[f_3_8]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( program(sK8)
| ~ sP10(sK10(sK8),sK9(sK8)) ),
inference(extension,[status(thm),parent(t6:2)],[f_3_15]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( sP11(sK8)
| sP12(sK8)
| sP14(sK11,sK11)
| ~ program(sK8) ),
inference(extension,[status(thm),parent(t8:2)],[f_4_8]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( ~ program(sK11)
| halts2(sK11,sK11)
| sP13(sK11)
| ~ sP14(sK11,sK11) ),
inference(extension,[status(thm),parent(t10:2)],[f_4_17]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( halts2(sK11,sK11)
| ~ sP13(sK11) ),
inference(extension,[status(thm),parent(t12:2)],[f_4_18]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( ~ program(sK11)
| ~ halts2(sK11,sK11)
| ~ sP14(sK11,sK11)
| ~ halts2(sK11,sK11) ),
inference(extension,[status(thm),parent(t14:2)],[f_4_16]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
$false,
inference(reduction,[status(thm),parent(t16:2)],[t16:2,t10:2]) ).
cnf(t19,plain,
$false,
inference(reduction,[status(thm),parent(t16:3)],[t16:3,t14:2]) ).
cnf(t20,plain,
( ~ sP14(sK11,sK11)
| program(sK11) ),
inference(extension,[status(thm),parent(t16:4)],[f_4_15]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:4]) ).
cnf(t22,plain,
$false,
inference(reduction,[status(thm),parent(t20:2)],[t20:2,t10:2]) ).
cnf(t23,plain,
( ~ program(sK11)
| ~ halts2(sK11,sK11)
| ~ sP14(sK11,sK11)
| ~ halts2(sK11,sK11) ),
inference(extension,[status(thm),parent(t12:3)],[f_4_16]) ).
cnf(t24,plain,
$false,
inference(connection,[status(thm),parent(t23:1)],[t23:1,t12:3]) ).
cnf(t25,plain,
$false,
inference(reduction,[status(thm),parent(t23:2)],[t23:2,t10:2]) ).
cnf(t26,plain,
$false,
inference(reduction,[status(thm),parent(t23:3)],[t23:3,t12:3]) ).
cnf(t27,plain,
( ~ sP14(sK11,sK11)
| program(sK11) ),
inference(extension,[status(thm),parent(t23:4)],[f_4_15]) ).
cnf(t28,plain,
$false,
inference(connection,[status(thm),parent(t27:1)],[t27:1,t23:4]) ).
cnf(t29,plain,
$false,
inference(reduction,[status(thm),parent(t27:2)],[t27:2,t10:2]) ).
cnf(t30,plain,
( ~ sP14(sK11,sK11)
| program(sK11) ),
inference(extension,[status(thm),parent(t12:4)],[f_4_15]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t12:4]) ).
cnf(t32,plain,
$false,
inference(reduction,[status(thm),parent(t30:2)],[t30:2,t10:2]) ).
cnf(t33,plain,
( ~ halts2(sK8,sK10(sK8))
| ~ outputs(sK8,bad)
| ~ sP12(sK8) ),
inference(extension,[status(thm),parent(t10:3)],[f_4_14]) ).
cnf(t34,plain,
$false,
inference(connection,[status(thm),parent(t33:1)],[t33:1,t10:3]) ).
cnf(t35,plain,
( ~ sP9(sK10(sK8))
| outputs(sK8,bad) ),
inference(extension,[status(thm),parent(t33:2)],[f_3_21]) ).
cnf(t36,plain,
$false,
inference(connection,[status(thm),parent(t35:1)],[t35:1,t33:2]) ).
cnf(t37,plain,
( ~ program(sK10(sK8))
| halts2(sK10(sK8),sK10(sK8))
| ~ sP10(sK10(sK8),sK9(sK8))
| sP9(sK10(sK8)) ),
inference(extension,[status(thm),parent(t35:2)],[f_3_17]) ).
cnf(t38,plain,
$false,
inference(connection,[status(thm),parent(t37:1)],[t37:1,t35:2]) ).
cnf(t39,plain,
$false,
inference(reduction,[status(thm),parent(t37:2)],[t37:2,t6:2]) ).
cnf(t40,plain,
( ~ sP12(sK8)
| ~ halts2(sK10(sK8),sK10(sK8)) ),
inference(extension,[status(thm),parent(t37:3)],[f_4_13]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t37:3]) ).
cnf(t42,plain,
$false,
inference(reduction,[status(thm),parent(t40:2)],[t40:2,t10:3]) ).
cnf(t43,plain,
( ~ sP12(sK8)
| program(sK10(sK8)) ),
inference(extension,[status(thm),parent(t37:4)],[f_4_12]) ).
cnf(t44,plain,
$false,
inference(connection,[status(thm),parent(t43:1)],[t43:1,t37:4]) ).
cnf(t45,plain,
$false,
inference(reduction,[status(thm),parent(t43:2)],[t43:2,t10:3]) ).
cnf(t46,plain,
( ~ sP9(sK10(sK8))
| halts2(sK8,sK10(sK8)) ),
inference(extension,[status(thm),parent(t33:3)],[f_3_20]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t33:3]) ).
cnf(t48,plain,
( ~ program(sK10(sK8))
| halts2(sK10(sK8),sK10(sK8))
| ~ sP10(sK10(sK8),sK9(sK8))
| sP9(sK10(sK8)) ),
inference(extension,[status(thm),parent(t46:2)],[f_3_17]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t46:2]) ).
cnf(t50,plain,
$false,
inference(reduction,[status(thm),parent(t48:2)],[t48:2,t6:2]) ).
cnf(t51,plain,
( ~ sP12(sK8)
| ~ halts2(sK10(sK8),sK10(sK8)) ),
inference(extension,[status(thm),parent(t48:3)],[f_4_13]) ).
cnf(t52,plain,
$false,
inference(connection,[status(thm),parent(t51:1)],[t51:1,t48:3]) ).
cnf(t53,plain,
$false,
inference(reduction,[status(thm),parent(t51:2)],[t51:2,t10:3]) ).
cnf(t54,plain,
( ~ sP12(sK8)
| program(sK10(sK8)) ),
inference(extension,[status(thm),parent(t48:4)],[f_4_12]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t48:4]) ).
cnf(t56,plain,
$false,
inference(reduction,[status(thm),parent(t54:2)],[t54:2,t10:3]) ).
cnf(t57,plain,
( ~ halts2(sK8,sK9(sK8))
| ~ outputs(sK8,good)
| ~ sP11(sK8) ),
inference(extension,[status(thm),parent(t10:4)],[f_4_11]) ).
cnf(t58,plain,
$false,
inference(connection,[status(thm),parent(t57:1)],[t57:1,t10:4]) ).
cnf(t59,plain,
( ~ sP8(sK9(sK8))
| outputs(sK8,good) ),
inference(extension,[status(thm),parent(t57:2)],[f_3_19]) ).
cnf(t60,plain,
$false,
inference(connection,[status(thm),parent(t59:1)],[t59:1,t57:2]) ).
cnf(t61,plain,
( ~ program(sK9(sK8))
| ~ halts2(sK9(sK8),sK9(sK8))
| ~ sP10(sK10(sK8),sK9(sK8))
| sP8(sK9(sK8)) ),
inference(extension,[status(thm),parent(t59:2)],[f_3_16]) ).
cnf(t62,plain,
$false,
inference(connection,[status(thm),parent(t61:1)],[t61:1,t59:2]) ).
cnf(t63,plain,
$false,
inference(reduction,[status(thm),parent(t61:2)],[t61:2,t6:2]) ).
cnf(t64,plain,
( ~ sP11(sK8)
| halts2(sK9(sK8),sK9(sK8)) ),
inference(extension,[status(thm),parent(t61:3)],[f_4_10]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t61:3]) ).
cnf(t66,plain,
$false,
inference(reduction,[status(thm),parent(t64:2)],[t64:2,t10:4]) ).
cnf(t67,plain,
( ~ sP11(sK8)
| program(sK9(sK8)) ),
inference(extension,[status(thm),parent(t61:4)],[f_4_9]) ).
cnf(t68,plain,
$false,
inference(connection,[status(thm),parent(t67:1)],[t67:1,t61:4]) ).
cnf(t69,plain,
$false,
inference(reduction,[status(thm),parent(t67:2)],[t67:2,t10:4]) ).
cnf(t70,plain,
( ~ sP8(sK9(sK8))
| halts2(sK8,sK9(sK8)) ),
inference(extension,[status(thm),parent(t57:3)],[f_3_18]) ).
cnf(t71,plain,
$false,
inference(connection,[status(thm),parent(t70:1)],[t70:1,t57:3]) ).
cnf(t72,plain,
( ~ program(sK9(sK8))
| ~ halts2(sK9(sK8),sK9(sK8))
| ~ sP10(sK10(sK8),sK9(sK8))
| sP8(sK9(sK8)) ),
inference(extension,[status(thm),parent(t70:2)],[f_3_16]) ).
cnf(t73,plain,
$false,
inference(connection,[status(thm),parent(t72:1)],[t72:1,t70:2]) ).
cnf(t74,plain,
$false,
inference(reduction,[status(thm),parent(t72:2)],[t72:2,t6:2]) ).
cnf(t75,plain,
( ~ sP11(sK8)
| halts2(sK9(sK8),sK9(sK8)) ),
inference(extension,[status(thm),parent(t72:3)],[f_4_10]) ).
cnf(t76,plain,
$false,
inference(connection,[status(thm),parent(t75:1)],[t75:1,t72:3]) ).
cnf(t77,plain,
$false,
inference(reduction,[status(thm),parent(t75:2)],[t75:2,t10:4]) ).
cnf(t78,plain,
( ~ sP11(sK8)
| program(sK9(sK8)) ),
inference(extension,[status(thm),parent(t72:4)],[f_4_9]) ).
cnf(t79,plain,
$false,
inference(connection,[status(thm),parent(t78:1)],[t78:1,t72:4]) ).
cnf(t80,plain,
$false,
inference(reduction,[status(thm),parent(t78:2)],[t78:2,t10:4]) ).
cnf(t81,plain,
( ~ halts2(sK7(sK3),sK7(sK3))
| ~ sP7(sK3) ),
inference(extension,[status(thm),parent(t6:3)],[f_3_13]) ).
cnf(t82,plain,
$false,
inference(connection,[status(thm),parent(t81:1)],[t81:1,t6:3]) ).
cnf(t83,plain,
( ~ program(sK7(sK3))
| sP4(sK7(sK3),sK3,sK7(sK3))
| ~ sP5(sK7(sK3),sK3,U_489,U_490,sK7(sK3))
| halts2(sK7(sK3),sK7(sK3)) ),
inference(extension,[status(thm),parent(t81:2)],[f_2_11]) ).
cnf(t84,plain,
$false,
inference(connection,[status(thm),parent(t83:1)],[t83:1,t81:2]) ).
cnf(t85,plain,
( sP2(sK3)
| ~ program(sK3)
| sP5(sK7(sK3),sK3,U_489,U_490,sK7(sK3)) ),
inference(extension,[status(thm),parent(t83:2)],[f_2_7]) ).
cnf(t86,plain,
$false,
inference(connection,[status(thm),parent(t85:1)],[t85:1,t83:2]) ).
cnf(t87,plain,
$false,
inference(reduction,[status(thm),parent(t85:2)],[t85:2,t4:2]) ).
cnf(t88,plain,
( ~ decides(sK3,sK4(sK3),sK5(sK3))
| ~ sP2(sK3) ),
inference(extension,[status(thm),parent(t85:3)],[f_2_9]) ).
cnf(t89,plain,
$false,
inference(connection,[status(thm),parent(t88:1)],[t88:1,t85:3]) ).
cnf(t90,plain,
( ~ program(sK4(sK3))
| ~ sP1(sK5(sK3),sK4(sK3))
| decides(sK3,sK4(sK3),sK5(sK3)) ),
inference(extension,[status(thm),parent(t88:2)],[f_1_11]) ).
cnf(t91,plain,
$false,
inference(connection,[status(thm),parent(t90:1)],[t90:1,t88:2]) ).
cnf(t92,plain,
$false,
inference(reduction,[status(thm),parent(t90:2)],[t90:2,t2:2]) ).
cnf(t93,plain,
( ~ sP2(sK3)
| program(sK4(sK3)) ),
inference(extension,[status(thm),parent(t90:3)],[f_2_8]) ).
cnf(t94,plain,
$false,
inference(connection,[status(thm),parent(t93:1)],[t93:1,t90:3]) ).
cnf(t95,plain,
$false,
inference(reduction,[status(thm),parent(t93:2)],[t93:2,t85:3]) ).
cnf(t96,plain,
( outputs(sK3,bad)
| ~ sP4(sK7(sK3),sK3,sK7(sK3)) ),
inference(extension,[status(thm),parent(t83:3)],[f_2_15]) ).
cnf(t97,plain,
$false,
inference(connection,[status(thm),parent(t96:1)],[t96:1,t83:3]) ).
cnf(t98,plain,
( ~ halts3(sK3,sK7(sK3),sK7(sK3))
| ~ sP7(sK3)
| ~ outputs(sK3,bad) ),
inference(extension,[status(thm),parent(t96:2)],[f_3_14]) ).
cnf(t99,plain,
$false,
inference(connection,[status(thm),parent(t98:1)],[t98:1,t96:2]) ).
cnf(t100,plain,
$false,
inference(reduction,[status(thm),parent(t98:2)],[t98:2,t6:3]) ).
cnf(t101,plain,
( ~ sP4(sK7(sK3),sK3,sK7(sK3))
| halts3(sK3,sK7(sK3),sK7(sK3)) ),
inference(extension,[status(thm),parent(t98:3)],[f_2_14]) ).
cnf(t102,plain,
$false,
inference(connection,[status(thm),parent(t101:1)],[t101:1,t98:3]) ).
cnf(t103,plain,
$false,
inference(reduction,[status(thm),parent(t101:2)],[t101:2,t83:3]) ).
cnf(t104,plain,
( ~ sP7(sK3)
| program(sK7(sK3)) ),
inference(extension,[status(thm),parent(t83:4)],[f_3_12]) ).
cnf(t105,plain,
$false,
inference(connection,[status(thm),parent(t104:1)],[t104:1,t83:4]) ).
cnf(t106,plain,
$false,
inference(reduction,[status(thm),parent(t104:2)],[t104:2,t6:3]) ).
cnf(t107,plain,
( halts2(sK6(sK3),sK6(sK3))
| ~ sP6(sK3) ),
inference(extension,[status(thm),parent(t6:4)],[f_3_10]) ).
cnf(t108,plain,
$false,
inference(connection,[status(thm),parent(t107:1)],[t107:1,t6:4]) ).
cnf(t109,plain,
( ~ program(sK6(sK3))
| sP3(sK3,sK6(sK3),sK6(sK3))
| ~ sP5(U_511,sK3,sK6(sK3),sK6(sK3),U_514)
| ~ halts2(sK6(sK3),sK6(sK3)) ),
inference(extension,[status(thm),parent(t107:2)],[f_2_10]) ).
cnf(t110,plain,
$false,
inference(connection,[status(thm),parent(t109:1)],[t109:1,t107:2]) ).
cnf(t111,plain,
( sP2(sK3)
| ~ program(sK3)
| sP5(U_511,sK3,sK6(sK3),sK6(sK3),U_514) ),
inference(extension,[status(thm),parent(t109:2)],[f_2_7]) ).
cnf(t112,plain,
$false,
inference(connection,[status(thm),parent(t111:1)],[t111:1,t109:2]) ).
cnf(t113,plain,
$false,
inference(reduction,[status(thm),parent(t111:2)],[t111:2,t4:2]) ).
cnf(t114,plain,
( ~ decides(sK3,sK4(sK3),sK5(sK3))
| ~ sP2(sK3) ),
inference(extension,[status(thm),parent(t111:3)],[f_2_9]) ).
cnf(t115,plain,
$false,
inference(connection,[status(thm),parent(t114:1)],[t114:1,t111:3]) ).
cnf(t116,plain,
( ~ program(sK4(sK3))
| ~ sP1(sK5(sK3),sK4(sK3))
| decides(sK3,sK4(sK3),sK5(sK3)) ),
inference(extension,[status(thm),parent(t114:2)],[f_1_11]) ).
cnf(t117,plain,
$false,
inference(connection,[status(thm),parent(t116:1)],[t116:1,t114:2]) ).
cnf(t118,plain,
$false,
inference(reduction,[status(thm),parent(t116:2)],[t116:2,t2:2]) ).
cnf(t119,plain,
( ~ sP2(sK3)
| program(sK4(sK3)) ),
inference(extension,[status(thm),parent(t116:3)],[f_2_8]) ).
cnf(t120,plain,
$false,
inference(connection,[status(thm),parent(t119:1)],[t119:1,t116:3]) ).
cnf(t121,plain,
$false,
inference(reduction,[status(thm),parent(t119:2)],[t119:2,t111:3]) ).
cnf(t122,plain,
( outputs(sK3,good)
| ~ sP3(sK3,sK6(sK3),sK6(sK3)) ),
inference(extension,[status(thm),parent(t109:3)],[f_2_13]) ).
cnf(t123,plain,
$false,
inference(connection,[status(thm),parent(t122:1)],[t122:1,t109:3]) ).
cnf(t124,plain,
( ~ halts3(sK3,sK6(sK3),sK6(sK3))
| ~ sP6(sK3)
| ~ outputs(sK3,good) ),
inference(extension,[status(thm),parent(t122:2)],[f_3_11]) ).
cnf(t125,plain,
$false,
inference(connection,[status(thm),parent(t124:1)],[t124:1,t122:2]) ).
cnf(t126,plain,
$false,
inference(reduction,[status(thm),parent(t124:2)],[t124:2,t6:4]) ).
cnf(t127,plain,
( ~ sP3(sK3,sK6(sK3),sK6(sK3))
| halts3(sK3,sK6(sK3),sK6(sK3)) ),
inference(extension,[status(thm),parent(t124:3)],[f_2_12]) ).
cnf(t128,plain,
$false,
inference(connection,[status(thm),parent(t127:1)],[t127:1,t124:3]) ).
cnf(t129,plain,
$false,
inference(reduction,[status(thm),parent(t127:2)],[t127:2,t109:3]) ).
cnf(t130,plain,
( ~ sP6(sK3)
| program(sK6(sK3)) ),
inference(extension,[status(thm),parent(t109:4)],[f_3_9]) ).
cnf(t131,plain,
$false,
inference(connection,[status(thm),parent(t130:1)],[t130:1,t109:4]) ).
cnf(t132,plain,
$false,
inference(reduction,[status(thm),parent(t130:2)],[t130:2,t6:4]) ).
cnf(t133,plain,
( ~ decides(sK12,sK1(sK12),sK2(sK12))
| ~ sP0(sK12) ),
inference(extension,[status(thm),parent(t2:3)],[f_1_9]) ).
cnf(t134,plain,
$false,
inference(connection,[status(thm),parent(t133:1)],[t133:1,t2:3]) ).
cnf(t135,plain,
( ~ program(sK1(sK12))
| decides(sK12,sK1(sK12),sK2(sK12)) ),
inference(extension,[status(thm),parent(t133:2)],[f_5_7]) ).
cnf(t136,plain,
$false,
inference(connection,[status(thm),parent(t135:1)],[t135:1,t133:2]) ).
cnf(t137,plain,
( ~ sP0(sK12)
| program(sK1(sK12)) ),
inference(extension,[status(thm),parent(t135:2)],[f_1_8]) ).
cnf(t138,plain,
$false,
inference(connection,[status(thm),parent(t137:1)],[t137:1,t135:2]) ).
cnf(t139,plain,
$false,
inference(reduction,[status(thm),parent(t137:2)],[t137:2,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM003+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 15:07:35 UTC 2026
% 0.10/0.37 % CPUTime :
% 38.45/38.76 % SZS status Theorem for theBenchmark
% 38.45/38.76 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------