%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : COM003+3 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/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 33.04s 33.35s
% Output : Proof 33.04s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% 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,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('theBenchmark.p',p3) ).
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_3,U_4,U_2] :
( 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_10,U_12,U_14] :
( outputs(U_10,bad)
| ~ sP4(U_10,U_12,U_14) )
& ! [U_10,U_12,U_14] :
( halts3(U_10,U_14,U_12)
| ~ sP4(U_10,U_12,U_14) )
& ! [U_11,U_10,U_13] :
( outputs(U_10,good)
| ~ sP3(U_11,U_10,U_13) )
& ! [U_11,U_10,U_13] :
( halts3(U_10,U_13,U_11)
| ~ sP3(U_11,U_10,U_13) )
& ! [U_11,U_10,U_12,U_13,U_14] :
( sP4(U_10,U_12,U_14)
| halts2(U_14,U_12)
| ~ program(U_14)
| ~ sP5(U_11,U_10,U_12,U_13,U_14) )
& ! [U_11,U_10,U_12,U_13,U_14] :
( sP3(U_11,U_10,U_13)
| ~ halts2(U_13,U_11)
| ~ program(U_13)
| ~ sP5(U_11,U_10,U_12,U_13,U_14) )
& ! [U_10] :
( ~ decides(U_10,sK4(U_10),sK5(U_10))
| ~ sP2(U_10) )
& ! [U_10] :
( program(sK4(U_10))
| ~ sP2(U_10) )
& ! [U_11,U_10,U_12,U_13,U_14] :
( sP5(U_11,U_10,U_12,U_13,U_14)
| 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_11,U_10,U_12,U_13,U_14)
| 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_11,U_10,U_13)
| ~ halts2(U_13,U_11)
| ~ program(U_13)
| ~ sP5(U_11,U_10,U_12,U_13,U_14) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_11,plain,
( sP4(U_10,U_12,U_14)
| halts2(U_14,U_12)
| ~ program(U_14)
| ~ sP5(U_11,U_10,U_12,U_13,U_14) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_12,plain,
( halts3(U_10,U_13,U_11)
| ~ sP3(U_11,U_10,U_13) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_13,plain,
( outputs(U_10,good)
| ~ sP3(U_11,U_10,U_13) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_14,plain,
( halts3(U_10,U_14,U_12)
| ~ sP4(U_10,U_12,U_14) ),
inference(clausify,[status(thm)],[f_2_6]) ).
cnf(f_2_15,plain,
( outputs(U_10,bad)
| ~ sP4(U_10,U_12,U_14) ),
inference(clausify,[status(thm)],[f_2_6]) ).
fof(f_3_1,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(fof_nnf,[status(thm)],[p3]) ).
fof(f_3_2,plain,
! [U_19] :
( ? [U_18] :
( ! [U_17] :
( ( ( outputs(U_18,bad)
& halts2(U_18,U_17) )
| ~ outputs(U_19,bad)
| ~ halts3(U_19,U_17,U_17)
| ~ program(U_17) )
& ( ~ halts2(U_18,U_17)
| ~ outputs(U_19,good)
| ~ halts3(U_19,U_17,U_17)
| ~ program(U_17) ) )
& program(U_18) )
| ? [U_16,U_15] :
( ( ( ~ outputs(U_19,bad)
| ~ halts3(U_19,U_16,U_15) )
& ~ halts2(U_16,U_15)
& program(U_16) )
| ( ( ~ outputs(U_19,good)
| ~ halts3(U_19,U_16,U_15) )
& halts2(U_16,U_15)
& program(U_16) ) )
| ~ program(U_19) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_19] :
( ? [U_18] :
( ! [U_25] :
( ( outputs(U_18,bad)
& halts2(U_18,U_25) )
| ~ outputs(U_19,bad)
| ~ halts3(U_19,U_25,U_25)
| ~ program(U_25) )
& ! [U_24] :
( ~ halts2(U_18,U_24)
| ~ outputs(U_19,good)
| ~ halts3(U_19,U_24,U_24)
| ~ program(U_24) )
& program(U_18) )
| ? [U_23,U_21] :
( ( ~ outputs(U_19,bad)
| ~ halts3(U_19,U_23,U_21) )
& ~ halts2(U_23,U_21)
& program(U_23) )
| ? [U_22,U_20] :
( ( ~ outputs(U_19,good)
| ~ halts3(U_19,U_22,U_20) )
& halts2(U_22,U_20)
& program(U_22) )
| ~ program(U_19) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
! [U_19] :
( ? [U_18] :
( ! [U_25] :
( ( outputs(U_18,bad)
& halts2(U_18,U_25) )
| ~ outputs(U_19,bad)
| ~ halts3(U_19,U_25,U_25)
| ~ program(U_25) )
& ! [U_24] :
( ~ halts2(U_18,U_24)
| ~ outputs(U_19,good)
| ~ halts3(U_19,U_24,U_24)
| ~ program(U_24) )
& program(U_18) )
| ? [U_23,U_21] :
( ( ~ outputs(U_19,bad)
| ~ halts3(U_19,U_23,U_21) )
& ~ halts2(U_23,U_21)
& program(U_23) )
| ? [U_20] :
( ( ~ outputs(U_19,good)
| ~ halts3(U_19,sK6(U_19),U_20) )
& halts2(sK6(U_19),U_20)
& program(sK6(U_19)) )
| ~ program(U_19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_22,sK6(U_19))],[f_3_3]) ).
fof(f_3_5,plain,
! [U_19] :
( ? [U_18] :
( ! [U_25] :
( ( outputs(U_18,bad)
& halts2(U_18,U_25) )
| ~ outputs(U_19,bad)
| ~ halts3(U_19,U_25,U_25)
| ~ program(U_25) )
& ! [U_24] :
( ~ halts2(U_18,U_24)
| ~ outputs(U_19,good)
| ~ halts3(U_19,U_24,U_24)
| ~ program(U_24) )
& program(U_18) )
| ? [U_23,U_21] :
( ( ~ outputs(U_19,bad)
| ~ halts3(U_19,U_23,U_21) )
& ~ halts2(U_23,U_21)
& program(U_23) )
| ( ( ~ outputs(U_19,good)
| ~ halts3(U_19,sK6(U_19),sK7(U_19)) )
& halts2(sK6(U_19),sK7(U_19))
& program(sK6(U_19)) )
| ~ program(U_19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_20,sK7(U_19))],[f_3_4]) ).
fof(f_3_6,plain,
! [U_19] :
( ? [U_18] :
( ! [U_25] :
( ( outputs(U_18,bad)
& halts2(U_18,U_25) )
| ~ outputs(U_19,bad)
| ~ halts3(U_19,U_25,U_25)
| ~ program(U_25) )
& ! [U_24] :
( ~ halts2(U_18,U_24)
| ~ outputs(U_19,good)
| ~ halts3(U_19,U_24,U_24)
| ~ program(U_24) )
& program(U_18) )
| ? [U_21] :
( ( ~ outputs(U_19,bad)
| ~ halts3(U_19,sK8(U_19),U_21) )
& ~ halts2(sK8(U_19),U_21)
& program(sK8(U_19)) )
| ( ( ~ outputs(U_19,good)
| ~ halts3(U_19,sK6(U_19),sK7(U_19)) )
& halts2(sK6(U_19),sK7(U_19))
& program(sK6(U_19)) )
| ~ program(U_19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_23,sK8(U_19))],[f_3_5]) ).
fof(f_3_7,plain,
! [U_19] :
( ? [U_18] :
( ! [U_25] :
( ( outputs(U_18,bad)
& halts2(U_18,U_25) )
| ~ outputs(U_19,bad)
| ~ halts3(U_19,U_25,U_25)
| ~ program(U_25) )
& ! [U_24] :
( ~ halts2(U_18,U_24)
| ~ outputs(U_19,good)
| ~ halts3(U_19,U_24,U_24)
| ~ program(U_24) )
& program(U_18) )
| ( ( ~ outputs(U_19,bad)
| ~ halts3(U_19,sK8(U_19),sK9(U_19)) )
& ~ halts2(sK8(U_19),sK9(U_19))
& program(sK8(U_19)) )
| ( ( ~ outputs(U_19,good)
| ~ halts3(U_19,sK6(U_19),sK7(U_19)) )
& halts2(sK6(U_19),sK7(U_19))
& program(sK6(U_19)) )
| ~ program(U_19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_21,sK9(U_19))],[f_3_6]) ).
fof(f_3_8,plain,
! [U_19] :
( ( ! [U_25] :
( ( outputs(sK10(U_19),bad)
& halts2(sK10(U_19),U_25) )
| ~ outputs(U_19,bad)
| ~ halts3(U_19,U_25,U_25)
| ~ program(U_25) )
& ! [U_24] :
( ~ halts2(sK10(U_19),U_24)
| ~ outputs(U_19,good)
| ~ halts3(U_19,U_24,U_24)
| ~ program(U_24) )
& program(sK10(U_19)) )
| ( ( ~ outputs(U_19,bad)
| ~ halts3(U_19,sK8(U_19),sK9(U_19)) )
& ~ halts2(sK8(U_19),sK9(U_19))
& program(sK8(U_19)) )
| ( ( ~ outputs(U_19,good)
| ~ halts3(U_19,sK6(U_19),sK7(U_19)) )
& halts2(sK6(U_19),sK7(U_19))
& program(sK6(U_19)) )
| ~ program(U_19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_18,sK10(U_19))],[f_3_7]) ).
fof(f_3_9,plain,
( ! [U_19,U_25] :
( outputs(sK10(U_19),bad)
| ~ sP8(U_19,U_25) )
& ! [U_19,U_25] :
( halts2(sK10(U_19),U_25)
| ~ sP8(U_19,U_25) )
& ! [U_19,U_25,U_24] :
( sP8(U_19,U_25)
| ~ outputs(U_19,bad)
| ~ halts3(U_19,U_25,U_25)
| ~ program(U_25)
| ~ sP9(U_19,U_25,U_24) )
& ! [U_19,U_25,U_24] :
( ~ halts2(sK10(U_19),U_24)
| ~ outputs(U_19,good)
| ~ halts3(U_19,U_24,U_24)
| ~ program(U_24)
| ~ sP9(U_19,U_25,U_24) )
& ! [U_19,U_25,U_24] :
( program(sK10(U_19))
| ~ sP9(U_19,U_25,U_24) )
& ! [U_19] :
( ~ outputs(U_19,bad)
| ~ halts3(U_19,sK8(U_19),sK9(U_19))
| ~ sP7(U_19) )
& ! [U_19] :
( ~ halts2(sK8(U_19),sK9(U_19))
| ~ sP7(U_19) )
& ! [U_19] :
( program(sK8(U_19))
| ~ sP7(U_19) )
& ! [U_19] :
( ~ outputs(U_19,good)
| ~ halts3(U_19,sK6(U_19),sK7(U_19))
| ~ sP6(U_19) )
& ! [U_19] :
( halts2(sK6(U_19),sK7(U_19))
| ~ sP6(U_19) )
& ! [U_19] :
( program(sK6(U_19))
| ~ sP6(U_19) )
& ! [U_19,U_25,U_24] :
( sP9(U_19,U_25,U_24)
| sP7(U_19)
| sP6(U_19)
| ~ program(U_19) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6,sP7,sP8,sP9])],[f_3_8]) ).
cnf(f_3_10,plain,
( sP9(U_19,U_25,U_24)
| sP7(U_19)
| sP6(U_19)
| ~ program(U_19) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_11,plain,
( program(sK6(U_19))
| ~ sP6(U_19) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_12,plain,
( halts2(sK6(U_19),sK7(U_19))
| ~ sP6(U_19) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_13,plain,
( ~ outputs(U_19,good)
| ~ halts3(U_19,sK6(U_19),sK7(U_19))
| ~ sP6(U_19) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_14,plain,
( program(sK8(U_19))
| ~ sP7(U_19) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_15,plain,
( ~ halts2(sK8(U_19),sK9(U_19))
| ~ sP7(U_19) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_16,plain,
( ~ outputs(U_19,bad)
| ~ halts3(U_19,sK8(U_19),sK9(U_19))
| ~ sP7(U_19) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_17,plain,
( program(sK10(U_19))
| ~ sP9(U_19,U_25,U_24) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_18,plain,
( ~ halts2(sK10(U_19),U_24)
| ~ outputs(U_19,good)
| ~ halts3(U_19,U_24,U_24)
| ~ program(U_24)
| ~ sP9(U_19,U_25,U_24) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_19,plain,
( sP8(U_19,U_25)
| ~ outputs(U_19,bad)
| ~ halts3(U_19,U_25,U_25)
| ~ program(U_25)
| ~ sP9(U_19,U_25,U_24) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_20,plain,
( halts2(sK10(U_19),U_25)
| ~ sP8(U_19,U_25) ),
inference(clausify,[status(thm)],[f_3_9]) ).
cnf(f_3_21,plain,
( outputs(sK10(U_19),bad)
| ~ sP8(U_19,U_25) ),
inference(clausify,[status(thm)],[f_3_9]) ).
fof(f_4_1,negated_conjecture,
? [X1] :
( ! [Y1] :
( program(Y1)
=> ! [Z1] : decides(X1,Y1,Z1) )
& algorithm(X1) ),
inference(negate,[status(cth)],[prove_this]) ).
fof(f_4_2,negated_conjecture,
? [X1] :
( ! [Y1] :
( ! [Z1] : decides(X1,Y1,Z1)
| ~ program(Y1) )
& algorithm(X1) ),
inference(fof_nnf,[status(thm)],[f_4_1]) ).
fof(f_4_3,negated_conjecture,
? [U_28] :
( ! [U_27] :
( ! [U_26] : decides(U_28,U_27,U_26)
| ~ program(U_27) )
& algorithm(U_28) ),
inference(variable_rename,[status(thm)],[f_4_2]) ).
fof(f_4_4,negated_conjecture,
( ! [U_27] :
( ! [U_26] : decides(sK11,U_27,U_26)
| ~ program(U_27) )
& algorithm(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_28,sK11)],[f_4_3]) ).
fof(f_4_5,negated_conjecture,
( ! [U_27,U_26] :
( decides(sK11,U_27,U_26)
| ~ program(U_27) )
& algorithm(sK11) ),
inference(definitional_conversion,[status(esa)],[f_4_4]) ).
cnf(f_4_6,negated_conjecture,
algorithm(sK11),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_7,negated_conjecture,
( decides(sK11,U_27,U_26)
| ~ program(U_27) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM003+3 : 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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 15:37:49 UTC 2026
% 0.09/0.37 % CPUTime :
% 33.04/33.35 % SZS status Theorem for theBenchmark
% 33.04/33.35 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------