%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : COM003+2 : TPTP v9.3.1. Bugfixed v2.2.0.
% 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 : n010.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 1.15s 11.60s
% Output : Proof 1.15s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(program_decides_def,axiom,
! [X] :
( program_decides(X)
<=> ! [Y] :
( program(Y)
=> ! [Z] : decides(X,Y,Z) ) ),
file('theBenchmark.p',program_decides_def) ).
fof(program_program_decides_def,axiom,
! [X] :
( program_program_decides(X)
<=> ( program_decides(X)
& program(X) ) ),
file('theBenchmark.p',program_program_decides_def) ).
fof(algorithm_program_decides_def,axiom,
! [X] :
( algorithm_program_decides(X)
<=> ( program_decides(X)
& algorithm(X) ) ),
file('theBenchmark.p',algorithm_program_decides_def) ).
fof(program_halts2_def,axiom,
! [X,Y] :
( program_halts2(X,Y)
<=> ( halts2(X,Y)
& program(X) ) ),
file('theBenchmark.p',program_halts2_def) ).
fof(halts3_outputs_def,axiom,
! [X,Y,Z,W] :
( halts3_outputs(X,Y,Z,W)
<=> ( outputs(X,W)
& halts3(X,Y,Z) ) ),
file('theBenchmark.p',halts3_outputs_def) ).
fof(program_not_halts2_def,axiom,
! [X,Y] :
( program_not_halts2(X,Y)
<=> ( ~ halts2(X,Y)
& program(X) ) ),
file('theBenchmark.p',program_not_halts2_def) ).
fof(halts2_outputs_def,axiom,
! [X,Y,W] :
( halts2_outputs(X,Y,W)
<=> ( outputs(X,W)
& halts2(X,Y) ) ),
file('theBenchmark.p',halts2_outputs_def) ).
fof(program_halts2_halts3_outputs_def,axiom,
! [X,Y,Z,W] :
( program_halts2_halts3_outputs(X,Y,Z,W)
<=> ( program_halts2(Y,Z)
=> halts3_outputs(X,Y,Z,W) ) ),
file('theBenchmark.p',program_halts2_halts3_outputs_def) ).
fof(program_not_halts2_halts3_outputs_def,axiom,
! [X,Y,Z,W] :
( program_not_halts2_halts3_outputs(X,Y,Z,W)
<=> ( program_not_halts2(Y,Z)
=> halts3_outputs(X,Y,Z,W) ) ),
file('theBenchmark.p',program_not_halts2_halts3_outputs_def) ).
fof(program_halts2_halts2_outputs_def,axiom,
! [X,Y,W] :
( program_halts2_halts2_outputs(X,Y,W)
<=> ( program_halts2(Y,Y)
=> halts2_outputs(X,Y,W) ) ),
file('theBenchmark.p',program_halts2_halts2_outputs_def) ).
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) ) ),
file('theBenchmark.p',program_not_halts2_halts2_outputs_def) ).
fof(p1,axiom,
( ? [X] : algorithm_program_decides(X)
=> ? [W] : program_program_decides(W) ),
file('theBenchmark.p',p1) ).
fof(p2,axiom,
! [W] :
( program_program_decides(W)
=> ! [Y,Z] :
( program_not_halts2_halts3_outputs(W,Y,Z,bad)
& program_halts2_halts3_outputs(W,Y,Z,good) ) ),
file('theBenchmark.p',p2) ).
fof(p3,axiom,
( ? [W] :
( ! [Y] :
( program_not_halts2_halts3_outputs(W,Y,Y,bad)
& program_halts2_halts3_outputs(W,Y,Y,good) )
& program(W) )
=> ? [V] :
( ! [Y] :
( program_not_halts2_halts2_outputs(V,Y,bad)
& program_halts2_halts2_outputs(V,Y,good) )
& program(V) ) ),
file('theBenchmark.p',p3) ).
fof(p4,axiom,
( ? [V] :
( ! [Y] :
( program_not_halts2_halts2_outputs(V,Y,bad)
& program_halts2_halts2_outputs(V,Y,good) )
& program(V) )
=> ? [U] :
( ! [Y] :
( program_not_halts2_halts2_outputs(U,Y,good)
& ( program_halts2(Y,Y)
=> ~ halts2(U,Y) ) )
& program(U) ) ),
file('theBenchmark.p',p4) ).
fof(prove_this,conjecture,
~ ? [X] : algorithm_program_decides(X),
file('theBenchmark.p',prove_this) ).
fof(f_1_1,plain,
! [X] :
( ( program_decides(X)
| ? [Y] :
( ? [Z] : ~ decides(X,Y,Z)
& program(Y) ) )
& ( ! [Y] :
( ! [Z] : decides(X,Y,Z)
| ~ program(Y) )
| ~ program_decides(X) ) ),
inference(fof_nnf,[status(thm)],[program_decides_def]) ).
fof(f_1_2,plain,
! [U_4] :
( ( program_decides(U_4)
| ? [U_3] :
( ? [U_2] : ~ decides(U_4,U_3,U_2)
& program(U_3) ) )
& ( ! [U_1] :
( ! [U_0] : decides(U_4,U_1,U_0)
| ~ program(U_1) )
| ~ program_decides(U_4) ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_6] :
( program_decides(U_6)
| ? [U_3] :
( ? [U_2] : ~ decides(U_6,U_3,U_2)
& program(U_3) ) )
& ! [U_5] :
( ! [U_1] :
( ! [U_0] : decides(U_5,U_1,U_0)
| ~ program(U_1) )
| ~ program_decides(U_5) ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
fof(f_1_4,plain,
( ! [U_6] :
( program_decides(U_6)
| ( ? [U_2] : ~ decides(U_6,sK1(U_6),U_2)
& program(sK1(U_6)) ) )
& ! [U_5] :
( ! [U_1] :
( ! [U_0] : decides(U_5,U_1,U_0)
| ~ program(U_1) )
| ~ program_decides(U_5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_3,sK1(U_6))],[f_1_3]) ).
fof(f_1_5,plain,
( ! [U_6] :
( program_decides(U_6)
| ( ~ decides(U_6,sK1(U_6),sK2(U_6))
& program(sK1(U_6)) ) )
& ! [U_5] :
( ! [U_1] :
( ! [U_0] : decides(U_5,U_1,U_0)
| ~ program(U_1) )
| ~ program_decides(U_5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_2,sK2(U_6))],[f_1_4]) ).
cnf(f_1_6,plain,
( decides(U_5,U_1,U_0)
| ~ program(U_1)
| ~ program_decides(U_5) ),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_7,plain,
( program(sK1(U_6))
| program_decides(U_6) ),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_8,plain,
( ~ decides(U_6,sK1(U_6),sK2(U_6))
| program_decides(U_6) ),
inference(clausify,[status(thm)],[f_1_5]) ).
fof(f_2_1,plain,
! [X] :
( ( program_program_decides(X)
| ~ program_decides(X)
| ~ program(X) )
& ( ( program_decides(X)
& program(X) )
| ~ program_program_decides(X) ) ),
inference(fof_nnf,[status(thm)],[program_program_decides_def]) ).
fof(f_2_2,plain,
! [U_7] :
( ( program_program_decides(U_7)
| ~ program_decides(U_7)
| ~ program(U_7) )
& ( ( program_decides(U_7)
& program(U_7) )
| ~ program_program_decides(U_7) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_9] :
( program_program_decides(U_9)
| ~ program_decides(U_9)
| ~ program(U_9) )
& ! [U_8] :
( ( program_decides(U_8)
& program(U_8) )
| ~ program_program_decides(U_8) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( program(U_8)
| ~ program_program_decides(U_8) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_5,plain,
( program_decides(U_8)
| ~ program_program_decides(U_8) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_6,plain,
( program_program_decides(U_9)
| ~ program_decides(U_9)
| ~ program(U_9) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [X] :
( ( algorithm_program_decides(X)
| ~ program_decides(X)
| ~ algorithm(X) )
& ( ( program_decides(X)
& algorithm(X) )
| ~ algorithm_program_decides(X) ) ),
inference(fof_nnf,[status(thm)],[algorithm_program_decides_def]) ).
fof(f_3_2,plain,
! [U_10] :
( ( algorithm_program_decides(U_10)
| ~ program_decides(U_10)
| ~ algorithm(U_10) )
& ( ( program_decides(U_10)
& algorithm(U_10) )
| ~ algorithm_program_decides(U_10) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_12] :
( algorithm_program_decides(U_12)
| ~ program_decides(U_12)
| ~ algorithm(U_12) )
& ! [U_11] :
( ( program_decides(U_11)
& algorithm(U_11) )
| ~ algorithm_program_decides(U_11) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( algorithm(U_11)
| ~ algorithm_program_decides(U_11) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( program_decides(U_11)
| ~ algorithm_program_decides(U_11) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_6,plain,
( algorithm_program_decides(U_12)
| ~ program_decides(U_12)
| ~ algorithm(U_12) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [X,Y] :
( ( program_halts2(X,Y)
| ~ halts2(X,Y)
| ~ program(X) )
& ( ( halts2(X,Y)
& program(X) )
| ~ program_halts2(X,Y) ) ),
inference(fof_nnf,[status(thm)],[program_halts2_def]) ).
fof(f_4_2,plain,
! [U_14,U_13] :
( ( program_halts2(U_14,U_13)
| ~ halts2(U_14,U_13)
| ~ program(U_14) )
& ( ( halts2(U_14,U_13)
& program(U_14) )
| ~ program_halts2(U_14,U_13) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_18,U_16] :
( program_halts2(U_18,U_16)
| ~ halts2(U_18,U_16)
| ~ program(U_18) )
& ! [U_17,U_15] :
( ( halts2(U_17,U_15)
& program(U_17) )
| ~ program_halts2(U_17,U_15) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( program(U_17)
| ~ program_halts2(U_17,U_15) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( halts2(U_17,U_15)
| ~ program_halts2(U_17,U_15) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( program_halts2(U_18,U_16)
| ~ halts2(U_18,U_16)
| ~ program(U_18) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [X,Y,Z,W] :
( ( halts3_outputs(X,Y,Z,W)
| ~ outputs(X,W)
| ~ halts3(X,Y,Z) )
& ( ( outputs(X,W)
& halts3(X,Y,Z) )
| ~ halts3_outputs(X,Y,Z,W) ) ),
inference(fof_nnf,[status(thm)],[halts3_outputs_def]) ).
fof(f_5_2,plain,
! [U_22,U_21,U_20,U_19] :
( ( halts3_outputs(U_22,U_21,U_20,U_19)
| ~ outputs(U_22,U_19)
| ~ halts3(U_22,U_21,U_20) )
& ( ( outputs(U_22,U_19)
& halts3(U_22,U_21,U_20) )
| ~ halts3_outputs(U_22,U_21,U_20,U_19) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_30,U_28,U_26,U_24] :
( halts3_outputs(U_30,U_28,U_26,U_24)
| ~ outputs(U_30,U_24)
| ~ halts3(U_30,U_28,U_26) )
& ! [U_29,U_27,U_25,U_23] :
( ( outputs(U_29,U_23)
& halts3(U_29,U_27,U_25) )
| ~ halts3_outputs(U_29,U_27,U_25,U_23) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( halts3(U_29,U_27,U_25)
| ~ halts3_outputs(U_29,U_27,U_25,U_23) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( outputs(U_29,U_23)
| ~ halts3_outputs(U_29,U_27,U_25,U_23) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,plain,
( halts3_outputs(U_30,U_28,U_26,U_24)
| ~ outputs(U_30,U_24)
| ~ halts3(U_30,U_28,U_26) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [X,Y] :
( ( program_not_halts2(X,Y)
| halts2(X,Y)
| ~ program(X) )
& ( ( ~ halts2(X,Y)
& program(X) )
| ~ program_not_halts2(X,Y) ) ),
inference(fof_nnf,[status(thm)],[program_not_halts2_def]) ).
fof(f_6_2,plain,
! [U_32,U_31] :
( ( program_not_halts2(U_32,U_31)
| halts2(U_32,U_31)
| ~ program(U_32) )
& ( ( ~ halts2(U_32,U_31)
& program(U_32) )
| ~ program_not_halts2(U_32,U_31) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_36,U_34] :
( program_not_halts2(U_36,U_34)
| halts2(U_36,U_34)
| ~ program(U_36) )
& ! [U_35,U_33] :
( ( ~ halts2(U_35,U_33)
& program(U_35) )
| ~ program_not_halts2(U_35,U_33) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( program(U_35)
| ~ program_not_halts2(U_35,U_33) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( ~ halts2(U_35,U_33)
| ~ program_not_halts2(U_35,U_33) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( program_not_halts2(U_36,U_34)
| halts2(U_36,U_34)
| ~ program(U_36) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [X,Y,W] :
( ( halts2_outputs(X,Y,W)
| ~ outputs(X,W)
| ~ halts2(X,Y) )
& ( ( outputs(X,W)
& halts2(X,Y) )
| ~ halts2_outputs(X,Y,W) ) ),
inference(fof_nnf,[status(thm)],[halts2_outputs_def]) ).
fof(f_7_2,plain,
! [U_39,U_38,U_37] :
( ( halts2_outputs(U_39,U_38,U_37)
| ~ outputs(U_39,U_37)
| ~ halts2(U_39,U_38) )
& ( ( outputs(U_39,U_37)
& halts2(U_39,U_38) )
| ~ halts2_outputs(U_39,U_38,U_37) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_45,U_43,U_41] :
( halts2_outputs(U_45,U_43,U_41)
| ~ outputs(U_45,U_41)
| ~ halts2(U_45,U_43) )
& ! [U_44,U_42,U_40] :
( ( outputs(U_44,U_40)
& halts2(U_44,U_42) )
| ~ halts2_outputs(U_44,U_42,U_40) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( halts2(U_44,U_42)
| ~ halts2_outputs(U_44,U_42,U_40) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( outputs(U_44,U_40)
| ~ halts2_outputs(U_44,U_42,U_40) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_6,plain,
( halts2_outputs(U_45,U_43,U_41)
| ~ outputs(U_45,U_41)
| ~ halts2(U_45,U_43) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [X,Y,Z,W] :
( ( program_halts2_halts3_outputs(X,Y,Z,W)
| ( ~ halts3_outputs(X,Y,Z,W)
& program_halts2(Y,Z) ) )
& ( halts3_outputs(X,Y,Z,W)
| ~ program_halts2(Y,Z)
| ~ program_halts2_halts3_outputs(X,Y,Z,W) ) ),
inference(fof_nnf,[status(thm)],[program_halts2_halts3_outputs_def]) ).
fof(f_8_2,plain,
! [U_49,U_48,U_47,U_46] :
( ( program_halts2_halts3_outputs(U_49,U_48,U_47,U_46)
| ( ~ halts3_outputs(U_49,U_48,U_47,U_46)
& program_halts2(U_48,U_47) ) )
& ( halts3_outputs(U_49,U_48,U_47,U_46)
| ~ program_halts2(U_48,U_47)
| ~ program_halts2_halts3_outputs(U_49,U_48,U_47,U_46) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_57,U_55,U_53,U_51] :
( program_halts2_halts3_outputs(U_57,U_55,U_53,U_51)
| ( ~ halts3_outputs(U_57,U_55,U_53,U_51)
& program_halts2(U_55,U_53) ) )
& ! [U_56,U_54,U_52,U_50] :
( halts3_outputs(U_56,U_54,U_52,U_50)
| ~ program_halts2(U_54,U_52)
| ~ program_halts2_halts3_outputs(U_56,U_54,U_52,U_50) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( halts3_outputs(U_56,U_54,U_52,U_50)
| ~ program_halts2(U_54,U_52)
| ~ program_halts2_halts3_outputs(U_56,U_54,U_52,U_50) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( program_halts2(U_55,U_53)
| program_halts2_halts3_outputs(U_57,U_55,U_53,U_51) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_6,plain,
( ~ halts3_outputs(U_57,U_55,U_53,U_51)
| program_halts2_halts3_outputs(U_57,U_55,U_53,U_51) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [X,Y,Z,W] :
( ( program_not_halts2_halts3_outputs(X,Y,Z,W)
| ( ~ halts3_outputs(X,Y,Z,W)
& program_not_halts2(Y,Z) ) )
& ( halts3_outputs(X,Y,Z,W)
| ~ program_not_halts2(Y,Z)
| ~ program_not_halts2_halts3_outputs(X,Y,Z,W) ) ),
inference(fof_nnf,[status(thm)],[program_not_halts2_halts3_outputs_def]) ).
fof(f_9_2,plain,
! [U_61,U_60,U_59,U_58] :
( ( program_not_halts2_halts3_outputs(U_61,U_60,U_59,U_58)
| ( ~ halts3_outputs(U_61,U_60,U_59,U_58)
& program_not_halts2(U_60,U_59) ) )
& ( halts3_outputs(U_61,U_60,U_59,U_58)
| ~ program_not_halts2(U_60,U_59)
| ~ program_not_halts2_halts3_outputs(U_61,U_60,U_59,U_58) ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_69,U_67,U_65,U_63] :
( program_not_halts2_halts3_outputs(U_69,U_67,U_65,U_63)
| ( ~ halts3_outputs(U_69,U_67,U_65,U_63)
& program_not_halts2(U_67,U_65) ) )
& ! [U_68,U_66,U_64,U_62] :
( halts3_outputs(U_68,U_66,U_64,U_62)
| ~ program_not_halts2(U_66,U_64)
| ~ program_not_halts2_halts3_outputs(U_68,U_66,U_64,U_62) ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( halts3_outputs(U_68,U_66,U_64,U_62)
| ~ program_not_halts2(U_66,U_64)
| ~ program_not_halts2_halts3_outputs(U_68,U_66,U_64,U_62) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( program_not_halts2(U_67,U_65)
| program_not_halts2_halts3_outputs(U_69,U_67,U_65,U_63) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_6,plain,
( ~ halts3_outputs(U_69,U_67,U_65,U_63)
| program_not_halts2_halts3_outputs(U_69,U_67,U_65,U_63) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [X,Y,W] :
( ( program_halts2_halts2_outputs(X,Y,W)
| ( ~ halts2_outputs(X,Y,W)
& program_halts2(Y,Y) ) )
& ( halts2_outputs(X,Y,W)
| ~ program_halts2(Y,Y)
| ~ program_halts2_halts2_outputs(X,Y,W) ) ),
inference(fof_nnf,[status(thm)],[program_halts2_halts2_outputs_def]) ).
fof(f_10_2,plain,
! [U_72,U_71,U_70] :
( ( program_halts2_halts2_outputs(U_72,U_71,U_70)
| ( ~ halts2_outputs(U_72,U_71,U_70)
& program_halts2(U_71,U_71) ) )
& ( halts2_outputs(U_72,U_71,U_70)
| ~ program_halts2(U_71,U_71)
| ~ program_halts2_halts2_outputs(U_72,U_71,U_70) ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_78,U_76,U_74] :
( program_halts2_halts2_outputs(U_78,U_76,U_74)
| ( ~ halts2_outputs(U_78,U_76,U_74)
& program_halts2(U_76,U_76) ) )
& ! [U_77,U_75,U_73] :
( halts2_outputs(U_77,U_75,U_73)
| ~ program_halts2(U_75,U_75)
| ~ program_halts2_halts2_outputs(U_77,U_75,U_73) ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( halts2_outputs(U_77,U_75,U_73)
| ~ program_halts2(U_75,U_75)
| ~ program_halts2_halts2_outputs(U_77,U_75,U_73) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_5,plain,
( program_halts2(U_76,U_76)
| program_halts2_halts2_outputs(U_78,U_76,U_74) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_6,plain,
( ~ halts2_outputs(U_78,U_76,U_74)
| program_halts2_halts2_outputs(U_78,U_76,U_74) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [X,Y,W] :
( ( program_not_halts2_halts2_outputs(X,Y,W)
| ( ~ halts2_outputs(X,Y,W)
& program_not_halts2(Y,Y) ) )
& ( halts2_outputs(X,Y,W)
| ~ program_not_halts2(Y,Y)
| ~ program_not_halts2_halts2_outputs(X,Y,W) ) ),
inference(fof_nnf,[status(thm)],[program_not_halts2_halts2_outputs_def]) ).
fof(f_11_2,plain,
! [U_81,U_80,U_79] :
( ( program_not_halts2_halts2_outputs(U_81,U_80,U_79)
| ( ~ halts2_outputs(U_81,U_80,U_79)
& program_not_halts2(U_80,U_80) ) )
& ( halts2_outputs(U_81,U_80,U_79)
| ~ program_not_halts2(U_80,U_80)
| ~ program_not_halts2_halts2_outputs(U_81,U_80,U_79) ) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ! [U_87,U_85,U_83] :
( program_not_halts2_halts2_outputs(U_87,U_85,U_83)
| ( ~ halts2_outputs(U_87,U_85,U_83)
& program_not_halts2(U_85,U_85) ) )
& ! [U_86,U_84,U_82] :
( halts2_outputs(U_86,U_84,U_82)
| ~ program_not_halts2(U_84,U_84)
| ~ program_not_halts2_halts2_outputs(U_86,U_84,U_82) ) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( halts2_outputs(U_86,U_84,U_82)
| ~ program_not_halts2(U_84,U_84)
| ~ program_not_halts2_halts2_outputs(U_86,U_84,U_82) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_5,plain,
( program_not_halts2(U_85,U_85)
| program_not_halts2_halts2_outputs(U_87,U_85,U_83) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_6,plain,
( ~ halts2_outputs(U_87,U_85,U_83)
| program_not_halts2_halts2_outputs(U_87,U_85,U_83) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
( ? [W] : program_program_decides(W)
| ! [X] : ~ algorithm_program_decides(X) ),
inference(fof_nnf,[status(thm)],[p1]) ).
fof(f_12_2,plain,
( ? [U_89] : program_program_decides(U_89)
| ! [U_88] : ~ algorithm_program_decides(U_88) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( program_program_decides(sK3)
| ! [U_88] : ~ algorithm_program_decides(U_88) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_89,sK3)],[f_12_2]) ).
cnf(f_12_4,plain,
( program_program_decides(sK3)
| ~ algorithm_program_decides(U_88) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [W] :
( ! [Y,Z] :
( program_not_halts2_halts3_outputs(W,Y,Z,bad)
& program_halts2_halts3_outputs(W,Y,Z,good) )
| ~ program_program_decides(W) ),
inference(fof_nnf,[status(thm)],[p2]) ).
fof(f_13_2,plain,
! [U_92] :
( ! [U_91,U_90] :
( program_not_halts2_halts3_outputs(U_92,U_91,U_90,bad)
& program_halts2_halts3_outputs(U_92,U_91,U_90,good) )
| ~ program_program_decides(U_92) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_92] :
( ( ! [U_96,U_94] : program_not_halts2_halts3_outputs(U_92,U_96,U_94,bad)
& ! [U_95,U_93] : program_halts2_halts3_outputs(U_92,U_95,U_93,good) )
| ~ program_program_decides(U_92) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( program_halts2_halts3_outputs(U_92,U_95,U_93,good)
| ~ program_program_decides(U_92) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_5,plain,
( program_not_halts2_halts3_outputs(U_92,U_96,U_94,bad)
| ~ program_program_decides(U_92) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
( ? [V] :
( ! [Y] :
( program_not_halts2_halts2_outputs(V,Y,bad)
& program_halts2_halts2_outputs(V,Y,good) )
& program(V) )
| ! [W] :
( ? [Y] :
( ~ program_not_halts2_halts3_outputs(W,Y,Y,bad)
| ~ program_halts2_halts3_outputs(W,Y,Y,good) )
| ~ program(W) ) ),
inference(fof_nnf,[status(thm)],[p3]) ).
fof(f_14_2,plain,
( ? [U_100] :
( ! [U_99] :
( program_not_halts2_halts2_outputs(U_100,U_99,bad)
& program_halts2_halts2_outputs(U_100,U_99,good) )
& program(U_100) )
| ! [U_98] :
( ? [U_97] :
( ~ program_not_halts2_halts3_outputs(U_98,U_97,U_97,bad)
| ~ program_halts2_halts3_outputs(U_98,U_97,U_97,good) )
| ~ program(U_98) ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ? [U_100] :
( ! [U_104] : program_not_halts2_halts2_outputs(U_100,U_104,bad)
& ! [U_103] : program_halts2_halts2_outputs(U_100,U_103,good)
& program(U_100) )
| ! [U_98] :
( ? [U_102] : ~ program_not_halts2_halts3_outputs(U_98,U_102,U_102,bad)
| ? [U_101] : ~ program_halts2_halts3_outputs(U_98,U_101,U_101,good)
| ~ program(U_98) ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
( ? [U_100] :
( ! [U_104] : program_not_halts2_halts2_outputs(U_100,U_104,bad)
& ! [U_103] : program_halts2_halts2_outputs(U_100,U_103,good)
& program(U_100) )
| ! [U_98] :
( ? [U_102] : ~ program_not_halts2_halts3_outputs(U_98,U_102,U_102,bad)
| ~ program_halts2_halts3_outputs(U_98,sK4(U_98),sK4(U_98),good)
| ~ program(U_98) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_101,sK4(U_98))],[f_14_3]) ).
fof(f_14_5,plain,
( ? [U_100] :
( ! [U_104] : program_not_halts2_halts2_outputs(U_100,U_104,bad)
& ! [U_103] : program_halts2_halts2_outputs(U_100,U_103,good)
& program(U_100) )
| ! [U_98] :
( ~ program_not_halts2_halts3_outputs(U_98,sK5(U_98),sK5(U_98),bad)
| ~ program_halts2_halts3_outputs(U_98,sK4(U_98),sK4(U_98),good)
| ~ program(U_98) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_102,sK5(U_98))],[f_14_4]) ).
fof(f_14_6,plain,
( ( ! [U_104] : program_not_halts2_halts2_outputs(sK6,U_104,bad)
& ! [U_103] : program_halts2_halts2_outputs(sK6,U_103,good)
& program(sK6) )
| ! [U_98] :
( ~ program_not_halts2_halts3_outputs(U_98,sK5(U_98),sK5(U_98),bad)
| ~ program_halts2_halts3_outputs(U_98,sK4(U_98),sK4(U_98),good)
| ~ program(U_98) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_100,sK6)],[f_14_5]) ).
cnf(f_14_7,plain,
( program(sK6)
| ~ program_not_halts2_halts3_outputs(U_98,sK5(U_98),sK5(U_98),bad)
| ~ program_halts2_halts3_outputs(U_98,sK4(U_98),sK4(U_98),good)
| ~ program(U_98) ),
inference(clausify,[status(thm)],[f_14_6]) ).
cnf(f_14_8,plain,
( program_halts2_halts2_outputs(sK6,U_103,good)
| ~ program_not_halts2_halts3_outputs(U_98,sK5(U_98),sK5(U_98),bad)
| ~ program_halts2_halts3_outputs(U_98,sK4(U_98),sK4(U_98),good)
| ~ program(U_98) ),
inference(clausify,[status(thm)],[f_14_6]) ).
cnf(f_14_9,plain,
( program_not_halts2_halts2_outputs(sK6,U_104,bad)
| ~ program_not_halts2_halts3_outputs(U_98,sK5(U_98),sK5(U_98),bad)
| ~ program_halts2_halts3_outputs(U_98,sK4(U_98),sK4(U_98),good)
| ~ program(U_98) ),
inference(clausify,[status(thm)],[f_14_6]) ).
fof(f_15_1,plain,
( ? [U] :
( ! [Y] :
( program_not_halts2_halts2_outputs(U,Y,good)
& ( ~ halts2(U,Y)
| ~ program_halts2(Y,Y) ) )
& program(U) )
| ! [V] :
( ? [Y] :
( ~ program_not_halts2_halts2_outputs(V,Y,bad)
| ~ program_halts2_halts2_outputs(V,Y,good) )
| ~ program(V) ) ),
inference(fof_nnf,[status(thm)],[p4]) ).
fof(f_15_2,plain,
( ? [U_108] :
( ! [U_107] :
( program_not_halts2_halts2_outputs(U_108,U_107,good)
& ( ~ halts2(U_108,U_107)
| ~ program_halts2(U_107,U_107) ) )
& program(U_108) )
| ! [U_106] :
( ? [U_105] :
( ~ program_not_halts2_halts2_outputs(U_106,U_105,bad)
| ~ program_halts2_halts2_outputs(U_106,U_105,good) )
| ~ program(U_106) ) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ? [U_108] :
( ! [U_112] : program_not_halts2_halts2_outputs(U_108,U_112,good)
& ! [U_111] :
( ~ halts2(U_108,U_111)
| ~ program_halts2(U_111,U_111) )
& program(U_108) )
| ! [U_106] :
( ? [U_110] : ~ program_not_halts2_halts2_outputs(U_106,U_110,bad)
| ? [U_109] : ~ program_halts2_halts2_outputs(U_106,U_109,good)
| ~ program(U_106) ) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
( ? [U_108] :
( ! [U_112] : program_not_halts2_halts2_outputs(U_108,U_112,good)
& ! [U_111] :
( ~ halts2(U_108,U_111)
| ~ program_halts2(U_111,U_111) )
& program(U_108) )
| ! [U_106] :
( ? [U_110] : ~ program_not_halts2_halts2_outputs(U_106,U_110,bad)
| ~ program_halts2_halts2_outputs(U_106,sK7(U_106),good)
| ~ program(U_106) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_109,sK7(U_106))],[f_15_3]) ).
fof(f_15_5,plain,
( ? [U_108] :
( ! [U_112] : program_not_halts2_halts2_outputs(U_108,U_112,good)
& ! [U_111] :
( ~ halts2(U_108,U_111)
| ~ program_halts2(U_111,U_111) )
& program(U_108) )
| ! [U_106] :
( ~ program_not_halts2_halts2_outputs(U_106,sK8(U_106),bad)
| ~ program_halts2_halts2_outputs(U_106,sK7(U_106),good)
| ~ program(U_106) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_110,sK8(U_106))],[f_15_4]) ).
fof(f_15_6,plain,
( ( ! [U_112] : program_not_halts2_halts2_outputs(sK9,U_112,good)
& ! [U_111] :
( ~ halts2(sK9,U_111)
| ~ program_halts2(U_111,U_111) )
& program(sK9) )
| ! [U_106] :
( ~ program_not_halts2_halts2_outputs(U_106,sK8(U_106),bad)
| ~ program_halts2_halts2_outputs(U_106,sK7(U_106),good)
| ~ program(U_106) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_108,sK9)],[f_15_5]) ).
cnf(f_15_7,plain,
( program(sK9)
| ~ program_not_halts2_halts2_outputs(U_106,sK8(U_106),bad)
| ~ program_halts2_halts2_outputs(U_106,sK7(U_106),good)
| ~ program(U_106) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_8,plain,
( ~ halts2(sK9,U_111)
| ~ program_halts2(U_111,U_111)
| ~ program_not_halts2_halts2_outputs(U_106,sK8(U_106),bad)
| ~ program_halts2_halts2_outputs(U_106,sK7(U_106),good)
| ~ program(U_106) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_9,plain,
( program_not_halts2_halts2_outputs(sK9,U_112,good)
| ~ program_not_halts2_halts2_outputs(U_106,sK8(U_106),bad)
| ~ program_halts2_halts2_outputs(U_106,sK7(U_106),good)
| ~ program(U_106) ),
inference(clausify,[status(thm)],[f_15_6]) ).
fof(f_16_1,negated_conjecture,
? [X] : algorithm_program_decides(X),
inference(negate,[status(cth)],[prove_this]) ).
fof(f_16_2,negated_conjecture,
? [U_113] : algorithm_program_decides(U_113),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,negated_conjecture,
algorithm_program_decides(sK10),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_113,sK10)],[f_16_2]) ).
fof(f_16_4,negated_conjecture,
algorithm_program_decides(sK10),
inference(definitional_conversion,[status(esa)],[f_16_3]) ).
cnf(f_16_5,negated_conjecture,
algorithm_program_decides(sK10),
inference(clausify,[status(thm)],[f_16_4]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM003+2 : TPTP v9.3.1. Bugfixed v2.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/10.57 % Computer : n010.cluster.edu
% 0.09/10.57 % Model : x86_64 x86_64
% 0.09/10.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.57 % Memory : 8046.5625MB
% 0.09/10.57 % OS : Linux 6.8.0-71-generic
% 0.09/10.57 % CPULimit : 300
% 0.09/10.57 % WCLimit : 300
% 0.09/10.57 % DateTime : Sun Sep 20 15:16:24 UTC 2026
% 0.09/10.58 % CPUTime :
% 1.15/11.60 % SZS status Theorem for theBenchmark
% 1.15/11.60 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------