%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COM003+2 : TPTP v9.2.1. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n026.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 : 300s
% DateTime : Tue May 5 04:12:55 PM UTC 2026
% Result : Theorem 1.38s 1.72s
% Output : CNFRefutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 58 ( 14 unt; 0 def)
% Number of atoms : 191 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 226 ( 93 ~; 86 |; 33 &)
% ( 6 <=>; 8 =>; 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 : 98 ( 17 sgn 41 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
~ ? [X1] : algorithm_program_decides(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(program_not_halts2_def,axiom,
! [X1,X2] :
( program_not_halts2(X1,X2)
<=> ( program(X1)
& ~ halts2(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_not_halts2_def) ).
fof(p3,axiom,
( ? [X4] :
( program(X4)
& ! [X2] :
( program_halts2_halts3_outputs(X4,X2,X2,good)
& program_not_halts2_halts3_outputs(X4,X2,X2,bad) ) )
=> ? [X5] :
( program(X5)
& ! [X2] :
( program_halts2_halts2_outputs(X5,X2,good)
& program_not_halts2_halts2_outputs(X5,X2,bad) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(p2,axiom,
! [X4] :
( program_program_decides(X4)
=> ! [X2,X3] :
( program_halts2_halts3_outputs(X4,X2,X3,good)
& program_not_halts2_halts3_outputs(X4,X2,X3,bad) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(program_program_decides_def,axiom,
! [X1] :
( program_program_decides(X1)
<=> ( program(X1)
& program_decides(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_program_decides_def) ).
fof(p1,axiom,
( ? [X1] : algorithm_program_decides(X1)
=> ? [X4] : program_program_decides(X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(program_halts2_def,axiom,
! [X1,X2] :
( program_halts2(X1,X2)
<=> ( program(X1)
& halts2(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_halts2_def) ).
fof(p4,axiom,
( ? [X5] :
( program(X5)
& ! [X2] :
( program_halts2_halts2_outputs(X5,X2,good)
& program_not_halts2_halts2_outputs(X5,X2,bad) ) )
=> ? [X6] :
( program(X6)
& ! [X2] :
( ( program_halts2(X2,X2)
=> ~ halts2(X6,X2) )
& program_not_halts2_halts2_outputs(X6,X2,good) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
fof(program_not_halts2_halts2_outputs_def,axiom,
! [X1,X2,X4] :
( program_not_halts2_halts2_outputs(X1,X2,X4)
<=> ( program_not_halts2(X2,X2)
=> halts2_outputs(X1,X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_not_halts2_halts2_outputs_def) ).
fof(halts2_outputs_def,axiom,
! [X1,X2,X4] :
( halts2_outputs(X1,X2,X4)
<=> ( halts2(X1,X2)
& outputs(X1,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',halts2_outputs_def) ).
fof(c_0_10,negated_conjecture,
~ ~ ? [X1] : algorithm_program_decides(X1),
inference(assume_negation,[status(cth)],[prove_this]) ).
fof(c_0_11,plain,
! [X1,X2] :
( program_not_halts2(X1,X2)
<=> ( program(X1)
& ~ halts2(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[program_not_halts2_def]) ).
fof(c_0_12,plain,
! [X89,X93] :
( ( program(esk6_0)
| ~ program(X89)
| ~ program_halts2_halts3_outputs(X89,esk4_1(X89),esk4_1(X89),good)
| ~ program_not_halts2_halts3_outputs(X89,esk5_1(X89),esk5_1(X89),bad) )
& ( program_halts2_halts2_outputs(esk6_0,X93,good)
| ~ program(X89)
| ~ program_halts2_halts3_outputs(X89,esk4_1(X89),esk4_1(X89),good)
| ~ program_not_halts2_halts3_outputs(X89,esk5_1(X89),esk5_1(X89),bad) )
& ( program_not_halts2_halts2_outputs(esk6_0,X93,bad)
| ~ program(X89)
| ~ program_halts2_halts3_outputs(X89,esk4_1(X89),esk4_1(X89),good)
| ~ program_not_halts2_halts3_outputs(X89,esk5_1(X89),esk5_1(X89),bad) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])])])])])]) ).
fof(c_0_13,plain,
! [X86,X87,X88] :
( ( program_halts2_halts3_outputs(X86,X87,X88,good)
| ~ program_program_decides(X86) )
& ( program_not_halts2_halts3_outputs(X86,X87,X88,bad)
| ~ program_program_decides(X86) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])]) ).
fof(c_0_14,plain,
! [X57] :
( ( program(X57)
| ~ program_program_decides(X57) )
& ( program_decides(X57)
| ~ program_program_decides(X57) )
& ( ~ program(X57)
| ~ program_decides(X57)
| program_program_decides(X57) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[program_program_decides_def])])]) ).
fof(c_0_15,plain,
! [X84] :
( ~ algorithm_program_decides(X84)
| program_program_decides(esk3_0) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])])]) ).
fof(c_0_16,negated_conjecture,
algorithm_program_decides(esk10_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_17,plain,
! [X59,X60] :
( ( program(X59)
| ~ program_halts2(X59,X60) )
& ( halts2(X59,X60)
| ~ program_halts2(X59,X60) )
& ( ~ program(X59)
| ~ halts2(X59,X60)
| program_halts2(X59,X60) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[program_halts2_def])])]) ).
fof(c_0_18,plain,
! [X65,X66] :
( ( program(X65)
| ~ program_not_halts2(X65,X66) )
& ( ~ halts2(X65,X66)
| ~ program_not_halts2(X65,X66) )
& ( ~ program(X65)
| halts2(X65,X66)
| program_not_halts2(X65,X66) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_19,plain,
( ? [X5] :
( program(X5)
& ! [X2] :
( program_halts2_halts2_outputs(X5,X2,good)
& program_not_halts2_halts2_outputs(X5,X2,bad) ) )
=> ? [X6] :
( program(X6)
& ! [X2] :
( ( program_halts2(X2,X2)
=> ~ halts2(X6,X2) )
& program_not_halts2_halts2_outputs(X6,X2,good) ) ) ),
inference(fof_simplification,[status(thm)],[p4]) ).
cnf(c_0_20,plain,
( program_not_halts2_halts2_outputs(esk6_0,X1,bad)
| ~ program(X2)
| ~ program_halts2_halts3_outputs(X2,esk4_1(X2),esk4_1(X2),good)
| ~ program_not_halts2_halts3_outputs(X2,esk5_1(X2),esk5_1(X2),bad) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,plain,
( program_not_halts2_halts3_outputs(X1,X2,X3,bad)
| ~ program_program_decides(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
( program(X1)
| ~ program_program_decides(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
( program_halts2_halts3_outputs(X1,X2,X3,good)
| ~ program_program_decides(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_24,plain,
( program_program_decides(esk3_0)
| ~ algorithm_program_decides(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,negated_conjecture,
algorithm_program_decides(esk10_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,plain,
( program_halts2_halts2_outputs(esk6_0,X1,good)
| ~ program(X2)
| ~ program_halts2_halts3_outputs(X2,esk4_1(X2),esk4_1(X2),good)
| ~ program_not_halts2_halts3_outputs(X2,esk5_1(X2),esk5_1(X2),bad) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_27,plain,
( program(esk6_0)
| ~ program(X1)
| ~ program_halts2_halts3_outputs(X1,esk4_1(X1),esk4_1(X1),good)
| ~ program_not_halts2_halts3_outputs(X1,esk5_1(X1),esk5_1(X1),bad) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_28,plain,
! [X81,X82,X83] :
( ( ~ program_not_halts2_halts2_outputs(X81,X82,X83)
| ~ program_not_halts2(X82,X82)
| halts2_outputs(X81,X82,X83) )
& ( program_not_halts2(X82,X82)
| program_not_halts2_halts2_outputs(X81,X82,X83) )
& ( ~ halts2_outputs(X81,X82,X83)
| program_not_halts2_halts2_outputs(X81,X82,X83) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[program_not_halts2_halts2_outputs_def])])]) ).
cnf(c_0_29,plain,
( program_halts2(X1,X2)
| ~ program(X1)
| ~ halts2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_30,plain,
( halts2(X1,X2)
| program_not_halts2(X1,X2)
| ~ program(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_31,plain,
! [X94,X98] :
( ( program(esk9_0)
| ~ program(X94)
| ~ program_halts2_halts2_outputs(X94,esk7_1(X94),good)
| ~ program_not_halts2_halts2_outputs(X94,esk8_1(X94),bad) )
& ( ~ program_halts2(X98,X98)
| ~ halts2(esk9_0,X98)
| ~ program(X94)
| ~ program_halts2_halts2_outputs(X94,esk7_1(X94),good)
| ~ program_not_halts2_halts2_outputs(X94,esk8_1(X94),bad) )
& ( program_not_halts2_halts2_outputs(esk9_0,X98,good)
| ~ program(X94)
| ~ program_halts2_halts2_outputs(X94,esk7_1(X94),good)
| ~ program_not_halts2_halts2_outputs(X94,esk8_1(X94),bad) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])])])]) ).
cnf(c_0_32,plain,
( program_not_halts2_halts2_outputs(esk6_0,X1,bad)
| ~ program_program_decides(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23]) ).
cnf(c_0_33,negated_conjecture,
program_program_decides(esk3_0),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_34,plain,
( program_halts2_halts2_outputs(esk6_0,X1,good)
| ~ program_program_decides(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_21]),c_0_22]),c_0_23]) ).
cnf(c_0_35,plain,
( program(esk6_0)
| ~ program_program_decides(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_21]),c_0_22]),c_0_23]) ).
cnf(c_0_36,plain,
( halts2_outputs(X1,X2,X3)
| ~ program_not_halts2_halts2_outputs(X1,X2,X3)
| ~ program_not_halts2(X2,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,plain,
( program_not_halts2(X1,X2)
| program_halts2(X1,X2)
| ~ program(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_38,plain,
( program_not_halts2_halts2_outputs(esk9_0,X1,good)
| ~ program(X2)
| ~ program_halts2_halts2_outputs(X2,esk7_1(X2),good)
| ~ program_not_halts2_halts2_outputs(X2,esk8_1(X2),bad) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_39,negated_conjecture,
program_not_halts2_halts2_outputs(esk6_0,X1,bad),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,negated_conjecture,
program_halts2_halts2_outputs(esk6_0,X1,good),
inference(spm,[status(thm)],[c_0_34,c_0_33]) ).
cnf(c_0_41,negated_conjecture,
program(esk6_0),
inference(spm,[status(thm)],[c_0_35,c_0_33]) ).
cnf(c_0_42,plain,
( halts2_outputs(X1,X2,X3)
| program_halts2(X2,X2)
| ~ program_not_halts2_halts2_outputs(X1,X2,X3)
| ~ program(X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_43,negated_conjecture,
program_not_halts2_halts2_outputs(esk9_0,X1,good),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_41])]) ).
cnf(c_0_44,plain,
( program(esk9_0)
| ~ program(X1)
| ~ program_halts2_halts2_outputs(X1,esk7_1(X1),good)
| ~ program_not_halts2_halts2_outputs(X1,esk8_1(X1),bad) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_45,plain,
! [X67,X68,X69] :
( ( halts2(X67,X68)
| ~ halts2_outputs(X67,X68,X69) )
& ( outputs(X67,X69)
| ~ halts2_outputs(X67,X68,X69) )
& ( ~ halts2(X67,X68)
| ~ outputs(X67,X69)
| halts2_outputs(X67,X68,X69) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[halts2_outputs_def])])]) ).
cnf(c_0_46,negated_conjecture,
( halts2_outputs(esk9_0,X1,good)
| program_halts2(X1,X1)
| ~ program(X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
program(esk9_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_39]),c_0_40]),c_0_41])]) ).
cnf(c_0_48,plain,
( halts2(X1,X2)
| ~ halts2_outputs(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_49,negated_conjecture,
( halts2_outputs(esk9_0,esk9_0,good)
| program_halts2(esk9_0,esk9_0) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,plain,
( halts2(X1,X2)
| ~ program_halts2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_51,plain,
( ~ program_halts2(X1,X1)
| ~ halts2(esk9_0,X1)
| ~ program(X2)
| ~ program_halts2_halts2_outputs(X2,esk7_1(X2),good)
| ~ program_not_halts2_halts2_outputs(X2,esk8_1(X2),bad) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_52,plain,
( ~ halts2(X1,X2)
| ~ program_not_halts2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_53,negated_conjecture,
halts2(esk9_0,esk9_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_54,negated_conjecture,
( ~ halts2(esk9_0,X1)
| ~ program_halts2(X1,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_39]),c_0_40]),c_0_41])]) ).
cnf(c_0_55,negated_conjecture,
~ program_not_halts2(esk9_0,esk9_0),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_56,negated_conjecture,
~ program_halts2(esk9_0,esk9_0),
inference(spm,[status(thm)],[c_0_54,c_0_53]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_37]),c_0_47])]),c_0_56]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : COM003+2 : TPTP v9.2.1. Bugfixed v2.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.31 % Computer : n026.cluster.edu
% 0.14/0.31 % Model : x86_64 x86_64
% 0.14/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.31 % Memory : 8042.1875MB
% 0.14/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.31 % CPULimit : 300
% 0.14/0.31 % WCLimit : 300
% 0.14/0.31 % DateTime : Mon May 4 16:19:08 EDT 2026
% 0.14/0.31 % CPUTime :
% 0.14/0.32 % start to proof: theBenchmark
% 1.38/1.72 % Version : CSE_E---1.7
% 1.38/1.72 % Problem : theBenchmark.p
% 1.38/1.72 % SZS status Theorem for theBenchmark.p
% 1.38/1.72 % SZS output start CNFRefutation
% See solution above
% 1.38/1.72 % Total time : 1.368s
%------------------------------------------------------------------------------