TSTP Solution File: COM003+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : COM003+2 : TPTP v8.1.2. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n002.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 : Wed Aug 30 18:36:03 EDT 2023
% Result : Theorem 0.21s 0.66s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 39
% Syntax : Number of formulae : 87 ( 14 unt; 29 typ; 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 types : 2 ( 0 usr)
% Number of type conns : 46 ( 23 >; 23 *; 0 +; 0 <<)
% Number of predicates : 18 ( 17 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-1 aty)
% Number of variables : 98 ( 17 sgn; 41 !; 10 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
program_decides: $i > $o ).
tff(decl_23,type,
program: $i > $o ).
tff(decl_24,type,
decides: ( $i * $i * $i ) > $o ).
tff(decl_25,type,
program_program_decides: $i > $o ).
tff(decl_26,type,
algorithm_program_decides: $i > $o ).
tff(decl_27,type,
algorithm: $i > $o ).
tff(decl_28,type,
program_halts2: ( $i * $i ) > $o ).
tff(decl_29,type,
halts2: ( $i * $i ) > $o ).
tff(decl_30,type,
halts3_outputs: ( $i * $i * $i * $i ) > $o ).
tff(decl_31,type,
halts3: ( $i * $i * $i ) > $o ).
tff(decl_32,type,
outputs: ( $i * $i ) > $o ).
tff(decl_33,type,
program_not_halts2: ( $i * $i ) > $o ).
tff(decl_34,type,
halts2_outputs: ( $i * $i * $i ) > $o ).
tff(decl_35,type,
program_halts2_halts3_outputs: ( $i * $i * $i * $i ) > $o ).
tff(decl_36,type,
program_not_halts2_halts3_outputs: ( $i * $i * $i * $i ) > $o ).
tff(decl_37,type,
program_halts2_halts2_outputs: ( $i * $i * $i ) > $o ).
tff(decl_38,type,
program_not_halts2_halts2_outputs: ( $i * $i * $i ) > $o ).
tff(decl_39,type,
good: $i ).
tff(decl_40,type,
bad: $i ).
tff(decl_41,type,
esk1_1: $i > $i ).
tff(decl_42,type,
esk2_1: $i > $i ).
tff(decl_43,type,
esk3_0: $i ).
tff(decl_44,type,
esk4_1: $i > $i ).
tff(decl_45,type,
esk5_1: $i > $i ).
tff(decl_46,type,
esk6_0: $i ).
tff(decl_47,type,
esk7_1: $i > $i ).
tff(decl_48,type,
esk8_1: $i > $i ).
tff(decl_49,type,
esk9_0: $i ).
tff(decl_50,type,
esk10_0: $i ).
fof(prove_this,conjecture,
~ ? [X1] : algorithm_program_decides(X1),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',p2) ).
fof(program_program_decides_def,axiom,
! [X1] :
( program_program_decides(X1)
<=> ( program(X1)
& program_decides(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',program_program_decides_def) ).
fof(p1,axiom,
( ? [X1] : algorithm_program_decides(X1)
=> ? [X4] : program_program_decides(X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(program_halts2_def,axiom,
! [X1,X2] :
( program_halts2(X1,X2)
<=> ( program(X1)
& halts2(X1,X2) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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,
! [X45,X49] :
( ( program(esk6_0)
| ~ program(X45)
| ~ program_halts2_halts3_outputs(X45,esk4_1(X45),esk4_1(X45),good)
| ~ program_not_halts2_halts3_outputs(X45,esk5_1(X45),esk5_1(X45),bad) )
& ( program_halts2_halts2_outputs(esk6_0,X49,good)
| ~ program(X45)
| ~ program_halts2_halts3_outputs(X45,esk4_1(X45),esk4_1(X45),good)
| ~ program_not_halts2_halts3_outputs(X45,esk5_1(X45),esk5_1(X45),bad) )
& ( program_not_halts2_halts2_outputs(esk6_0,X49,bad)
| ~ program(X45)
| ~ program_halts2_halts3_outputs(X45,esk4_1(X45),esk4_1(X45),good)
| ~ program_not_halts2_halts3_outputs(X45,esk5_1(X45),esk5_1(X45),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,
! [X42,X43,X44] :
( ( program_halts2_halts3_outputs(X42,X43,X44,good)
| ~ program_program_decides(X42) )
& ( program_not_halts2_halts3_outputs(X42,X43,X44,bad)
| ~ program_program_decides(X42) ) ),
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,
! [X13] :
( ( program(X13)
| ~ program_program_decides(X13) )
& ( program_decides(X13)
| ~ program_program_decides(X13) )
& ( ~ program(X13)
| ~ program_decides(X13)
| program_program_decides(X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[program_program_decides_def])])]) ).
fof(c_0_15,plain,
! [X40] :
( ~ algorithm_program_decides(X40)
| 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,
! [X15,X16] :
( ( program(X15)
| ~ program_halts2(X15,X16) )
& ( halts2(X15,X16)
| ~ program_halts2(X15,X16) )
& ( ~ program(X15)
| ~ halts2(X15,X16)
| program_halts2(X15,X16) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[program_halts2_def])])]) ).
fof(c_0_18,plain,
! [X21,X22] :
( ( program(X21)
| ~ program_not_halts2(X21,X22) )
& ( ~ halts2(X21,X22)
| ~ program_not_halts2(X21,X22) )
& ( ~ program(X21)
| halts2(X21,X22)
| program_not_halts2(X21,X22) ) ),
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,
! [X37,X38,X39] :
( ( ~ program_not_halts2_halts2_outputs(X37,X38,X39)
| ~ program_not_halts2(X38,X38)
| halts2_outputs(X37,X38,X39) )
& ( program_not_halts2(X38,X38)
| program_not_halts2_halts2_outputs(X37,X38,X39) )
& ( ~ halts2_outputs(X37,X38,X39)
| program_not_halts2_halts2_outputs(X37,X38,X39) ) ),
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,
! [X50,X54] :
( ( program(esk9_0)
| ~ program(X50)
| ~ program_halts2_halts2_outputs(X50,esk7_1(X50),good)
| ~ program_not_halts2_halts2_outputs(X50,esk8_1(X50),bad) )
& ( ~ program_halts2(X54,X54)
| ~ halts2(esk9_0,X54)
| ~ program(X50)
| ~ program_halts2_halts2_outputs(X50,esk7_1(X50),good)
| ~ program_not_halts2_halts2_outputs(X50,esk8_1(X50),bad) )
& ( program_not_halts2_halts2_outputs(esk9_0,X54,good)
| ~ program(X50)
| ~ program_halts2_halts2_outputs(X50,esk7_1(X50),good)
| ~ program_not_halts2_halts2_outputs(X50,esk8_1(X50),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,
! [X23,X24,X25] :
( ( halts2(X23,X24)
| ~ halts2_outputs(X23,X24,X25) )
& ( outputs(X23,X25)
| ~ halts2_outputs(X23,X24,X25) )
& ( ~ halts2(X23,X24)
| ~ outputs(X23,X25)
| halts2_outputs(X23,X24,X25) ) ),
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
% 0.10/0.13 % Problem : COM003+2 : TPTP v8.1.2. Bugfixed v2.2.0.
% 0.10/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.15/0.35 % Computer : n002.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Aug 29 13:52:35 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 0.21/0.66 % Version : CSE_E---1.5
% 0.21/0.66 % Problem : theBenchmark.p
% 0.21/0.66 % Proof found
% 0.21/0.66 % SZS status Theorem for theBenchmark.p
% 0.21/0.66 % SZS output start Proof
% See solution above
% 0.21/0.67 % Total time : 0.075000 s
% 0.21/0.67 % SZS output end Proof
% 0.21/0.67 % Total time : 0.079000 s
%------------------------------------------------------------------------------