%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : COM003+2 : TPTP v9.3.1. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 12:12:07 PM UTC 2026
% Result : Theorem 0.11s 0.46s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 82 ( 17 unt; 0 def)
% Number of atoms : 249 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 294 ( 127 ~; 114 |; 33 &)
% ( 12 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 20 ( 19 usr; 7 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-1 aty)
% Number of variables : 111 ( 22 sgn 47 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
~ ? [X1] : algorithm_program_decides(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(p1,axiom,
( ? [X1] : algorithm_program_decides(X1)
=> ? [X4] : program_program_decides(X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(halts2_outputs_def,axiom,
! [X1,X2,X4] :
( halts2_outputs(X1,X2,X4)
<=> ( outputs(X1,X4)
& halts2(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',halts2_outputs_def) ).
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(p2,axiom,
! [X4] :
( program_program_decides(X4)
=> ! [X2,X3] :
( program_not_halts2_halts3_outputs(X4,X2,X3,bad)
& program_halts2_halts3_outputs(X4,X2,X3,good) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(program_program_decides_def,axiom,
! [X1] :
( program_program_decides(X1)
<=> ( program_decides(X1)
& program(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',program_program_decides_def) ).
fof(program_not_halts2_def,axiom,
! [X1,X2] :
( program_not_halts2(X1,X2)
<=> ( ~ halts2(X1,X2)
& program(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',program_not_halts2_def) ).
fof(p3,axiom,
( ? [X4] :
( ! [X2] :
( program_not_halts2_halts3_outputs(X4,X2,X2,bad)
& program_halts2_halts3_outputs(X4,X2,X2,good) )
& program(X4) )
=> ? [X5] :
( ! [X2] :
( program_not_halts2_halts2_outputs(X5,X2,bad)
& program_halts2_halts2_outputs(X5,X2,good) )
& program(X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(p4,axiom,
( ? [X5] :
( ! [X2] :
( program_not_halts2_halts2_outputs(X5,X2,bad)
& program_halts2_halts2_outputs(X5,X2,good) )
& program(X5) )
=> ? [X6] :
( ! [X2] :
( program_not_halts2_halts2_outputs(X6,X2,good)
& ( program_halts2(X2,X2)
=> ~ halts2(X6,X2) ) )
& program(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
fof(program_halts2_def,axiom,
! [X1,X2] :
( program_halts2(X1,X2)
<=> ( halts2(X1,X2)
& program(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',program_halts2_def) ).
fof(c_0_10,negated_conjecture,
~ ~ ? [X1] : algorithm_program_decides(X1),
inference(assume_negation,[status(cth)],[prove_this]) ).
fof(c_0_11,plain,
! [X40] :
( program_program_decides(esk3_0)
| ~ algorithm_program_decides(X40) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])])])]) ).
fof(c_0_12,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_13,plain,
! [X23,X24,X25] :
( ( halts2_outputs(X23,X24,X25)
| ~ outputs(X23,X25)
| ~ halts2(X23,X24) )
& ( ~ halts2_outputs(X23,X24,X25)
| outputs(X23,X25) )
& ( ~ halts2_outputs(X23,X24,X25)
| halts2(X23,X24) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[halts2_outputs_def])])])]) ).
fof(c_0_14,plain,
! [X37,X38,X39] :
( ( program_not_halts2_halts2_outputs(X37,X38,X39)
| ~ halts2_outputs(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) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[program_not_halts2_halts2_outputs_def])])])]) ).
fof(c_0_15,plain,
! [X42,X43,X44] :
( ( ~ program_program_decides(X42)
| program_not_halts2_halts3_outputs(X42,X43,X44,bad) )
& ( ~ program_program_decides(X42)
| program_halts2_halts3_outputs(X42,X43,X44,good) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])])]) ).
cnf(c_0_16,plain,
( ~ algorithm_program_decides(X1)
| program_program_decides(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
algorithm_program_decides(esk10_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_18,plain,
! [X13] :
( ( program_program_decides(X13)
| ~ program_decides(X13)
| ~ program(X13) )
& ( ~ program_program_decides(X13)
| program_decides(X13) )
& ( ~ program_program_decides(X13)
| program(X13) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[program_program_decides_def])])])]) ).
fof(c_0_19,plain,
! [X1,X2] :
( program_not_halts2(X1,X2)
<=> ( ~ halts2(X1,X2)
& program(X1) ) ),
inference(fof_simplification,[status(thm)],[program_not_halts2_def]) ).
cnf(c_0_20,plain,
( ~ halts2_outputs(X1,X2,X3)
| halts2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( ~ program_not_halts2(X2,X2)
| ~ program_not_halts2_halts2_outputs(X1,X2,X3)
| halts2_outputs(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_22,plain,
( ~ epred3_0
<=> ! [X1] : program_not_halts2_halts2_outputs(esk9_0,X1,good) ),
introduced(definition) ).
fof(c_0_23,plain,
! [X45,X49] :
( ( ~ program_not_halts2_halts3_outputs(X45,esk5_1(X45),esk5_1(X45),bad)
| ~ program_halts2_halts3_outputs(X45,esk4_1(X45),esk4_1(X45),good)
| ~ program(X45)
| program_not_halts2_halts2_outputs(esk6_0,X49,bad) )
& ( ~ program_not_halts2_halts3_outputs(X45,esk5_1(X45),esk5_1(X45),bad)
| ~ program_halts2_halts3_outputs(X45,esk4_1(X45),esk4_1(X45),good)
| ~ program(X45)
| program_halts2_halts2_outputs(esk6_0,X49,good) )
& ( ~ program_not_halts2_halts3_outputs(X45,esk5_1(X45),esk5_1(X45),bad)
| ~ program_halts2_halts3_outputs(X45,esk4_1(X45),esk4_1(X45),good)
| ~ program(X45)
| program(esk6_0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_24,plain,
( ~ epred5_0
<=> ! [X2] :
( ~ program_not_halts2_halts3_outputs(X2,esk5_1(X2),esk5_1(X2),bad)
| ~ program_halts2_halts3_outputs(X2,esk4_1(X2),esk4_1(X2),good)
| ~ program(X2) ) ),
introduced(definition) ).
cnf(c_0_25,plain,
( ~ program_program_decides(X1)
| program_not_halts2_halts3_outputs(X1,X2,X3,bad) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_26,negated_conjecture,
program_program_decides(esk3_0),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_27,plain,
( ~ program_program_decides(X1)
| program_halts2_halts3_outputs(X1,X2,X3,good) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_28,plain,
( ~ program_program_decides(X1)
| program(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_29,plain,
! [X21,X22] :
( ( program_not_halts2(X21,X22)
| halts2(X21,X22)
| ~ program(X21) )
& ( ~ program_not_halts2(X21,X22)
| ~ halts2(X21,X22) )
& ( ~ program_not_halts2(X21,X22)
| program(X21) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])]) ).
cnf(c_0_30,plain,
( ~ program_not_halts2(X2,X2)
| ~ program_not_halts2_halts2_outputs(X1,X2,X3)
| halts2(X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_31,plain,
( program_not_halts2_halts2_outputs(esk9_0,X1,good)
| epred3_0 ),
inference(split_equiv,[status(thm)],[c_0_22]) ).
fof(c_0_32,plain,
( ? [X5] :
( ! [X2] :
( program_not_halts2_halts2_outputs(X5,X2,bad)
& program_halts2_halts2_outputs(X5,X2,good) )
& program(X5) )
=> ? [X6] :
( ! [X2] :
( program_not_halts2_halts2_outputs(X6,X2,good)
& ( program_halts2(X2,X2)
=> ~ halts2(X6,X2) ) )
& program(X6) ) ),
inference(fof_simplification,[status(thm)],[p4]) ).
fof(c_0_33,plain,
( ~ epred6_0
<=> ! [X1] : program_not_halts2_halts2_outputs(esk6_0,X1,bad) ),
introduced(definition) ).
cnf(c_0_34,plain,
( ~ program_not_halts2_halts3_outputs(X2,esk5_1(X2),esk5_1(X2),bad)
| ~ program_halts2_halts3_outputs(X2,esk4_1(X2),esk4_1(X2),good)
| ~ program(X2)
| program_not_halts2_halts2_outputs(esk6_0,X1,bad) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_35,plain,
( ~ 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)
| epred5_0 ),
inference(split_equiv,[status(thm)],[c_0_24]) ).
cnf(c_0_36,negated_conjecture,
program_not_halts2_halts3_outputs(esk3_0,X1,X2,bad),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_37,negated_conjecture,
program_halts2_halts3_outputs(esk3_0,X1,X2,good),
inference(spm,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_38,negated_conjecture,
program(esk3_0),
inference(spm,[status(thm)],[c_0_28,c_0_26]) ).
cnf(c_0_39,plain,
( ~ program_not_halts2(X1,X2)
| ~ halts2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_40,plain,
( ~ program_not_halts2(X1,X1)
| halts2(esk9_0,X1)
| epred3_0 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
fof(c_0_41,plain,
! [X50,X54] :
( ( ~ program_not_halts2_halts2_outputs(X50,esk8_1(X50),bad)
| ~ program_halts2_halts2_outputs(X50,esk7_1(X50),good)
| ~ program(X50)
| program_not_halts2_halts2_outputs(esk9_0,X54,good) )
& ( ~ program_not_halts2_halts2_outputs(X50,esk8_1(X50),bad)
| ~ program_halts2_halts2_outputs(X50,esk7_1(X50),good)
| ~ program(X50)
| ~ halts2(esk9_0,X54)
| ~ program_halts2(X54,X54) )
& ( ~ program_not_halts2_halts2_outputs(X50,esk8_1(X50),bad)
| ~ program_halts2_halts2_outputs(X50,esk7_1(X50),good)
| ~ program(X50)
| program(esk9_0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_32])])])])])])]) ).
cnf(c_0_42,plain,
( ~ program_not_halts2_halts3_outputs(X1,esk5_1(X1),esk5_1(X1),bad)
| ~ program_halts2_halts3_outputs(X1,esk4_1(X1),esk4_1(X1),good)
| ~ program(X1)
| program(esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_43,plain,
( ~ epred5_0
| ~ epred6_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_34,c_0_33]),c_0_24]) ).
cnf(c_0_44,negated_conjecture,
epred5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_38])]) ).
fof(c_0_45,plain,
( ~ epred4_0
<=> ! [X1] : program_halts2_halts2_outputs(esk6_0,X1,good) ),
introduced(definition) ).
cnf(c_0_46,plain,
( ~ program_not_halts2_halts3_outputs(X2,esk5_1(X2),esk5_1(X2),bad)
| ~ program_halts2_halts3_outputs(X2,esk4_1(X2),esk4_1(X2),good)
| ~ program(X2)
| program_halts2_halts2_outputs(esk6_0,X1,good) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_47,plain,
( ~ program_not_halts2(X1,X1)
| ~ program_not_halts2(esk9_0,X1)
| epred3_0 ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,plain,
( program_not_halts2_halts2_outputs(X2,X1,X3)
| program_not_halts2(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_49,plain,
( ~ program_not_halts2_halts2_outputs(X1,esk8_1(X1),bad)
| ~ program_halts2_halts2_outputs(X1,esk7_1(X1),good)
| ~ program(X1)
| program(esk9_0) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_50,plain,
( program_not_halts2_halts2_outputs(esk6_0,X1,bad)
| epred6_0 ),
inference(split_equiv,[status(thm)],[c_0_33]) ).
cnf(c_0_51,negated_conjecture,
program(esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_36]),c_0_37]),c_0_38])]) ).
cnf(c_0_52,plain,
~ epred6_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]) ).
cnf(c_0_53,plain,
( ~ epred4_0
| ~ epred5_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_46,c_0_45]),c_0_24]) ).
cnf(c_0_54,plain,
( program_not_halts2_halts2_outputs(X1,esk9_0,X2)
| epred3_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_48]) ).
fof(c_0_55,plain,
( ~ epred2_0
<=> ! [X1] :
( ~ halts2(esk9_0,X1)
| ~ program_halts2(X1,X1) ) ),
introduced(definition) ).
cnf(c_0_56,plain,
( ~ program_halts2_halts2_outputs(esk6_0,esk7_1(esk6_0),good)
| program(esk9_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51])]),c_0_52]) ).
cnf(c_0_57,plain,
( program_halts2_halts2_outputs(esk6_0,X1,good)
| epred4_0 ),
inference(split_equiv,[status(thm)],[c_0_45]) ).
cnf(c_0_58,plain,
~ epred4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_44])]) ).
fof(c_0_59,plain,
! [X15,X16] :
( ( program_halts2(X15,X16)
| ~ halts2(X15,X16)
| ~ program(X15) )
& ( ~ program_halts2(X15,X16)
| halts2(X15,X16) )
& ( ~ program_halts2(X15,X16)
| program(X15) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[program_halts2_def])])])]) ).
fof(c_0_60,plain,
( ~ epred1_0
<=> ! [X2] :
( ~ program_not_halts2_halts2_outputs(X2,esk8_1(X2),bad)
| ~ program_halts2_halts2_outputs(X2,esk7_1(X2),good)
| ~ program(X2) ) ),
introduced(definition) ).
cnf(c_0_61,plain,
( ~ program_not_halts2(esk9_0,esk9_0)
| halts2(X1,esk9_0)
| epred3_0 ),
inference(spm,[status(thm)],[c_0_30,c_0_54]) ).
cnf(c_0_62,plain,
( ~ program_halts2(X1,X1)
| ~ halts2(esk9_0,X1)
| epred2_0 ),
inference(split_equiv,[status(thm)],[c_0_55]) ).
cnf(c_0_63,plain,
( ~ program(X1)
| program_not_halts2(X1,X2)
| halts2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_64,plain,
program(esk9_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]) ).
cnf(c_0_65,plain,
( ~ halts2(X1,X2)
| ~ program(X1)
| program_halts2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_66,plain,
( ~ program(X1)
| ~ program_halts2_halts2_outputs(X1,esk7_1(X1),good)
| ~ program_not_halts2_halts2_outputs(X1,esk8_1(X1),bad)
| epred1_0 ),
inference(split_equiv,[status(thm)],[c_0_60]) ).
cnf(c_0_67,plain,
( ~ program_not_halts2(esk9_0,esk9_0)
| epred3_0 ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_61])]) ).
cnf(c_0_68,plain,
( ~ program_halts2(X1,X1)
| program_not_halts2(esk9_0,X1)
| epred2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64])]) ).
cnf(c_0_69,plain,
( ~ program(X1)
| program_halts2(X1,X2)
| program_not_halts2(X1,X2) ),
inference(spm,[status(thm)],[c_0_65,c_0_63]) ).
cnf(c_0_70,plain,
( ~ program_not_halts2_halts2_outputs(X2,esk8_1(X2),bad)
| ~ program_halts2_halts2_outputs(X2,esk7_1(X2),good)
| ~ program(X2)
| program_not_halts2_halts2_outputs(esk9_0,X1,good) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_71,plain,
( ~ program_halts2_halts2_outputs(esk6_0,esk7_1(esk6_0),good)
| epred1_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_50]),c_0_51])]),c_0_52]) ).
cnf(c_0_72,plain,
( ~ program_not_halts2_halts2_outputs(X2,esk8_1(X2),bad)
| ~ program_halts2_halts2_outputs(X2,esk7_1(X2),good)
| ~ program(X2)
| ~ halts2(esk9_0,X1)
| ~ program_halts2(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_73,plain,
( ~ program_halts2(esk9_0,esk9_0)
| epred2_0
| epred3_0 ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_74,plain,
( program_halts2(esk9_0,esk9_0)
| epred3_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_69]),c_0_64])]) ).
cnf(c_0_75,plain,
( ~ epred1_0
| ~ epred3_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_70,c_0_22]),c_0_60]) ).
cnf(c_0_76,plain,
epred1_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_57]),c_0_58]) ).
cnf(c_0_77,plain,
( ~ epred1_0
| ~ epred2_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_72,c_0_60]),c_0_55]) ).
cnf(c_0_78,plain,
( epred2_0
| epred3_0 ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_79,plain,
~ epred3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_76])]) ).
cnf(c_0_80,plain,
~ epred2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_76])]) ).
cnf(c_0_81,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_78,c_0_79]),c_0_80]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM003+2 : TPTP v9.3.1. Bugfixed v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n013.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 14:13:20 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.46 % Version: 3.5.1
% 0.11/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.46 % Starting sh5l with 300s (1) cores
% 0.11/0.46 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 966084 completed with status 0
% 0.11/0.46 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.11/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.46 % No SInE strategy applied
% 0.11/0.46 % Search class: FGHNF-FFMF11-SFFFFFNN
% 0.11/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.11/0.46 % Starting G-E--_107_C18_F1_PI_AE_Q4_CS_SP_PS_S4S with 136s (1) cores
% 0.11/0.46 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.11/0.46 % Starting G-N--_023_B07_F1_SP_PI_Q7_CS_SP_CO_S5PRR_S0Y with 136s (1) cores
% 0.11/0.46 % G-N--_023_B07_F1_SP_PI_Q7_CS_SP_CO_S5PRR_S0Y with pid 966092 completed with status 0
% 0.11/0.46 % Result found by G-N--_023_B07_F1_SP_PI_Q7_CS_SP_CO_S5PRR_S0Y
% 0.11/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.46 % No SInE strategy applied
% 0.11/0.46 % Search class: FGHNF-FFMF11-SFFFFFNN
% 0.11/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.11/0.46 % Starting G-E--_107_C18_F1_PI_AE_Q4_CS_SP_PS_S4S with 136s (1) cores
% 0.11/0.46 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.11/0.46 % Starting G-N--_023_B07_F1_SP_PI_Q7_CS_SP_CO_S5PRR_S0Y with 136s (1) cores
% 0.11/0.46 % Preprocessing time : 0.001 s
% 0.11/0.46
% 0.11/0.46 % Proof found!
% 0.11/0.46 % SZS status Theorem
% 0.11/0.46 % SZS output start CNFRefutation
% See solution above
% 0.11/0.46 % Parsed axioms : 16
% 0.11/0.46 % Removed by relevancy pruning/SinE : 0
% 0.11/0.46 % Initial clauses : 43
% 0.11/0.46 % Removed in clause preprocessing : 0
% 0.11/0.46 % Initial clauses in saturation : 43
% 0.11/0.46 % Processed clauses : 420
% 0.11/0.46 % ...of these trivial : 1
% 0.11/0.46 % ...subsumed : 136
% 0.11/0.46 % ...remaining for further processing : 282
% 0.11/0.46 % Other redundant clauses eliminated : 0
% 0.11/0.46 % Clauses deleted for lack of memory : 0
% 0.11/0.46 % Backward-subsumed : 29
% 0.11/0.46 % Backward-rewritten : 20
% 0.11/0.46 % Generated clauses : 701
% 0.11/0.46 % ...of the previous two non-redundant : 598
% 0.11/0.46 % ...aggressively subsumed : 0
% 0.11/0.46 % Contextual simplify-reflections : 14
% 0.11/0.46 % Paramodulations : 647
% 0.11/0.46 % Factorizations : 0
% 0.11/0.46 % NegExts : 0
% 0.11/0.46 % Equation resolutions : 0
% 0.11/0.46 % Disequality decompositions : 0
% 0.11/0.46 % Total rewrite steps : 145
% 0.11/0.46 % ...of those cached : 124
% 0.11/0.46 % Propositional unsat checks : 0
% 0.11/0.46 % Propositional check models : 0
% 0.11/0.46 % Propositional check unsatisfiable : 0
% 0.11/0.46 % Propositional clauses : 0
% 0.11/0.46 % Propositional clauses after purity: 0
% 0.11/0.46 % Propositional unsat core size : 0
% 0.11/0.46 % Propositional preprocessing time : 0.000
% 0.11/0.46 % Propositional encoding time : 0.000
% 0.11/0.46 % Propositional solver time : 0.000
% 0.11/0.46 % Success case prop preproc time : 0.000
% 0.11/0.46 % Success case prop encoding time : 0.000
% 0.11/0.46 % Success case prop solver time : 0.000
% 0.11/0.46 % Current number of processed clauses : 200
% 0.11/0.46 % Positive orientable unit clauses : 19
% 0.11/0.46 % Positive unorientable unit clauses: 0
% 0.11/0.46 % Negative unit clauses : 6
% 0.11/0.46 % Non-unit-clauses : 175
% 0.11/0.46 % Current number of unprocessed clauses: 144
% 0.11/0.46 % ...number of literals in the above : 505
% 0.11/0.46 % Current number of archived formulas : 0
% 0.11/0.46 % Current number of archived clauses : 69
% 0.11/0.46 % Clause-clause subsumption calls (NU) : 13171
% 0.11/0.46 % Rec. Clause-clause subsumption calls : 8867
% 0.11/0.46 % Non-unit clause-clause subsumptions : 189
% 0.11/0.46 % Unit Clause-clause subsumption calls : 819
% 0.11/0.46 % Rewrite failures with RHS unbound : 0
% 0.11/0.46 % BW rewrite match attempts : 14
% 0.11/0.46 % BW rewrite match successes : 11
% 0.11/0.46 % Condensation attempts : 420
% 0.11/0.46 % Condensation successes : 7
% 0.11/0.46 % Termbank termtop insertions : 9521
% 0.11/0.46 % Search garbage collected termcells : 621
% 0.11/0.46
% 0.11/0.46 % -------------------------------------------------
% 0.11/0.46 % User time : 0.015 s
% 0.11/0.46 % System time : 0.005 s
% 0.11/0.46 % Total time : 0.020 s
% 0.11/0.46 % Maximum resident set size: 3652 pages
% 0.11/0.46
% 0.11/0.46 % -------------------------------------------------
% 0.11/0.46 % User time : 0.083 s
% 0.11/0.46 % System time : 0.013 s
% 0.11/0.46 % Total time : 0.097 s
% 0.11/0.46 % Maximum resident set size: 4608 pages
% 0.11/0.46 % E exiting
%------------------------------------------------------------------------------