%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COM003_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 12:11:15 PM UTC 2026
% Result : Theorem 0.16s 0.65s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 58 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 349 ( 0 equ)
% Maximal formula atoms : 80 ( 6 avg)
% Number of connectives : 471 ( 180 ~; 207 |; 57 &)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-1 aty)
% Number of variables : 131 ( 0 sgn 119 !; 12 ?; 131 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
output: $tType ).
tff(decl_sort2,type,
algorithm: $tType ).
tff(decl_sort3,type,
program: $tType ).
tff(decl_sort4,type,
input: $tType ).
tff(decl_23,type,
bad: output ).
tff(decl_24,type,
good: output ).
tff(decl_25,type,
decides: ( input * ( program * algorithm ) ) > $o ).
tff(decl_26,type,
halts2: ( input * program ) > $o ).
tff(decl_27,type,
halts3: ( input * ( program * program ) ) > $o ).
tff(decl_28,type,
outputs: ( output * program ) > $o ).
tff(decl_29,type,
algorithm_of: program > algorithm ).
tff(decl_30,type,
as_input: program > input ).
tff(decl_31,type,
esk1_0: algorithm ).
tff(decl_32,type,
esk2_1: algorithm > program ).
tff(decl_33,type,
esk3_1: algorithm > input ).
tff(decl_34,type,
esk4_0: program ).
tff(decl_35,type,
esk5_1: program > program ).
tff(decl_36,type,
esk6_1: program > program ).
tff(decl_37,type,
esk7_0: program ).
tff(decl_38,type,
esk8_1: program > program ).
tff(decl_39,type,
esk9_1: program > program ).
tff(decl_40,type,
esk10_0: program ).
tff(prove_this,conjecture,
~ ? [X7: algorithm] :
! [X8: program,X9: input] : decides(X7,X8,X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(p2,axiom,
! [X4: program,X2: program,X3: input] :
( decides(algorithm_of(X4),X2,X3)
=> ! [X2: program,X3: input] :
( ( ~ halts2(X2,X3)
=> ( outputs(X4,bad)
& halts3(X4,X2,X3) ) )
& ( halts2(X2,X3)
=> ( outputs(X4,good)
& halts3(X4,X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
tff(p1,axiom,
( ? [X1: algorithm] :
! [X2: program,X3: input] : decides(X1,X2,X3)
=> ? [X4: program] :
! [X2: program,X3: input] : decides(algorithm_of(X4),X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
tff(p4,axiom,
( ? [X5: program] :
! [X2: program] :
( ( ~ halts2(X2,as_input(X2))
=> ( outputs(X5,bad)
& halts2(X5,as_input(X2)) ) )
& ( halts2(X2,as_input(X2))
=> ( outputs(X5,good)
& halts2(X5,as_input(X2)) ) ) )
=> ? [X6: program] :
! [X2: program] :
( ( ~ halts2(X2,as_input(X2))
=> ( outputs(X6,bad)
& halts2(X6,as_input(X2)) ) )
& ( halts2(X2,as_input(X2))
=> ~ halts2(X6,as_input(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
tff(p3,axiom,
( ? [X4: program] :
! [X2: program] :
( ( ~ halts2(X2,as_input(X2))
=> ( outputs(X4,bad)
& halts3(X4,X2,as_input(X2)) ) )
& ( halts2(X2,as_input(X2))
=> ( outputs(X4,good)
& halts3(X4,X2,as_input(X2)) ) ) )
=> ? [X5: program] :
! [X2: program] :
( ( ~ halts2(X2,as_input(X2))
=> ( outputs(X5,bad)
& halts2(X5,as_input(X2)) ) )
& ( halts2(X2,as_input(X2))
=> ( outputs(X5,good)
& halts2(X5,as_input(X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
tff(c_0_5,negated_conjecture,
~ ~ ? [X7: algorithm] :
! [X8: program,X9: input] : decides(X7,X8,X9),
inference(assume_negation,[status(cth)],[prove_this]) ).
tff(c_0_6,plain,
! [X4: program,X2: program,X3: input] :
( decides(algorithm_of(X4),X2,X3)
=> ! [X2: program,X3: input] :
( ( ~ halts2(X2,X3)
=> ( outputs(X4,bad)
& halts3(X4,X2,X3) ) )
& ( halts2(X2,X3)
=> ( outputs(X4,good)
& halts3(X4,X2,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[p2]) ).
tff(c_0_7,plain,
! [X13: algorithm,X17: program,X18: input] :
( decides(algorithm_of(esk4_0),X17,X18)
| ~ decides(X13,esk2_1(X13),esk3_1(X13)) ),
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])])])])]) ).
tff(c_0_8,negated_conjecture,
! [X11: program,X12: input] : decides(esk1_0,X11,X12),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
tff(c_0_9,plain,
( ? [X5: program] :
! [X2: program] :
( ( ~ halts2(X2,as_input(X2))
=> ( outputs(X5,bad)
& halts2(X5,as_input(X2)) ) )
& ( halts2(X2,as_input(X2))
=> ( outputs(X5,good)
& halts2(X5,as_input(X2)) ) ) )
=> ? [X6: program] :
! [X2: program] :
( ( ~ halts2(X2,as_input(X2))
=> ( outputs(X6,bad)
& halts2(X6,as_input(X2)) ) )
& ( halts2(X2,as_input(X2))
=> ~ halts2(X6,as_input(X2)) ) ) ),
inference(fof_simplification,[status(thm)],[p4]) ).
tff(c_0_10,plain,
! [X19: program,X20: program,X21: input,X22: program,X23: input] :
( ( ~ decides(algorithm_of(X19),X20,X21)
| halts2(X22,X23)
| outputs(X19,bad) )
& ( ~ decides(algorithm_of(X19),X20,X21)
| halts2(X22,X23)
| halts3(X19,X22,X23) )
& ( ~ decides(algorithm_of(X19),X20,X21)
| ~ halts2(X22,X23)
| outputs(X19,good) )
& ( ~ decides(algorithm_of(X19),X20,X21)
| ~ halts2(X22,X23)
| halts3(X19,X22,X23) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).
tcf(c_0_11,plain,
! [X3: input,X2: program,X1: algorithm] :
( ~ decides(X1,esk2_1(X1),esk3_1(X1))
| decides(algorithm_of(esk4_0),X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
tcf(c_0_12,negated_conjecture,
! [X2: program,X3: input] : decides(esk1_0,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
tff(c_0_13,plain,
( ? [X4: program] :
! [X2: program] :
( ( ~ halts2(X2,as_input(X2))
=> ( outputs(X4,bad)
& halts3(X4,X2,as_input(X2)) ) )
& ( halts2(X2,as_input(X2))
=> ( outputs(X4,good)
& halts3(X4,X2,as_input(X2)) ) ) )
=> ? [X5: program] :
! [X2: program] :
( ( ~ halts2(X2,as_input(X2))
=> ( outputs(X5,bad)
& halts2(X5,as_input(X2)) ) )
& ( halts2(X2,as_input(X2))
=> ( outputs(X5,good)
& halts2(X5,as_input(X2)) ) ) ) ),
inference(fof_simplification,[status(thm)],[p3]) ).
tff(c_0_14,plain,
! [X29: program,X33: program] :
( ( ~ outputs(X29,good)
| ~ halts2(X29,as_input(esk8_1(X29)))
| ~ outputs(X29,bad)
| ~ halts2(X29,as_input(esk9_1(X29)))
| halts2(X33,as_input(X33))
| outputs(esk10_0,bad) )
& ( ~ outputs(X29,good)
| ~ halts2(X29,as_input(esk8_1(X29)))
| ~ outputs(X29,bad)
| ~ halts2(X29,as_input(esk9_1(X29)))
| halts2(X33,as_input(X33))
| halts2(esk10_0,as_input(X33)) )
& ( ~ outputs(X29,good)
| ~ halts2(X29,as_input(esk8_1(X29)))
| ~ outputs(X29,bad)
| ~ halts2(X29,as_input(esk9_1(X29)))
| ~ halts2(esk10_0,as_input(X33))
| ~ halts2(X33,as_input(X33)) )
& ( ~ outputs(X29,good)
| ~ halts2(X29,as_input(esk8_1(X29)))
| ~ halts2(esk9_1(X29),as_input(esk9_1(X29)))
| halts2(X33,as_input(X33))
| outputs(esk10_0,bad) )
& ( ~ outputs(X29,good)
| ~ halts2(X29,as_input(esk8_1(X29)))
| ~ halts2(esk9_1(X29),as_input(esk9_1(X29)))
| halts2(X33,as_input(X33))
| halts2(esk10_0,as_input(X33)) )
& ( ~ outputs(X29,good)
| ~ halts2(X29,as_input(esk8_1(X29)))
| ~ halts2(esk9_1(X29),as_input(esk9_1(X29)))
| ~ halts2(esk10_0,as_input(X33))
| ~ halts2(X33,as_input(X33)) )
& ( halts2(esk8_1(X29),as_input(esk8_1(X29)))
| ~ outputs(X29,bad)
| ~ halts2(X29,as_input(esk9_1(X29)))
| halts2(X33,as_input(X33))
| outputs(esk10_0,bad) )
& ( halts2(esk8_1(X29),as_input(esk8_1(X29)))
| ~ outputs(X29,bad)
| ~ halts2(X29,as_input(esk9_1(X29)))
| halts2(X33,as_input(X33))
| halts2(esk10_0,as_input(X33)) )
& ( halts2(esk8_1(X29),as_input(esk8_1(X29)))
| ~ outputs(X29,bad)
| ~ halts2(X29,as_input(esk9_1(X29)))
| ~ halts2(esk10_0,as_input(X33))
| ~ halts2(X33,as_input(X33)) )
& ( halts2(esk8_1(X29),as_input(esk8_1(X29)))
| ~ halts2(esk9_1(X29),as_input(esk9_1(X29)))
| halts2(X33,as_input(X33))
| outputs(esk10_0,bad) )
& ( halts2(esk8_1(X29),as_input(esk8_1(X29)))
| ~ halts2(esk9_1(X29),as_input(esk9_1(X29)))
| halts2(X33,as_input(X33))
| halts2(esk10_0,as_input(X33)) )
& ( halts2(esk8_1(X29),as_input(esk8_1(X29)))
| ~ halts2(esk9_1(X29),as_input(esk9_1(X29)))
| ~ halts2(esk10_0,as_input(X33))
| ~ halts2(X33,as_input(X33)) ) ),
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_9])])])])])])]) ).
tcf(c_0_15,plain,
! [X2: program,X3: input,X4: program,X5: program,X9: input] :
( ~ decides(algorithm_of(X2),X5,X9)
| halts2(X4,X3)
| outputs(X2,bad) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tcf(c_0_16,negated_conjecture,
! [X2: program,X3: input] : decides(algorithm_of(esk4_0),X2,X3),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
tcf(c_0_17,plain,
! [X2: program,X3: input,X4: program,X5: program,X9: input] :
( ~ decides(algorithm_of(X2),X5,X9)
| ~ halts2(X4,X3)
| outputs(X2,good) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tff(c_0_18,plain,
! [X24: program,X28: program] :
( ( ~ outputs(X24,good)
| ~ halts3(X24,esk5_1(X24),as_input(esk5_1(X24)))
| ~ outputs(X24,bad)
| ~ halts3(X24,esk6_1(X24),as_input(esk6_1(X24)))
| halts2(X28,as_input(X28))
| outputs(esk7_0,bad) )
& ( ~ outputs(X24,good)
| ~ halts3(X24,esk5_1(X24),as_input(esk5_1(X24)))
| ~ outputs(X24,bad)
| ~ halts3(X24,esk6_1(X24),as_input(esk6_1(X24)))
| halts2(X28,as_input(X28))
| halts2(esk7_0,as_input(X28)) )
& ( ~ outputs(X24,good)
| ~ halts3(X24,esk5_1(X24),as_input(esk5_1(X24)))
| ~ outputs(X24,bad)
| ~ halts3(X24,esk6_1(X24),as_input(esk6_1(X24)))
| ~ halts2(X28,as_input(X28))
| outputs(esk7_0,good) )
& ( ~ outputs(X24,good)
| ~ halts3(X24,esk5_1(X24),as_input(esk5_1(X24)))
| ~ outputs(X24,bad)
| ~ halts3(X24,esk6_1(X24),as_input(esk6_1(X24)))
| ~ halts2(X28,as_input(X28))
| halts2(esk7_0,as_input(X28)) )
& ( ~ outputs(X24,good)
| ~ halts3(X24,esk5_1(X24),as_input(esk5_1(X24)))
| ~ halts2(esk6_1(X24),as_input(esk6_1(X24)))
| halts2(X28,as_input(X28))
| outputs(esk7_0,bad) )
& ( ~ outputs(X24,good)
| ~ halts3(X24,esk5_1(X24),as_input(esk5_1(X24)))
| ~ halts2(esk6_1(X24),as_input(esk6_1(X24)))
| halts2(X28,as_input(X28))
| halts2(esk7_0,as_input(X28)) )
& ( ~ outputs(X24,good)
| ~ halts3(X24,esk5_1(X24),as_input(esk5_1(X24)))
| ~ halts2(esk6_1(X24),as_input(esk6_1(X24)))
| ~ halts2(X28,as_input(X28))
| outputs(esk7_0,good) )
& ( ~ outputs(X24,good)
| ~ halts3(X24,esk5_1(X24),as_input(esk5_1(X24)))
| ~ halts2(esk6_1(X24),as_input(esk6_1(X24)))
| ~ halts2(X28,as_input(X28))
| halts2(esk7_0,as_input(X28)) )
& ( halts2(esk5_1(X24),as_input(esk5_1(X24)))
| ~ outputs(X24,bad)
| ~ halts3(X24,esk6_1(X24),as_input(esk6_1(X24)))
| halts2(X28,as_input(X28))
| outputs(esk7_0,bad) )
& ( halts2(esk5_1(X24),as_input(esk5_1(X24)))
| ~ outputs(X24,bad)
| ~ halts3(X24,esk6_1(X24),as_input(esk6_1(X24)))
| halts2(X28,as_input(X28))
| halts2(esk7_0,as_input(X28)) )
& ( halts2(esk5_1(X24),as_input(esk5_1(X24)))
| ~ outputs(X24,bad)
| ~ halts3(X24,esk6_1(X24),as_input(esk6_1(X24)))
| ~ halts2(X28,as_input(X28))
| outputs(esk7_0,good) )
& ( halts2(esk5_1(X24),as_input(esk5_1(X24)))
| ~ outputs(X24,bad)
| ~ halts3(X24,esk6_1(X24),as_input(esk6_1(X24)))
| ~ halts2(X28,as_input(X28))
| halts2(esk7_0,as_input(X28)) )
& ( halts2(esk5_1(X24),as_input(esk5_1(X24)))
| ~ halts2(esk6_1(X24),as_input(esk6_1(X24)))
| halts2(X28,as_input(X28))
| outputs(esk7_0,bad) )
& ( halts2(esk5_1(X24),as_input(esk5_1(X24)))
| ~ halts2(esk6_1(X24),as_input(esk6_1(X24)))
| halts2(X28,as_input(X28))
| halts2(esk7_0,as_input(X28)) )
& ( halts2(esk5_1(X24),as_input(esk5_1(X24)))
| ~ halts2(esk6_1(X24),as_input(esk6_1(X24)))
| ~ halts2(X28,as_input(X28))
| outputs(esk7_0,good) )
& ( halts2(esk5_1(X24),as_input(esk5_1(X24)))
| ~ halts2(esk6_1(X24),as_input(esk6_1(X24)))
| ~ halts2(X28,as_input(X28))
| halts2(esk7_0,as_input(X28)) ) ),
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_13])])])])])])]) ).
tcf(c_0_19,plain,
! [X2: program,X3: input,X4: program,X5: program,X9: input] :
( ~ decides(algorithm_of(X2),X5,X9)
| ~ halts2(X4,X3)
| halts3(X2,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tcf(c_0_20,plain,
! [X2: program,X3: input,X4: program,X5: program,X9: input] :
( ~ decides(algorithm_of(X2),X5,X9)
| halts2(X4,X3)
| halts3(X2,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tcf(c_0_21,plain,
! [X2: program,X4: program] :
( ~ outputs(X4,good)
| ~ halts2(X4,as_input(esk8_1(X4)))
| ~ halts2(esk9_1(X4),as_input(esk9_1(X4)))
| ~ halts2(esk10_0,as_input(X2))
| ~ halts2(X2,as_input(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
tcf(c_0_22,negated_conjecture,
! [X2: program,X3: input] :
( halts2(X2,X3)
| outputs(esk4_0,bad) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
tcf(c_0_23,negated_conjecture,
! [X2: program,X3: input] :
( ~ halts2(X2,X3)
| outputs(esk4_0,good) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
tcf(c_0_24,plain,
! [X2: program,X4: program] :
( ~ outputs(X4,bad)
| ~ halts3(X4,esk6_1(X4),as_input(esk6_1(X4)))
| ~ halts2(X2,as_input(X2))
| halts2(esk5_1(X4),as_input(esk5_1(X4)))
| halts2(esk7_0,as_input(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
tcf(c_0_25,plain,
! [X2: program,X4: program] :
( ~ outputs(X4,bad)
| ~ halts3(X4,esk6_1(X4),as_input(esk6_1(X4)))
| halts2(esk5_1(X4),as_input(esk5_1(X4)))
| halts2(X2,as_input(X2))
| halts2(esk7_0,as_input(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
tcf(c_0_26,plain,
! [X2: program,X3: input,X4: program,X5: program,X9: input] :
( ~ decides(algorithm_of(X2),X5,X9)
| halts3(X2,X4,X3) ),
inference(csr,[status(thm)],[c_0_19,c_0_20]) ).
tcf(c_0_27,negated_conjecture,
! [X2: program] :
( ~ outputs(X2,good)
| outputs(esk4_0,bad) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_22]),c_0_22]),c_0_22]) ).
tcf(c_0_28,negated_conjecture,
( outputs(esk4_0,good)
| outputs(esk4_0,bad) ),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
tcf(c_0_29,plain,
! [X4: program,X2: program] :
( ~ halts3(X2,esk6_1(X2),as_input(esk6_1(X2)))
| ~ outputs(X2,bad)
| halts2(esk7_0,as_input(X4))
| halts2(esk5_1(X2),as_input(esk5_1(X2))) ),
inference(csr,[status(thm)],[c_0_24,c_0_25]) ).
tcf(c_0_30,negated_conjecture,
! [X2: program,X3: input] : halts3(esk4_0,X2,X3),
inference(spm,[status(thm)],[c_0_26,c_0_16]) ).
tcf(c_0_31,negated_conjecture,
outputs(esk4_0,bad),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
tcf(c_0_32,negated_conjecture,
! [X2: program] :
( halts2(esk7_0,as_input(X2))
| halts2(esk5_1(esk4_0),as_input(esk5_1(esk4_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
tcf(c_0_33,plain,
! [X2: program,X4: program] :
( ~ outputs(X4,good)
| ~ halts3(X4,esk5_1(X4),as_input(esk5_1(X4)))
| ~ halts2(esk6_1(X4),as_input(esk6_1(X4)))
| ~ halts2(X2,as_input(X2))
| halts2(esk7_0,as_input(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
tcf(c_0_34,plain,
! [X2: program,X4: program] :
( ~ outputs(X4,good)
| ~ halts3(X4,esk5_1(X4),as_input(esk5_1(X4)))
| ~ halts2(esk6_1(X4),as_input(esk6_1(X4)))
| halts2(X2,as_input(X2))
| halts2(esk7_0,as_input(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
tcf(c_0_35,plain,
! [X2: program,X4: program] :
( ~ outputs(X4,good)
| ~ halts3(X4,esk5_1(X4),as_input(esk5_1(X4)))
| ~ outputs(X4,bad)
| ~ halts3(X4,esk6_1(X4),as_input(esk6_1(X4)))
| halts2(X2,as_input(X2))
| halts2(esk7_0,as_input(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
tcf(c_0_36,negated_conjecture,
outputs(esk4_0,good),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_32]),c_0_23]) ).
tcf(c_0_37,plain,
! [X2: program,X4: program] :
( ~ outputs(X4,good)
| ~ halts3(X4,esk5_1(X4),as_input(esk5_1(X4)))
| ~ outputs(X4,bad)
| ~ halts3(X4,esk6_1(X4),as_input(esk6_1(X4)))
| halts2(X2,as_input(X2))
| outputs(esk7_0,bad) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
tcf(c_0_38,plain,
! [X2: program,X4: program] :
( ~ halts2(esk6_1(X4),as_input(esk6_1(X4)))
| ~ halts3(X4,esk5_1(X4),as_input(esk5_1(X4)))
| ~ outputs(X4,good)
| halts2(esk7_0,as_input(X2)) ),
inference(csr,[status(thm)],[c_0_33,c_0_34]) ).
tcf(c_0_39,plain,
! [X2: program,X4: program] :
( ~ outputs(X4,good)
| ~ halts3(X4,esk5_1(X4),as_input(esk5_1(X4)))
| ~ outputs(X4,bad)
| ~ halts3(X4,esk6_1(X4),as_input(esk6_1(X4)))
| ~ halts2(X2,as_input(X2))
| outputs(esk7_0,good) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
tcf(c_0_40,negated_conjecture,
! [X2: program] :
( halts2(X2,as_input(X2))
| halts2(esk7_0,as_input(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_30]),c_0_31]),c_0_36]),c_0_30])]) ).
tcf(c_0_41,plain,
! [X2: program,X4: program] :
( ~ outputs(X4,good)
| ~ halts3(X4,esk5_1(X4),as_input(esk5_1(X4)))
| ~ outputs(X4,bad)
| ~ halts3(X4,esk6_1(X4),as_input(esk6_1(X4)))
| ~ halts2(X2,as_input(X2))
| halts2(esk7_0,as_input(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
tcf(c_0_42,negated_conjecture,
! [X2: program] :
( halts2(X2,as_input(X2))
| outputs(esk7_0,bad) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_30]),c_0_31]),c_0_36]),c_0_30])]) ).
tcf(c_0_43,negated_conjecture,
! [X2: program] :
( ~ halts2(esk6_1(esk4_0),as_input(esk6_1(esk4_0)))
| halts2(esk7_0,as_input(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_30]),c_0_36])]) ).
tcf(c_0_44,negated_conjecture,
! [X2: program] :
( ~ halts2(X2,as_input(X2))
| outputs(esk7_0,good) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_30]),c_0_31]),c_0_36]),c_0_30])]) ).
tcf(c_0_45,negated_conjecture,
halts2(esk7_0,as_input(esk7_0)),
inference(ef,[status(thm)],[c_0_40]) ).
tcf(c_0_46,plain,
! [X2: program,X4: program] :
( ~ halts3(X4,esk6_1(X4),as_input(esk6_1(X4)))
| ~ halts3(X4,esk5_1(X4),as_input(esk5_1(X4)))
| ~ outputs(X4,good)
| ~ outputs(X4,bad)
| halts2(esk7_0,as_input(X2)) ),
inference(csr,[status(thm)],[c_0_41,c_0_40]) ).
tcf(c_0_47,negated_conjecture,
! [X2: program,X4: program] :
( ~ halts2(esk10_0,as_input(X4))
| ~ halts2(X2,as_input(esk8_1(X2)))
| ~ outputs(X2,good)
| outputs(esk7_0,bad) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_42]),c_0_42]) ).
tcf(c_0_48,negated_conjecture,
! [X2: program] :
( halts2(esk7_0,as_input(X2))
| outputs(esk7_0,bad) ),
inference(spm,[status(thm)],[c_0_43,c_0_42]) ).
tcf(c_0_49,negated_conjecture,
outputs(esk7_0,good),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
tcf(c_0_50,plain,
! [X2: program,X4: program] :
( ~ outputs(X4,good)
| ~ halts2(X4,as_input(esk8_1(X4)))
| ~ outputs(X4,bad)
| ~ halts2(X4,as_input(esk9_1(X4)))
| halts2(X2,as_input(X2))
| halts2(esk10_0,as_input(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
tcf(c_0_51,negated_conjecture,
! [X2: program] : halts2(esk7_0,as_input(X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_30]),c_0_31]),c_0_36]),c_0_30])]) ).
tcf(c_0_52,plain,
! [X2: program,X4: program] :
( ~ outputs(X4,good)
| ~ halts2(X4,as_input(esk8_1(X4)))
| ~ outputs(X4,bad)
| ~ halts2(X4,as_input(esk9_1(X4)))
| ~ halts2(esk10_0,as_input(X2))
| ~ halts2(X2,as_input(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
tcf(c_0_53,negated_conjecture,
! [X2: program] :
( ~ halts2(esk10_0,as_input(X2))
| outputs(esk7_0,bad) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]) ).
tcf(c_0_54,negated_conjecture,
! [X2: program] :
( halts2(X2,as_input(X2))
| halts2(esk10_0,as_input(X2)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_49]),c_0_51])]),c_0_42]) ).
tcf(c_0_55,negated_conjecture,
! [X2: program] :
( ~ halts2(X2,as_input(X2))
| ~ halts2(esk10_0,as_input(X2)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_51]),c_0_49]),c_0_51])]),c_0_53]) ).
tcf(c_0_56,negated_conjecture,
halts2(esk10_0,as_input(esk10_0)),
inference(ef,[status(thm)],[c_0_54]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_56])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM003_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.58 % Computer : n016.cluster.edu
% 0.12/0.58 % Model : x86_64 x86_64
% 0.12/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.58 % Memory : 8046.5625MB
% 0.12/0.58 % OS : Linux 6.8.0-71-generic
% 0.12/0.58 % CPULimit : 300
% 0.12/0.58 % WCLimit : 300
% 0.12/0.58 % DateTime : Mon Sep 21 14:18:38 UTC 2026
% 0.12/0.58 % CPUTime :
% 0.12/0.58 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.62 Running first-order theorem proving
% 0.12/0.62 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
% 0.16/0.65 % Version: 3.5.1
% 0.16/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.65 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.65 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.65 % Starting sh5l with 300s (1) cores
% 0.16/0.65 % new_bool_1 with pid 2637539 completed with status 0
% 0.16/0.65 % Result found by new_bool_1
% 0.16/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.65 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.65 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.65 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/0.65 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.65 % Search class: FGHNF-FFMF11-SFFFFFNN
% 0.16/0.65 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.65 % Starting SubtermCWHack with 28s (1) cores
% 0.16/0.65 % SubtermCWHack with pid 2637542 completed with status 0
% 0.16/0.65 % Result found by SubtermCWHack
% 0.16/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.65 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.65 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.65 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/0.65 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.65 % Search class: FGHNF-FFMF11-SFFFFFNN
% 0.16/0.65 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.65 % Starting SubtermCWHack with 28s (1) cores
% 0.16/0.65 % Preprocessing time : 0.002 s
% 0.16/0.65
% 0.16/0.65 % Proof found!
% 0.16/0.65 % SZS status Theorem
% 0.16/0.65 % SZS output start CNFRefutation
% See solution above
% 0.16/0.65 % Parsed axioms : 17
% 0.16/0.65 % Removed by relevancy pruning/SinE : 12
% 0.16/0.65 % Initial clauses : 34
% 0.16/0.65 % Removed in clause preprocessing : 0
% 0.16/0.65 % Initial clauses in saturation : 34
% 0.16/0.65 % Processed clauses : 93
% 0.16/0.65 % ...of these trivial : 2
% 0.16/0.65 % ...subsumed : 19
% 0.16/0.65 % ...remaining for further processing : 72
% 0.16/0.65 % Other redundant clauses eliminated : 0
% 0.16/0.65 % Clauses deleted for lack of memory : 0
% 0.16/0.65 % Backward-subsumed : 41
% 0.16/0.65 % Backward-rewritten : 15
% 0.16/0.65 % Generated clauses : 120
% 0.16/0.65 % ...of the previous two non-redundant : 113
% 0.16/0.65 % ...aggressively subsumed : 0
% 0.16/0.65 % Contextual simplify-reflections : 16
% 0.16/0.65 % Paramodulations : 110
% 0.16/0.65 % Factorizations : 10
% 0.16/0.65 % NegExts : 0
% 0.16/0.65 % Equation resolutions : 0
% 0.16/0.65 % Disequality decompositions : 0
% 0.16/0.65 % Total rewrite steps : 43
% 0.16/0.65 % ...of those cached : 27
% 0.16/0.65 % Propositional unsat checks : 0
% 0.16/0.65 % Propositional check models : 0
% 0.16/0.65 % Propositional check unsatisfiable : 0
% 0.16/0.65 % Propositional clauses : 0
% 0.16/0.65 % Propositional clauses after purity: 0
% 0.16/0.65 % Propositional unsat core size : 0
% 0.16/0.65 % Propositional preprocessing time : 0.000
% 0.16/0.65 % Propositional encoding time : 0.000
% 0.16/0.65 % Propositional solver time : 0.000
% 0.16/0.65 % Success case prop preproc time : 0.000
% 0.16/0.65 % Success case prop encoding time : 0.000
% 0.16/0.65 % Success case prop solver time : 0.000
% 0.16/0.65 % Current number of processed clauses : 16
% 0.16/0.65 % Positive orientable unit clauses : 8
% 0.16/0.65 % Positive unorientable unit clauses: 0
% 0.16/0.65 % Negative unit clauses : 0
% 0.16/0.65 % Non-unit-clauses : 8
% 0.16/0.65 % Current number of unprocessed clauses: 27
% 0.16/0.65 % ...number of literals in the above : 132
% 0.16/0.65 % Current number of archived formulas : 0
% 0.16/0.65 % Current number of archived clauses : 56
% 0.16/0.65 % Clause-clause subsumption calls (NU) : 627
% 0.16/0.65 % Rec. Clause-clause subsumption calls : 246
% 0.16/0.65 % Non-unit clause-clause subsumptions : 68
% 0.16/0.65 % Unit Clause-clause subsumption calls : 54
% 0.16/0.65 % Rewrite failures with RHS unbound : 0
% 0.16/0.65 % BW rewrite match attempts : 12
% 0.16/0.65 % BW rewrite match successes : 12
% 0.16/0.65 % Condensation attempts : 0
% 0.16/0.65 % Condensation successes : 0
% 0.16/0.65 % Termbank termtop insertions : 5583
% 0.16/0.65 % Search garbage collected termcells : 375
% 0.16/0.65
% 0.16/0.65 % -------------------------------------------------
% 0.16/0.65 % User time : 0.012 s
% 0.16/0.65 % System time : 0.005 s
% 0.16/0.65 % Total time : 0.016 s
% 0.16/0.65 % Maximum resident set size: 3648 pages
% 0.16/0.65
% 0.16/0.65 % -------------------------------------------------
% 0.16/0.65 % User time : 0.014 s
% 0.16/0.65 % System time : 0.009 s
% 0.16/0.65 % Total time : 0.023 s
% 0.16/0.65 % Maximum resident set size: 4864 pages
% 0.16/0.65 % E exiting
%------------------------------------------------------------------------------