%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : PRO009+2 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n014.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 05:01:53 PM UTC 2026
% Result : Theorem 1.27s 1.73s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 10 unt; 0 def)
% Number of atoms : 123 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 148 ( 59 ~; 56 |; 28 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 53 ( 0 sgn 24 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X100] :
( occurrence_of(X100,tptp0)
=> ? [X101,X102] :
( occurrence_of(X101,tptp3)
& root_occ(X101,X100)
& ( occurrence_of(X102,tptp2)
| occurrence_of(X102,tptp1) )
& min_precedes(X101,X102,tptp0)
& leaf_occ(X102,X100) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(sos_32,axiom,
! [X96] :
( occurrence_of(X96,tptp0)
=> ? [X97,X98,X99] :
( occurrence_of(X97,tptp3)
& root_occ(X97,X96)
& occurrence_of(X98,tptp4)
& next_subocc(X97,X98,tptp0)
& ( occurrence_of(X99,tptp2)
| occurrence_of(X99,tptp1) )
& next_subocc(X98,X99,tptp0)
& leaf_occ(X99,X96) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_32) ).
fof(sos_04,axiom,
! [X16,X17,X18] :
( next_subocc(X16,X17,X18)
<=> ( min_precedes(X16,X17,X18)
& ~ ? [X19] :
( min_precedes(X16,X19,X18)
& min_precedes(X19,X17,X18) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_04) ).
fof(sos,axiom,
! [X1,X2,X3,X4] :
( ( min_precedes(X1,X2,X4)
& min_precedes(X2,X3,X4) )
=> min_precedes(X1,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos) ).
fof(c_0_4,negated_conjecture,
~ ! [X100] :
( occurrence_of(X100,tptp0)
=> ? [X101,X102] :
( occurrence_of(X101,tptp3)
& root_occ(X101,X100)
& ( occurrence_of(X102,tptp2)
| occurrence_of(X102,tptp1) )
& min_precedes(X101,X102,tptp0)
& leaf_occ(X102,X100) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_5,plain,
! [X317] :
( ( occurrence_of(esk15_1(X317),tptp3)
| ~ occurrence_of(X317,tptp0) )
& ( root_occ(esk15_1(X317),X317)
| ~ occurrence_of(X317,tptp0) )
& ( occurrence_of(esk16_1(X317),tptp4)
| ~ occurrence_of(X317,tptp0) )
& ( next_subocc(esk15_1(X317),esk16_1(X317),tptp0)
| ~ occurrence_of(X317,tptp0) )
& ( occurrence_of(esk17_1(X317),tptp2)
| occurrence_of(esk17_1(X317),tptp1)
| ~ occurrence_of(X317,tptp0) )
& ( next_subocc(esk16_1(X317),esk17_1(X317),tptp0)
| ~ occurrence_of(X317,tptp0) )
& ( leaf_occ(esk17_1(X317),X317)
| ~ occurrence_of(X317,tptp0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_32])])])]) ).
fof(c_0_6,negated_conjecture,
! [X322,X323] :
( occurrence_of(esk18_0,tptp0)
& ( ~ occurrence_of(X323,tptp2)
| ~ occurrence_of(X322,tptp3)
| ~ root_occ(X322,esk18_0)
| ~ min_precedes(X322,X323,tptp0)
| ~ leaf_occ(X323,esk18_0) )
& ( ~ occurrence_of(X323,tptp1)
| ~ occurrence_of(X322,tptp3)
| ~ root_occ(X322,esk18_0)
| ~ min_precedes(X322,X323,tptp0)
| ~ leaf_occ(X323,esk18_0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])]) ).
cnf(c_0_7,plain,
( leaf_occ(esk17_1(X1),X1)
| ~ occurrence_of(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
occurrence_of(esk18_0,tptp0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X220,X221,X222,X223,X224,X225,X226] :
( ( min_precedes(X220,X221,X222)
| ~ next_subocc(X220,X221,X222) )
& ( ~ min_precedes(X220,X223,X222)
| ~ min_precedes(X223,X221,X222)
| ~ next_subocc(X220,X221,X222) )
& ( min_precedes(X224,esk1_3(X224,X225,X226),X226)
| ~ min_precedes(X224,X225,X226)
| next_subocc(X224,X225,X226) )
& ( min_precedes(esk1_3(X224,X225,X226),X225,X226)
| ~ min_precedes(X224,X225,X226)
| next_subocc(X224,X225,X226) ) ),
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)],[sos_04])])])])])]) ).
cnf(c_0_10,plain,
( next_subocc(esk16_1(X1),esk17_1(X1),tptp0)
| ~ occurrence_of(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,negated_conjecture,
( ~ occurrence_of(X1,tptp1)
| ~ occurrence_of(X2,tptp3)
| ~ root_occ(X2,esk18_0)
| ~ min_precedes(X2,X1,tptp0)
| ~ leaf_occ(X1,esk18_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,negated_conjecture,
leaf_occ(esk17_1(esk18_0),esk18_0),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_13,plain,
( occurrence_of(esk17_1(X1),tptp2)
| occurrence_of(esk17_1(X1),tptp1)
| ~ occurrence_of(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,negated_conjecture,
( ~ occurrence_of(X1,tptp2)
| ~ occurrence_of(X2,tptp3)
| ~ root_occ(X2,esk18_0)
| ~ min_precedes(X2,X1,tptp0)
| ~ leaf_occ(X1,esk18_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_15,plain,
! [X205,X206,X207,X208] :
( ~ min_precedes(X205,X206,X208)
| ~ min_precedes(X206,X207,X208)
| min_precedes(X205,X207,X208) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos])]) ).
cnf(c_0_16,plain,
( min_precedes(X1,X2,X3)
| ~ next_subocc(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,negated_conjecture,
next_subocc(esk16_1(esk18_0),esk17_1(esk18_0),tptp0),
inference(spm,[status(thm)],[c_0_10,c_0_8]) ).
cnf(c_0_18,plain,
( next_subocc(esk15_1(X1),esk16_1(X1),tptp0)
| ~ occurrence_of(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_19,negated_conjecture,
( ~ root_occ(X1,esk18_0)
| ~ occurrence_of(esk17_1(esk18_0),tptp1)
| ~ occurrence_of(X1,tptp3)
| ~ min_precedes(X1,esk17_1(esk18_0),tptp0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_20,negated_conjecture,
( occurrence_of(esk17_1(esk18_0),tptp1)
| occurrence_of(esk17_1(esk18_0),tptp2) ),
inference(spm,[status(thm)],[c_0_13,c_0_8]) ).
cnf(c_0_21,negated_conjecture,
( ~ root_occ(X1,esk18_0)
| ~ occurrence_of(esk17_1(esk18_0),tptp2)
| ~ occurrence_of(X1,tptp3)
| ~ min_precedes(X1,esk17_1(esk18_0),tptp0) ),
inference(spm,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_22,plain,
( root_occ(esk15_1(X1),X1)
| ~ occurrence_of(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_23,plain,
( occurrence_of(esk15_1(X1),tptp3)
| ~ occurrence_of(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_24,plain,
( min_precedes(X1,X4,X3)
| ~ min_precedes(X1,X2,X3)
| ~ min_precedes(X2,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,negated_conjecture,
min_precedes(esk16_1(esk18_0),esk17_1(esk18_0),tptp0),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_26,negated_conjecture,
next_subocc(esk15_1(esk18_0),esk16_1(esk18_0),tptp0),
inference(spm,[status(thm)],[c_0_18,c_0_8]) ).
cnf(c_0_27,negated_conjecture,
( ~ root_occ(X1,esk18_0)
| ~ occurrence_of(X1,tptp3)
| ~ min_precedes(X1,esk17_1(esk18_0),tptp0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_28,negated_conjecture,
root_occ(esk15_1(esk18_0),esk18_0),
inference(spm,[status(thm)],[c_0_22,c_0_8]) ).
cnf(c_0_29,negated_conjecture,
occurrence_of(esk15_1(esk18_0),tptp3),
inference(spm,[status(thm)],[c_0_23,c_0_8]) ).
cnf(c_0_30,negated_conjecture,
( min_precedes(X1,esk17_1(esk18_0),tptp0)
| ~ min_precedes(X1,esk16_1(esk18_0),tptp0) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,negated_conjecture,
min_precedes(esk15_1(esk18_0),esk16_1(esk18_0),tptp0),
inference(spm,[status(thm)],[c_0_16,c_0_26]) ).
cnf(c_0_32,negated_conjecture,
~ min_precedes(esk15_1(esk18_0),esk17_1(esk18_0),tptp0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : PRO009+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n014.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 01:31:06 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.27/1.73 % Version : CSE_E---1.7
% 1.27/1.73 % Problem : theBenchmark.p
% 1.27/1.73 % SZS status Theorem for theBenchmark.p
% 1.27/1.73 % SZS output start CNFRefutation
% See solution above
% 1.27/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------