%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : PRO014+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 : n022.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 05:01:55 PM UTC 2026
% Result : Theorem 1.32s 1.73s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 44 ( 13 unt; 0 def)
% Number of atoms : 214 ( 0 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 272 ( 102 ~; 115 |; 49 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 74 ( 0 sgn 30 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_32,axiom,
! [X96,X97] :
( ( occurrence_of(X97,tptp0)
& subactivity_occurrence(X96,X97)
& arboreal(X96)
& ~ leaf_occ(X96,X97) )
=> ? [X98,X99,X100] :
( occurrence_of(X98,tptp3)
& next_subocc(X96,X98,tptp0)
& occurrence_of(X99,tptp4)
& next_subocc(X98,X99,tptp0)
& ( occurrence_of(X100,tptp2)
| occurrence_of(X100,tptp1) )
& next_subocc(X99,X100,tptp0)
& leaf(X100,tptp0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_32) ).
fof(goals,conjecture,
! [X101,X102] :
( ( occurrence_of(X102,tptp0)
& subactivity_occurrence(X101,X102)
& arboreal(X101)
& ~ leaf_occ(X101,X102) )
=> ? [X103,X104] :
( occurrence_of(X103,tptp3)
& next_subocc(X101,X103,tptp0)
& ( occurrence_of(X104,tptp2)
| occurrence_of(X104,tptp1) )
& min_precedes(X103,X104,tptp0)
& leaf(X104,tptp0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
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,plain,
! [X96,X97] :
( ( occurrence_of(X97,tptp0)
& subactivity_occurrence(X96,X97)
& arboreal(X96)
& ~ leaf_occ(X96,X97) )
=> ? [X98,X99,X100] :
( occurrence_of(X98,tptp3)
& next_subocc(X96,X98,tptp0)
& occurrence_of(X99,tptp4)
& next_subocc(X98,X99,tptp0)
& ( occurrence_of(X100,tptp2)
| occurrence_of(X100,tptp1) )
& next_subocc(X99,X100,tptp0)
& leaf(X100,tptp0) ) ),
inference(fof_simplification,[status(thm)],[sos_32]) ).
fof(c_0_5,negated_conjecture,
~ ! [X101,X102] :
( ( occurrence_of(X102,tptp0)
& subactivity_occurrence(X101,X102)
& arboreal(X101)
& ~ leaf_occ(X101,X102) )
=> ? [X103,X104] :
( occurrence_of(X103,tptp3)
& next_subocc(X101,X103,tptp0)
& ( occurrence_of(X104,tptp2)
| occurrence_of(X104,tptp1) )
& min_precedes(X103,X104,tptp0)
& leaf(X104,tptp0) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goals])]) ).
fof(c_0_6,plain,
! [X321,X322] :
( ( occurrence_of(esk15_1(X321),tptp3)
| ~ occurrence_of(X322,tptp0)
| ~ subactivity_occurrence(X321,X322)
| ~ arboreal(X321)
| leaf_occ(X321,X322) )
& ( next_subocc(X321,esk15_1(X321),tptp0)
| ~ occurrence_of(X322,tptp0)
| ~ subactivity_occurrence(X321,X322)
| ~ arboreal(X321)
| leaf_occ(X321,X322) )
& ( occurrence_of(esk16_1(X321),tptp4)
| ~ occurrence_of(X322,tptp0)
| ~ subactivity_occurrence(X321,X322)
| ~ arboreal(X321)
| leaf_occ(X321,X322) )
& ( next_subocc(esk15_1(X321),esk16_1(X321),tptp0)
| ~ occurrence_of(X322,tptp0)
| ~ subactivity_occurrence(X321,X322)
| ~ arboreal(X321)
| leaf_occ(X321,X322) )
& ( occurrence_of(esk17_1(X321),tptp2)
| occurrence_of(esk17_1(X321),tptp1)
| ~ occurrence_of(X322,tptp0)
| ~ subactivity_occurrence(X321,X322)
| ~ arboreal(X321)
| leaf_occ(X321,X322) )
& ( next_subocc(esk16_1(X321),esk17_1(X321),tptp0)
| ~ occurrence_of(X322,tptp0)
| ~ subactivity_occurrence(X321,X322)
| ~ arboreal(X321)
| leaf_occ(X321,X322) )
& ( leaf(esk17_1(X321),tptp0)
| ~ occurrence_of(X322,tptp0)
| ~ subactivity_occurrence(X321,X322)
| ~ arboreal(X321)
| leaf_occ(X321,X322) ) ),
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_4])])])])])]) ).
fof(c_0_7,negated_conjecture,
! [X328,X329] :
( occurrence_of(esk19_0,tptp0)
& subactivity_occurrence(esk18_0,esk19_0)
& arboreal(esk18_0)
& ~ leaf_occ(esk18_0,esk19_0)
& ( ~ occurrence_of(X329,tptp2)
| ~ occurrence_of(X328,tptp3)
| ~ next_subocc(esk18_0,X328,tptp0)
| ~ min_precedes(X328,X329,tptp0)
| ~ leaf(X329,tptp0) )
& ( ~ occurrence_of(X329,tptp1)
| ~ occurrence_of(X328,tptp3)
| ~ next_subocc(esk18_0,X328,tptp0)
| ~ min_precedes(X328,X329,tptp0)
| ~ leaf(X329,tptp0) ) ),
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_5])])])])]) ).
cnf(c_0_8,plain,
( next_subocc(esk16_1(X1),esk17_1(X1),tptp0)
| leaf_occ(X1,X2)
| ~ occurrence_of(X2,tptp0)
| ~ subactivity_occurrence(X1,X2)
| ~ arboreal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
occurrence_of(esk19_0,tptp0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( leaf(esk17_1(X1),tptp0)
| leaf_occ(X1,X2)
| ~ occurrence_of(X2,tptp0)
| ~ subactivity_occurrence(X1,X2)
| ~ arboreal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,plain,
! [X224,X225,X226,X227,X228,X229,X230] :
( ( min_precedes(X224,X225,X226)
| ~ next_subocc(X224,X225,X226) )
& ( ~ min_precedes(X224,X227,X226)
| ~ min_precedes(X227,X225,X226)
| ~ next_subocc(X224,X225,X226) )
& ( min_precedes(X228,esk1_3(X228,X229,X230),X230)
| ~ min_precedes(X228,X229,X230)
| next_subocc(X228,X229,X230) )
& ( min_precedes(esk1_3(X228,X229,X230),X229,X230)
| ~ min_precedes(X228,X229,X230)
| next_subocc(X228,X229,X230) ) ),
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_12,negated_conjecture,
( next_subocc(esk16_1(X1),esk17_1(X1),tptp0)
| leaf_occ(X1,esk19_0)
| ~ subactivity_occurrence(X1,esk19_0)
| ~ arboreal(X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,negated_conjecture,
subactivity_occurrence(esk18_0,esk19_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
arboreal(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,negated_conjecture,
~ leaf_occ(esk18_0,esk19_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,plain,
( next_subocc(esk15_1(X1),esk16_1(X1),tptp0)
| leaf_occ(X1,X2)
| ~ occurrence_of(X2,tptp0)
| ~ subactivity_occurrence(X1,X2)
| ~ arboreal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,negated_conjecture,
( leaf(esk17_1(X1),tptp0)
| leaf_occ(X1,esk19_0)
| ~ subactivity_occurrence(X1,esk19_0)
| ~ arboreal(X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_18,plain,
( occurrence_of(esk17_1(X1),tptp2)
| occurrence_of(esk17_1(X1),tptp1)
| leaf_occ(X1,X2)
| ~ occurrence_of(X2,tptp0)
| ~ subactivity_occurrence(X1,X2)
| ~ arboreal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_19,plain,
! [X209,X210,X211,X212] :
( ~ min_precedes(X209,X210,X212)
| ~ min_precedes(X210,X211,X212)
| min_precedes(X209,X211,X212) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos])]) ).
cnf(c_0_20,plain,
( min_precedes(X1,X2,X3)
| ~ next_subocc(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,negated_conjecture,
next_subocc(esk16_1(esk18_0),esk17_1(esk18_0),tptp0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_22,negated_conjecture,
( next_subocc(esk15_1(X1),esk16_1(X1),tptp0)
| leaf_occ(X1,esk19_0)
| ~ subactivity_occurrence(X1,esk19_0)
| ~ arboreal(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_9]) ).
cnf(c_0_23,negated_conjecture,
( ~ occurrence_of(X1,tptp1)
| ~ occurrence_of(X2,tptp3)
| ~ next_subocc(esk18_0,X2,tptp0)
| ~ min_precedes(X2,X1,tptp0)
| ~ leaf(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_24,negated_conjecture,
leaf(esk17_1(esk18_0),tptp0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_25,negated_conjecture,
( leaf_occ(X1,esk19_0)
| occurrence_of(esk17_1(X1),tptp1)
| occurrence_of(esk17_1(X1),tptp2)
| ~ subactivity_occurrence(X1,esk19_0)
| ~ arboreal(X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_9]) ).
cnf(c_0_26,negated_conjecture,
( ~ occurrence_of(X1,tptp2)
| ~ occurrence_of(X2,tptp3)
| ~ next_subocc(esk18_0,X2,tptp0)
| ~ min_precedes(X2,X1,tptp0)
| ~ leaf(X1,tptp0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_27,plain,
( occurrence_of(esk15_1(X1),tptp3)
| leaf_occ(X1,X2)
| ~ occurrence_of(X2,tptp0)
| ~ subactivity_occurrence(X1,X2)
| ~ arboreal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_28,plain,
( next_subocc(X1,esk15_1(X1),tptp0)
| leaf_occ(X1,X2)
| ~ occurrence_of(X2,tptp0)
| ~ subactivity_occurrence(X1,X2)
| ~ arboreal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_29,plain,
( min_precedes(X1,X4,X3)
| ~ min_precedes(X1,X2,X3)
| ~ min_precedes(X2,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_30,negated_conjecture,
min_precedes(esk16_1(esk18_0),esk17_1(esk18_0),tptp0),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_31,negated_conjecture,
next_subocc(esk15_1(esk18_0),esk16_1(esk18_0),tptp0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_32,negated_conjecture,
( ~ next_subocc(esk18_0,X1,tptp0)
| ~ 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_23,c_0_24]) ).
cnf(c_0_33,negated_conjecture,
( occurrence_of(esk17_1(esk18_0),tptp2)
| occurrence_of(esk17_1(esk18_0),tptp1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_34,negated_conjecture,
( ~ next_subocc(esk18_0,X1,tptp0)
| ~ 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_26,c_0_24]) ).
cnf(c_0_35,negated_conjecture,
( leaf_occ(X1,esk19_0)
| occurrence_of(esk15_1(X1),tptp3)
| ~ subactivity_occurrence(X1,esk19_0)
| ~ arboreal(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_9]) ).
cnf(c_0_36,negated_conjecture,
( next_subocc(X1,esk15_1(X1),tptp0)
| leaf_occ(X1,esk19_0)
| ~ subactivity_occurrence(X1,esk19_0)
| ~ arboreal(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_9]) ).
cnf(c_0_37,negated_conjecture,
( min_precedes(X1,esk17_1(esk18_0),tptp0)
| ~ min_precedes(X1,esk16_1(esk18_0),tptp0) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_38,negated_conjecture,
min_precedes(esk15_1(esk18_0),esk16_1(esk18_0),tptp0),
inference(spm,[status(thm)],[c_0_20,c_0_31]) ).
cnf(c_0_39,negated_conjecture,
( ~ next_subocc(esk18_0,X1,tptp0)
| ~ occurrence_of(X1,tptp3)
| ~ min_precedes(X1,esk17_1(esk18_0),tptp0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_40,negated_conjecture,
occurrence_of(esk15_1(esk18_0),tptp3),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_41,negated_conjecture,
next_subocc(esk18_0,esk15_1(esk18_0),tptp0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_42,negated_conjecture,
min_precedes(esk15_1(esk18_0),esk17_1(esk18_0),tptp0),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : PRO014+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 : n022.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 :
% 0.15/0.33 % start to proof: theBenchmark
% 1.32/1.73 % Version : CSE_E---1.7
% 1.32/1.73 % Problem : theBenchmark.p
% 1.32/1.73 % SZS status Theorem for theBenchmark.p
% 1.32/1.73 % SZS output start CNFRefutation
% See solution above
% 1.32/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------