%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : PRO009+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.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 : Fri Sep 25 02:31:20 PM UTC 2026
% Result : Theorem 16.50s 2.67s
% Output : Proof 16.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 77 ( 20 unt; 0 def)
% Number of atoms : 252 ( 18 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 291 ( 116 ~; 112 |; 53 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 117 ( 1 sgn 64 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X8,X9,X10,X11] :
( ( ~ min_precedes(X10,X11,X8)
& arboreal(X10)
& leaf_occ(X11,X9)
& subactivity_occurrence(X10,X9)
& occurrence_of(X9,X8) )
=> X11 = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_02) ).
fof(f2_nnf,plain,
! [X8,X9,X10,X11] :
( X11 = X10
| min_precedes(X10,X11,X8)
| ~ arboreal(X10)
| ~ leaf_occ(X11,X9)
| ~ subactivity_occurrence(X10,X9)
| ~ occurrence_of(X9,X8) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X9,X8,X10,X11] :
( X11 = X10
| min_precedes(X10,X11,X8)
| ~ arboreal(X10)
| ~ leaf_occ(X11,X9)
| ~ subactivity_occurrence(X10,X9)
| ~ occurrence_of(X9,X8) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c3,plain,
( X3 = X2
| min_precedes(X2,X3,X0)
| ~ arboreal(X2)
| ~ leaf_occ(X3,X1)
| ~ subactivity_occurrence(X2,X1)
| ~ occurrence_of(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f45,conjecture,
! [X105] :
( occurrence_of(X105,tptp0)
=> ? [X106,X107] :
( leaf_occ(X107,X105)
& min_precedes(X106,X107,tptp0)
& ( occurrence_of(X107,tptp1)
| occurrence_of(X107,tptp2) )
& root_occ(X106,X105)
& occurrence_of(X106,tptp3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f45_neg,negated_conjecture,
~ ! [X105] :
( occurrence_of(X105,tptp0)
=> ? [X106,X107] :
( leaf_occ(X107,X105)
& min_precedes(X106,X107,tptp0)
& ( occurrence_of(X107,tptp1)
| occurrence_of(X107,tptp2) )
& root_occ(X106,X105)
& occurrence_of(X106,tptp3) ) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f45_nnf,plain,
? [X105] :
( ! [X106,X107] :
( ~ leaf_occ(X107,X105)
| ~ min_precedes(X106,X107,tptp0)
| ( ~ occurrence_of(X107,tptp1)
& ~ occurrence_of(X107,tptp2) )
| ~ root_occ(X106,X105)
| ~ occurrence_of(X106,tptp3) )
& occurrence_of(X105,tptp0) ),
inference(nnf_transformation,[status(thm)],[f45_neg]) ).
fof(f45_sk,plain,
! [X106,X107] :
( ( ~ leaf_occ(X107,sk15)
| ~ min_precedes(X106,X107,tptp0)
| ( ~ occurrence_of(X107,tptp1)
& ~ occurrence_of(X107,tptp2) )
| ~ root_occ(X106,sk15)
| ~ occurrence_of(X106,tptp3) )
& occurrence_of(sk15,tptp0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk15])],[f45_nnf]) ).
cnf(c79,plain,
occurrence_of(sk15,tptp0),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(p86,plain,
( X1 = X0
| min_precedes(X0,X1,tptp0)
| ~ arboreal(X0)
| ~ leaf_occ(X1,sk15)
| ~ subactivity_occurrence(X0,sk15) ),
inference(resolution,[status(thm)],[c3,c79]) ).
fof(f32,axiom,
! [X101] :
( occurrence_of(X101,tptp0)
=> ? [X102,X103,X104] :
( leaf_occ(X104,X101)
& next_subocc(X103,X104,tptp0)
& ( occurrence_of(X104,tptp1)
| occurrence_of(X104,tptp2) )
& next_subocc(X102,X103,tptp0)
& occurrence_of(X103,tptp4)
& root_occ(X102,X101)
& occurrence_of(X102,tptp3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_32) ).
fof(f32_nnf,plain,
! [X101] :
( ? [X102,X103,X104] :
( leaf_occ(X104,X101)
& next_subocc(X103,X104,tptp0)
& ( occurrence_of(X104,tptp1)
| occurrence_of(X104,tptp2) )
& next_subocc(X102,X103,tptp0)
& occurrence_of(X103,tptp4)
& root_occ(X102,X101)
& occurrence_of(X102,tptp3) )
| ~ occurrence_of(X101,tptp0) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [X101] :
( ( leaf_occ(sk14(X101),X101)
& next_subocc(sk13(X101),sk14(X101),tptp0)
& ( occurrence_of(sk14(X101),tptp1)
| occurrence_of(sk14(X101),tptp2) )
& next_subocc(sk12(X101),sk13(X101),tptp0)
& occurrence_of(sk13(X101),tptp4)
& root_occ(sk12(X101),X101)
& occurrence_of(sk12(X101),tptp3) )
| ~ occurrence_of(X101,tptp0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk12,sk13,sk14])],[f32_nnf]) ).
cnf(c61,plain,
( root_occ(sk12(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p109,plain,
root_occ(sk12(sk15),sk15),
inference(resolution,[status(thm)],[c61,c79]) ).
fof(f19,axiom,
! [X58,X59] :
( root_occ(X58,X59)
<=> ? [X60] :
( root(X58,X60)
& subactivity_occurrence(X58,X59)
& occurrence_of(X59,X60) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_19) ).
fof(f19_nnf,plain,
! [X58,X59] :
( ( ! [X60] :
( ~ root(X58,X60)
| ~ subactivity_occurrence(X58,X59)
| ~ occurrence_of(X59,X60) )
| root_occ(X58,X59) )
& ( ? [X60] :
( root(X58,X60)
& subactivity_occurrence(X58,X59)
& occurrence_of(X59,X60) )
| ~ root_occ(X58,X59) ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X58,X59,X60] :
( ( ~ root(X58,X60)
| ~ subactivity_occurrence(X58,X59)
| ~ occurrence_of(X59,X60)
| root_occ(X58,X59) )
& ( ( root(X58,sk9(X58,X59))
& subactivity_occurrence(X58,X59)
& occurrence_of(X59,sk9(X58,X59)) )
| ~ root_occ(X58,X59) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9])],[f19_nnf]) ).
cnf(c38,plain,
( subactivity_occurrence(X0,X1)
| ~ root_occ(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p110,plain,
subactivity_occurrence(sk12(sk15),sk15),
inference(resolution,[status(thm)],[p109,c38]) ).
cnf(p451,plain,
( X0 = sk12(sk15)
| min_precedes(sk12(sk15),X0,tptp0)
| ~ arboreal(sk12(sk15))
| ~ leaf_occ(X0,sk15) ),
inference(resolution,[status(thm)],[p86,p110]) ).
cnf(c66,plain,
( leaf_occ(sk14(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p124,plain,
leaf_occ(sk14(sk15),sk15),
inference(resolution,[status(thm)],[c66,c79]) ).
cnf(p2029,plain,
( sk14(sk15) = sk12(sk15)
| min_precedes(sk12(sk15),sk14(sk15),tptp0)
| ~ arboreal(sk12(sk15)) ),
inference(resolution,[status(thm)],[p451,p124]) ).
fof(f16,axiom,
! [X51,X52] :
( occurrence_of(X51,X52)
=> ( arboreal(X51)
<=> atomic(X52) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_16) ).
fof(f16_nnf,plain,
! [X51,X52] :
( ( ( ~ atomic(X52)
| arboreal(X51) )
& ( atomic(X52)
| ~ arboreal(X51) ) )
| ~ occurrence_of(X51,X52) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X51,X52] :
( ( ( ~ atomic(X52)
| arboreal(X51) )
& ( atomic(X52)
| ~ arboreal(X51) ) )
| ~ occurrence_of(X51,X52) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c31,plain,
( ~ atomic(X1)
| arboreal(X0)
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(c60,plain,
( occurrence_of(sk12(X0),tptp3)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p96,plain,
occurrence_of(sk12(sk15),tptp3),
inference(resolution,[status(thm)],[c60,c79]) ).
cnf(p173,plain,
( ~ atomic(tptp3)
| arboreal(sk12(sk15)) ),
inference(resolution,[status(thm)],[c31,p96]) ).
fof(f38,axiom,
atomic(tptp3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_38) ).
fof(f38_nnf,plain,
atomic(tptp3),
inference(nnf_transformation,[status(thm)],[f38]) ).
cnf(c72,plain,
atomic(tptp3),
inference(cnf_transformation,[status(esa)],[f38_nnf]) ).
cnf(p178,plain,
arboreal(sk12(sk15)),
inference(resolution,[status(thm)],[p173,c72]) ).
cnf(p2713,plain,
( sk14(sk15) = sk12(sk15)
| min_precedes(sk12(sk15),sk14(sk15),tptp0) ),
inference(resolution,[status(thm)],[p2029,p178]) ).
cnf(c81,plain,
( ~ leaf_occ(X2,sk15)
| ~ min_precedes(X1,X2,tptp0)
| ~ occurrence_of(X2,tptp1)
| ~ root_occ(X1,sk15)
| ~ occurrence_of(X1,tptp3) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(p402,plain,
( ~ leaf_occ(X0,sk15)
| ~ min_precedes(sk12(sk15),X0,tptp0)
| ~ occurrence_of(X0,tptp1)
| ~ root_occ(sk12(sk15),sk15) ),
inference(resolution,[status(thm)],[c81,p96]) ).
cnf(p1537,plain,
( ~ leaf_occ(X0,sk15)
| ~ min_precedes(sk12(sk15),X0,tptp0)
| ~ occurrence_of(X0,tptp1) ),
inference(resolution,[status(thm)],[p402,p109]) ).
cnf(c64,plain,
( occurrence_of(sk14(X0),tptp1)
| occurrence_of(sk14(X0),tptp2)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p391,plain,
( occurrence_of(sk14(sk15),tptp1)
| occurrence_of(sk14(sk15),tptp2) ),
inference(resolution,[status(thm)],[c64,c79]) ).
cnf(p1538,plain,
( occurrence_of(sk14(sk15),tptp2)
| ~ leaf_occ(sk14(sk15),sk15)
| ~ min_precedes(sk12(sk15),sk14(sk15),tptp0) ),
inference(resolution,[status(thm)],[p1537,p391]) ).
cnf(p2724,plain,
( occurrence_of(sk14(sk15),tptp2)
| ~ leaf_occ(sk14(sk15),sk15)
| sk14(sk15) = sk12(sk15) ),
inference(resolution,[status(thm)],[p2713,p1538]) ).
cnf(p3202,plain,
( occurrence_of(sk14(sk15),tptp2)
| sk14(sk15) = sk12(sk15) ),
inference(resolution,[status(thm)],[p2724,p124]) ).
cnf(c65,plain,
( next_subocc(sk13(X0),sk14(X0),tptp0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p334,plain,
next_subocc(sk13(sk15),sk14(sk15),tptp0),
inference(resolution,[status(thm)],[c65,c79]) ).
fof(f26,axiom,
! [X78,X79,X80] :
( next_subocc(X78,X79,X80)
<=> ( ~ ? [X81] :
( min_precedes(X81,X79,X80)
& min_precedes(X78,X81,X80) )
& min_precedes(X78,X79,X80) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_26) ).
fof(f26_nnf,plain,
! [X78,X79,X80] :
( ( ? [X81] :
( min_precedes(X81,X79,X80)
& min_precedes(X78,X81,X80) )
| ~ min_precedes(X78,X79,X80)
| next_subocc(X78,X79,X80) )
& ( ( ! [X81] :
( ~ min_precedes(X81,X79,X80)
| ~ min_precedes(X78,X81,X80) )
& min_precedes(X78,X79,X80) )
| ~ next_subocc(X78,X79,X80) ) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [X78,X79,X80,X81] :
( ( ( min_precedes(sk11(X78,X79,X80),X79,X80)
& min_precedes(X78,sk11(X78,X79,X80),X80) )
| ~ min_precedes(X78,X79,X80)
| next_subocc(X78,X79,X80) )
& ( ( ( ~ min_precedes(X81,X79,X80)
| ~ min_precedes(X78,X81,X80) )
& min_precedes(X78,X79,X80) )
| ~ next_subocc(X78,X79,X80) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f26_nnf]) ).
cnf(c51,plain,
( min_precedes(X0,X1,X2)
| ~ next_subocc(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p346,plain,
min_precedes(sk13(sk15),sk14(sk15),tptp0),
inference(resolution,[status(thm)],[p334,c51]) ).
fof(f22,axiom,
! [X65,X66,X67] :
( min_precedes(X65,X66,X67)
=> ~ root(X66,X67) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_22) ).
fof(f22_nnf,plain,
! [X65,X66,X67] :
( ~ root(X66,X67)
| ~ min_precedes(X65,X66,X67) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [X65,X66,X67] :
( ~ root(X66,X67)
| ~ min_precedes(X65,X66,X67) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c45,plain,
( ~ root(X1,X2)
| ~ min_precedes(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p350,plain,
~ root(sk14(sk15),tptp0),
inference(resolution,[status(thm)],[p346,c45]) ).
cnf(p3213,plain,
( ~ root(sk12(sk15),tptp0)
| occurrence_of(sk14(sk15),tptp2) ),
inference(superposition,[status(thm)],[p3202,p350]) ).
cnf(c37,plain,
( occurrence_of(X1,sk9(X0,X1))
| ~ root_occ(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p211,plain,
occurrence_of(sk15,sk9(sk12(sk15),sk15)),
inference(resolution,[status(thm)],[c37,p109]) ).
fof(f8,axiom,
! [X28,X29,X30] :
( ( occurrence_of(X28,X30)
& occurrence_of(X28,X29) )
=> X29 = X30 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
fof(f8_nnf,plain,
! [X28,X29,X30] :
( X29 = X30
| ~ occurrence_of(X28,X30)
| ~ occurrence_of(X28,X29) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X28,X29,X30] :
( X29 = X30
| ~ occurrence_of(X28,X30)
| ~ occurrence_of(X28,X29) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c14,plain,
( X1 = X2
| ~ occurrence_of(X0,X2)
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p125,plain,
( tptp0 = X0
| ~ occurrence_of(sk15,X0) ),
inference(resolution,[status(thm)],[c14,c79]) ).
cnf(p220,plain,
tptp0 = sk9(sk12(sk15),sk15),
inference(resolution,[status(thm)],[p211,p125]) ).
cnf(c39,plain,
( root(X0,sk9(X0,X1))
| ~ root_occ(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p225,plain,
root(sk12(sk15),sk9(sk12(sk15),sk15)),
inference(resolution,[status(thm)],[c39,p109]) ).
cnf(p230,plain,
root(sk12(sk15),tptp0),
inference(superposition,[status(thm)],[p220,p225]) ).
cnf(p3644,plain,
occurrence_of(sk14(sk15),tptp2),
inference(resolution,[status(thm)],[p3213,p230]) ).
cnf(c80,plain,
( ~ leaf_occ(X2,sk15)
| ~ min_precedes(X1,X2,tptp0)
| ~ occurrence_of(X2,tptp2)
| ~ root_occ(X1,sk15)
| ~ occurrence_of(X1,tptp3) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(p396,plain,
( ~ leaf_occ(X0,sk15)
| ~ min_precedes(sk12(sk15),X0,tptp0)
| ~ occurrence_of(X0,tptp2)
| ~ root_occ(sk12(sk15),sk15) ),
inference(resolution,[status(thm)],[c80,p96]) ).
cnf(p1517,plain,
( ~ leaf_occ(X0,sk15)
| ~ min_precedes(sk12(sk15),X0,tptp0)
| ~ occurrence_of(X0,tptp2) ),
inference(resolution,[status(thm)],[p396,p109]) ).
cnf(p3700,plain,
( ~ leaf_occ(sk14(sk15),sk15)
| ~ min_precedes(sk12(sk15),sk14(sk15),tptp0) ),
inference(resolution,[status(thm)],[p3644,p1517]) ).
cnf(p3736,plain,
( sk14(sk15) = sk12(sk15)
| ~ leaf_occ(sk14(sk15),sk15) ),
inference(resolution,[status(thm)],[p3700,p2713]) ).
cnf(p3737,plain,
sk14(sk15) = sk12(sk15),
inference(resolution,[status(thm)],[p3736,p124]) ).
cnf(p3764,plain,
~ root(sk12(sk15),tptp0),
inference(demodulation,[status(thm)],[p3737,p350]) ).
cnf(p4807,plain,
$false,
inference(resolution,[status(thm)],[p3764,p230]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PRO009+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n007.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 06:25:52 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 16.50/2.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.50/2.67 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------