%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : PRO009+2 : 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 17.46s 7.76s
% Output : Proof 17.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 44 ( 12 unt; 0 def)
% Number of atoms : 149 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 173 ( 68 ~; 61 |; 39 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 67 ( 0 sgn 32 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f32,axiom,
! [X95] :
( occurrence_of(X95,tptp0)
=> ? [X96,X97,X98] :
( leaf_occ(X98,X95)
& next_subocc(X97,X98,tptp0)
& ( occurrence_of(X98,tptp1)
| occurrence_of(X98,tptp2) )
& next_subocc(X96,X97,tptp0)
& occurrence_of(X97,tptp4)
& root_occ(X96,X95)
& occurrence_of(X96,tptp3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_32) ).
fof(f32_nnf,plain,
! [X95] :
( ? [X96,X97,X98] :
( leaf_occ(X98,X95)
& next_subocc(X97,X98,tptp0)
& ( occurrence_of(X98,tptp1)
| occurrence_of(X98,tptp2) )
& next_subocc(X96,X97,tptp0)
& occurrence_of(X97,tptp4)
& root_occ(X96,X95)
& occurrence_of(X96,tptp3) )
| ~ occurrence_of(X95,tptp0) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [X95] :
( ( leaf_occ(sk16(X95),X95)
& next_subocc(sk15(X95),sk16(X95),tptp0)
& ( occurrence_of(sk16(X95),tptp1)
| occurrence_of(sk16(X95),tptp2) )
& next_subocc(sk14(X95),sk15(X95),tptp0)
& occurrence_of(sk15(X95),tptp4)
& root_occ(sk14(X95),X95)
& occurrence_of(sk14(X95),tptp3) )
| ~ occurrence_of(X95,tptp0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk14,sk15,sk16])],[f32_nnf]) ).
cnf(c67,plain,
( occurrence_of(sk16(X0),tptp1)
| occurrence_of(sk16(X0),tptp2)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
fof(f45,conjecture,
! [X99] :
( occurrence_of(X99,tptp0)
=> ? [X100,X101] :
( leaf_occ(X101,X99)
& min_precedes(X100,X101,tptp0)
& ( occurrence_of(X101,tptp1)
| occurrence_of(X101,tptp2) )
& root_occ(X100,X99)
& occurrence_of(X100,tptp3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f45_neg,negated_conjecture,
~ ! [X99] :
( occurrence_of(X99,tptp0)
=> ? [X100,X101] :
( leaf_occ(X101,X99)
& min_precedes(X100,X101,tptp0)
& ( occurrence_of(X101,tptp1)
| occurrence_of(X101,tptp2) )
& root_occ(X100,X99)
& occurrence_of(X100,tptp3) ) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f45_nnf,plain,
? [X99] :
( ! [X100,X101] :
( ~ leaf_occ(X101,X99)
| ~ min_precedes(X100,X101,tptp0)
| ( ~ occurrence_of(X101,tptp1)
& ~ occurrence_of(X101,tptp2) )
| ~ root_occ(X100,X99)
| ~ occurrence_of(X100,tptp3) )
& occurrence_of(X99,tptp0) ),
inference(nnf_transformation,[status(thm)],[f45_neg]) ).
fof(f45_sk,plain,
! [X100,X101] :
( ( ~ leaf_occ(X101,sk17)
| ~ min_precedes(X100,X101,tptp0)
| ( ~ occurrence_of(X101,tptp1)
& ~ occurrence_of(X101,tptp2) )
| ~ root_occ(X100,sk17)
| ~ occurrence_of(X100,tptp3) )
& occurrence_of(sk17,tptp0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk17])],[f45_nnf]) ).
cnf(c82,plain,
occurrence_of(sk17,tptp0),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(p407,plain,
( occurrence_of(sk16(sk17),tptp1)
| occurrence_of(sk16(sk17),tptp2) ),
inference(resolution,[status(thm)],[c67,c82]) ).
cnf(c64,plain,
( root_occ(sk14(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p106,plain,
root_occ(sk14(sk17),sk17),
inference(resolution,[status(thm)],[c64,c82]) ).
cnf(c63,plain,
( occurrence_of(sk14(X0),tptp3)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p95,plain,
occurrence_of(sk14(sk17),tptp3),
inference(resolution,[status(thm)],[c63,c82]) ).
cnf(c84,plain,
( ~ leaf_occ(X2,sk17)
| ~ min_precedes(X1,X2,tptp0)
| ~ occurrence_of(X2,tptp1)
| ~ root_occ(X1,sk17)
| ~ occurrence_of(X1,tptp3) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(p97,plain,
( ~ leaf_occ(X0,sk17)
| ~ min_precedes(sk14(sk17),X0,tptp0)
| ~ occurrence_of(X0,tptp1)
| ~ root_occ(sk14(sk17),sk17) ),
inference(resolution,[status(thm)],[p95,c84]) ).
cnf(p112,plain,
( ~ leaf_occ(X0,sk17)
| ~ min_precedes(sk14(sk17),X0,tptp0)
| ~ occurrence_of(X0,tptp1) ),
inference(resolution,[status(thm)],[p106,p97]) ).
cnf(p603,plain,
( ~ leaf_occ(sk16(sk17),sk17)
| ~ min_precedes(sk14(sk17),sk16(sk17),tptp0)
| occurrence_of(sk16(sk17),tptp2) ),
inference(resolution,[status(thm)],[p407,p112]) ).
cnf(c66,plain,
( next_subocc(sk14(X0),sk15(X0),tptp0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p393,plain,
next_subocc(sk14(sk17),sk15(sk17),tptp0),
inference(resolution,[status(thm)],[c66,c82]) ).
fof(f4,axiom,
! [X15,X16,X17] :
( next_subocc(X15,X16,X17)
<=> ( ~ ? [X18] :
( min_precedes(X18,X16,X17)
& min_precedes(X15,X18,X17) )
& min_precedes(X15,X16,X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_04) ).
fof(f4_nnf,plain,
! [X15,X16,X17] :
( ( ? [X18] :
( min_precedes(X18,X16,X17)
& min_precedes(X15,X18,X17) )
| ~ min_precedes(X15,X16,X17)
| next_subocc(X15,X16,X17) )
& ( ( ! [X18] :
( ~ min_precedes(X18,X16,X17)
| ~ min_precedes(X15,X18,X17) )
& min_precedes(X15,X16,X17) )
| ~ next_subocc(X15,X16,X17) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X15,X16,X17,X18] :
( ( ( min_precedes(sk0(X15,X16,X17),X16,X17)
& min_precedes(X15,sk0(X15,X16,X17),X17) )
| ~ min_precedes(X15,X16,X17)
| next_subocc(X15,X16,X17) )
& ( ( ( ~ min_precedes(X18,X16,X17)
| ~ min_precedes(X15,X18,X17) )
& min_precedes(X15,X16,X17) )
| ~ next_subocc(X15,X16,X17) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f4_nnf]) ).
cnf(c4,plain,
( min_precedes(X0,X1,X2)
| ~ next_subocc(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p409,plain,
min_precedes(sk14(sk17),sk15(sk17),tptp0),
inference(resolution,[status(thm)],[p393,c4]) ).
fof(f0,axiom,
! [X0,X1,X2,X3] :
( ( min_precedes(X1,X2,X3)
& min_precedes(X0,X1,X3) )
=> min_precedes(X0,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos) ).
fof(f0_nnf,plain,
! [X0,X1,X2,X3] :
( min_precedes(X0,X2,X3)
| ~ min_precedes(X1,X2,X3)
| ~ min_precedes(X0,X1,X3) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X0,X1,X3,X2] :
( min_precedes(X0,X2,X3)
| ~ min_precedes(X1,X2,X3)
| ~ min_precedes(X0,X1,X3) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( min_precedes(X0,X2,X3)
| ~ min_precedes(X1,X2,X3)
| ~ min_precedes(X0,X1,X3) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p411,plain,
( min_precedes(sk14(sk17),X0,tptp0)
| ~ min_precedes(sk15(sk17),X0,tptp0) ),
inference(resolution,[status(thm)],[p409,c0]) ).
cnf(c68,plain,
( next_subocc(sk15(X0),sk16(X0),tptp0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p424,plain,
next_subocc(sk15(sk17),sk16(sk17),tptp0),
inference(resolution,[status(thm)],[c68,c82]) ).
cnf(p428,plain,
min_precedes(sk15(sk17),sk16(sk17),tptp0),
inference(resolution,[status(thm)],[p424,c4]) ).
cnf(p1037,plain,
min_precedes(sk14(sk17),sk16(sk17),tptp0),
inference(resolution,[status(thm)],[p411,p428]) ).
cnf(p2714,plain,
( ~ leaf_occ(sk16(sk17),sk17)
| occurrence_of(sk16(sk17),tptp2) ),
inference(resolution,[status(thm)],[p603,p1037]) ).
cnf(c69,plain,
( leaf_occ(sk16(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p431,plain,
leaf_occ(sk16(sk17),sk17),
inference(resolution,[status(thm)],[c69,c82]) ).
cnf(p2715,plain,
occurrence_of(sk16(sk17),tptp2),
inference(resolution,[status(thm)],[p2714,p431]) ).
cnf(c83,plain,
( ~ leaf_occ(X2,sk17)
| ~ min_precedes(X1,X2,tptp0)
| ~ occurrence_of(X2,tptp2)
| ~ root_occ(X1,sk17)
| ~ occurrence_of(X1,tptp3) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(p96,plain,
( ~ leaf_occ(X0,sk17)
| ~ min_precedes(sk14(sk17),X0,tptp0)
| ~ occurrence_of(X0,tptp2)
| ~ root_occ(sk14(sk17),sk17) ),
inference(resolution,[status(thm)],[p95,c83]) ).
cnf(p110,plain,
( ~ leaf_occ(X0,sk17)
| ~ min_precedes(sk14(sk17),X0,tptp0)
| ~ occurrence_of(X0,tptp2) ),
inference(resolution,[status(thm)],[p106,p96]) ).
cnf(p2718,plain,
( ~ leaf_occ(sk16(sk17),sk17)
| ~ min_precedes(sk14(sk17),sk16(sk17),tptp0) ),
inference(resolution,[status(thm)],[p2715,p110]) ).
cnf(p2814,plain,
~ leaf_occ(sk16(sk17),sk17),
inference(resolution,[status(thm)],[p2718,p1037]) ).
cnf(p2829,plain,
$false,
inference(resolution,[status(thm)],[p2814,p431]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PRO009+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.37 % Computer : n007.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 06:26:13 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 17.46/7.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.46/7.76 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------