%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : PRO010+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 : n004.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 02:31:21 PM UTC 2026
% Result : Theorem 14.75s 7.37s
% Output : Proof 14.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 11 unt; 0 def)
% Number of atoms : 110 ( 10 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 113 ( 36 ~; 30 |; 38 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 65 ( 3 sgn 29 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f32,axiom,
! [X95] :
( occurrence_of(X95,tptp0)
=> ? [X96,X97,X98] :
( leaf_occ(X98,X95)
& next_subocc(X97,X98,tptp0)
& ( occurrence_of(X98,tptp2)
| occurrence_of(X98,tptp1) )
& 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,tptp2)
| occurrence_of(X98,tptp1) )
& 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),tptp2)
| occurrence_of(sk16(X95),tptp1) )
& 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(c69,plain,
( leaf_occ(sk16(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
fof(f45,conjecture,
! [X99] :
( occurrence_of(X99,tptp0)
=> ? [X100,X101] :
( ( occurrence_of(X101,tptp2)
=> ~ ? [X103] :
( min_precedes(X100,X103,tptp0)
& occurrence_of(X103,tptp1) ) )
& ( occurrence_of(X101,tptp1)
=> ~ ? [X102] :
( min_precedes(X100,X102,tptp0)
& occurrence_of(X102,tptp2) ) )
& leaf_occ(X101,X99) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f45_neg,negated_conjecture,
~ ! [X99] :
( occurrence_of(X99,tptp0)
=> ? [X100,X101] :
( ( occurrence_of(X101,tptp2)
=> ~ ? [X103] :
( min_precedes(X100,X103,tptp0)
& occurrence_of(X103,tptp1) ) )
& ( occurrence_of(X101,tptp1)
=> ~ ? [X102] :
( min_precedes(X100,X102,tptp0)
& occurrence_of(X102,tptp2) ) )
& leaf_occ(X101,X99) ) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f45_nnf,plain,
? [X99] :
( ! [X100,X101] :
( ( ? [X103] :
( min_precedes(X100,X103,tptp0)
& occurrence_of(X103,tptp1) )
& occurrence_of(X101,tptp2) )
| ( ? [X102] :
( min_precedes(X100,X102,tptp0)
& occurrence_of(X102,tptp2) )
& occurrence_of(X101,tptp1) )
| ~ leaf_occ(X101,X99) )
& occurrence_of(X99,tptp0) ),
inference(nnf_transformation,[status(thm)],[f45_neg]) ).
fof(f45_sk,plain,
! [X101,X100] :
( ( ( min_precedes(X100,sk19(X100,X101),tptp0)
& occurrence_of(sk19(X100,X101),tptp1)
& occurrence_of(X101,tptp2) )
| ( min_precedes(X100,sk18(X100,X101),tptp0)
& occurrence_of(sk18(X100,X101),tptp2)
& occurrence_of(X101,tptp1) )
| ~ leaf_occ(X101,sk17) )
& occurrence_of(sk17,tptp0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk17,sk18,sk19])],[f45_nnf]) ).
cnf(c82,plain,
occurrence_of(sk17,tptp0),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(p440,plain,
leaf_occ(sk16(sk17),sk17),
inference(resolution,[status(thm)],[c69,c82]) ).
cnf(c89,plain,
( occurrence_of(X2,tptp2)
| min_precedes(X1,sk18(X1,X2),tptp0)
| ~ leaf_occ(X2,sk17) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(p445,plain,
( occurrence_of(sk16(sk17),tptp2)
| min_precedes(X0,sk18(X0,sk16(sk17)),tptp0) ),
inference(resolution,[status(thm)],[p440,c89]) ).
fof(f21,axiom,
! [X60,X61,X62] :
( ( leaf_occ(X61,X60)
& occurrence_of(X60,X62) )
=> ~ ? [X63] : min_precedes(X61,X63,X62) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_21) ).
fof(f21_nnf,plain,
! [X60,X61,X62] :
( ! [X63] : ~ min_precedes(X61,X63,X62)
| ~ leaf_occ(X61,X60)
| ~ occurrence_of(X60,X62) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [X60,X62,X61,X63] :
( ~ min_precedes(X61,X63,X62)
| ~ leaf_occ(X61,X60)
| ~ occurrence_of(X60,X62) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c42,plain,
( ~ min_precedes(X1,X3,X2)
| ~ leaf_occ(X1,X0)
| ~ occurrence_of(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p189,plain,
( ~ min_precedes(X0,X1,tptp0)
| ~ leaf_occ(X0,sk17) ),
inference(resolution,[status(thm)],[c42,c82]) ).
cnf(p454,plain,
~ min_precedes(sk16(sk17),X0,tptp0),
inference(resolution,[status(thm)],[p440,p189]) ).
cnf(p1408,plain,
occurrence_of(sk16(sk17),tptp2),
inference(resolution,[status(thm)],[p445,p454]) ).
cnf(c85,plain,
( min_precedes(X1,sk19(X1,X2),tptp0)
| occurrence_of(X2,tptp1)
| ~ leaf_occ(X2,sk17) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(p444,plain,
( min_precedes(X0,sk19(X0,sk16(sk17)),tptp0)
| occurrence_of(sk16(sk17),tptp1) ),
inference(resolution,[status(thm)],[p440,c85]) ).
cnf(p1303,plain,
occurrence_of(sk16(sk17),tptp1),
inference(resolution,[status(thm)],[p444,p454]) ).
fof(f22,axiom,
! [X64,X65,X66] :
( ( occurrence_of(X64,X66)
& occurrence_of(X64,X65) )
=> X65 = X66 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_22) ).
fof(f22_nnf,plain,
! [X64,X65,X66] :
( X65 = X66
| ~ occurrence_of(X64,X66)
| ~ occurrence_of(X64,X65) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [X64,X65,X66] :
( X65 = X66
| ~ occurrence_of(X64,X66)
| ~ occurrence_of(X64,X65) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c43,plain,
( X1 = X2
| ~ occurrence_of(X0,X2)
| ~ occurrence_of(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p1321,plain,
( tptp1 = X0
| ~ occurrence_of(sk16(sk17),X0) ),
inference(resolution,[status(thm)],[p1303,c43]) ).
cnf(p1417,plain,
tptp1 = tptp2,
inference(resolution,[status(thm)],[p1408,p1321]) ).
fof(f44,axiom,
tptp1 != tptp2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_44) ).
fof(f44_nnf,plain,
tptp1 != tptp2,
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
tptp1 != tptp2,
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c81,plain,
tptp1 != tptp2,
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(p1418,plain,
$false,
inference(resolution,[status(thm)],[p1417,c81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PRO010+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.38 % Computer : n004.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Thu Sep 24 06:27:41 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 14.75/7.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.75/7.37 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------