TSTP Solution File: PRO011+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : PRO011+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 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 Apr 30 20:36:44 EDT 2024
% Result : Theorem 0.20s 0.37s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 10 unt; 0 def)
% Number of atoms : 194 ( 6 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 205 ( 54 ~; 56 |; 83 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 119 ( 85 !; 34 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X4,X5,X6] :
( ( occurrence_of(X4,X5)
& occurrence_of(X4,X6) )
=> X5 = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X56,X57] :
( leaf(X56,X57)
<=> ( ( root(X56,X57)
| ? [X58] : min_precedes(X58,X56,X57) )
& ~ ? [X59] : min_precedes(X56,X59,X57) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [X102,X103] :
( leaf_occ(X102,X103)
<=> ? [X104] :
( occurrence_of(X103,X104)
& subactivity_occurrence(X102,X103)
& leaf(X102,X104) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [X105] :
( occurrence_of(X105,tptp0)
=> ? [X106,X107,X108] :
( occurrence_of(X106,tptp3)
& root_occ(X106,X105)
& occurrence_of(X107,tptp4)
& next_subocc(X106,X107,tptp0)
& ( occurrence_of(X108,tptp1)
| occurrence_of(X108,tptp2) )
& next_subocc(X107,X108,tptp0)
& leaf_occ(X108,X105) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,conjecture,
! [X109] :
( occurrence_of(X109,tptp0)
=> ? [X110,X111] :
( leaf_occ(X111,X109)
& ( occurrence_of(X111,tptp1)
=> ~ ? [X112] :
( occurrence_of(X112,tptp2)
& subactivity_occurrence(X112,X109)
& min_precedes(X110,X112,tptp0) ) )
& ( occurrence_of(X111,tptp2)
=> ~ ? [X113] :
( occurrence_of(X113,tptp1)
& subactivity_occurrence(X113,X109)
& min_precedes(X110,X113,tptp0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
~ ! [X109] :
( occurrence_of(X109,tptp0)
=> ? [X110,X111] :
( leaf_occ(X111,X109)
& ( occurrence_of(X111,tptp1)
=> ~ ? [X112] :
( occurrence_of(X112,tptp2)
& subactivity_occurrence(X112,X109)
& min_precedes(X110,X112,tptp0) ) )
& ( occurrence_of(X111,tptp2)
=> ~ ? [X113] :
( occurrence_of(X113,tptp1)
& subactivity_occurrence(X113,X109)
& min_precedes(X110,X113,tptp0) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
fof(f58,plain,
! [X4,X5,X6] :
( ~ occurrence_of(X4,X5)
| ~ occurrence_of(X4,X6)
| X5 = X6 ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f59,plain,
! [X5,X6] :
( ! [X4] :
( ~ occurrence_of(X4,X5)
| ~ occurrence_of(X4,X6) )
| X5 = X6 ),
inference(miniscoping,[status(esa)],[f58]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ~ occurrence_of(X0,X1)
| ~ occurrence_of(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f121,plain,
! [X56,X57] :
( leaf(X56,X57)
<=> ( ( root(X56,X57)
| ? [X58] : min_precedes(X58,X56,X57) )
& ! [X59] : ~ min_precedes(X56,X59,X57) ) ),
inference(pre_NNF_transformation,[status(esa)],[f22]) ).
fof(f122,plain,
! [X56,X57] :
( ( ~ leaf(X56,X57)
| ( ( root(X56,X57)
| ? [X58] : min_precedes(X58,X56,X57) )
& ! [X59] : ~ min_precedes(X56,X59,X57) ) )
& ( leaf(X56,X57)
| ( ~ root(X56,X57)
& ! [X58] : ~ min_precedes(X58,X56,X57) )
| ? [X59] : min_precedes(X56,X59,X57) ) ),
inference(NNF_transformation,[status(esa)],[f121]) ).
fof(f123,plain,
( ! [X56,X57] :
( ~ leaf(X56,X57)
| ( ( root(X56,X57)
| ? [X58] : min_precedes(X58,X56,X57) )
& ! [X59] : ~ min_precedes(X56,X59,X57) ) )
& ! [X56,X57] :
( leaf(X56,X57)
| ( ~ root(X56,X57)
& ! [X58] : ~ min_precedes(X58,X56,X57) )
| ? [X59] : min_precedes(X56,X59,X57) ) ),
inference(miniscoping,[status(esa)],[f122]) ).
fof(f124,plain,
( ! [X56,X57] :
( ~ leaf(X56,X57)
| ( ( root(X56,X57)
| min_precedes(sk0_5(X57,X56),X56,X57) )
& ! [X59] : ~ min_precedes(X56,X59,X57) ) )
& ! [X56,X57] :
( leaf(X56,X57)
| ( ~ root(X56,X57)
& ! [X58] : ~ min_precedes(X58,X56,X57) )
| min_precedes(X56,sk0_6(X57,X56),X57) ) ),
inference(skolemization,[status(esa)],[f123]) ).
fof(f126,plain,
! [X0,X1,X2] :
( ~ leaf(X0,X1)
| ~ min_precedes(X0,X2,X1) ),
inference(cnf_transformation,[status(esa)],[f124]) ).
fof(f184,plain,
! [X102,X103] :
( ( ~ leaf_occ(X102,X103)
| ? [X104] :
( occurrence_of(X103,X104)
& subactivity_occurrence(X102,X103)
& leaf(X102,X104) ) )
& ( leaf_occ(X102,X103)
| ! [X104] :
( ~ occurrence_of(X103,X104)
| ~ subactivity_occurrence(X102,X103)
| ~ leaf(X102,X104) ) ) ),
inference(NNF_transformation,[status(esa)],[f35]) ).
fof(f185,plain,
( ! [X102,X103] :
( ~ leaf_occ(X102,X103)
| ? [X104] :
( occurrence_of(X103,X104)
& subactivity_occurrence(X102,X103)
& leaf(X102,X104) ) )
& ! [X102,X103] :
( leaf_occ(X102,X103)
| ! [X104] :
( ~ occurrence_of(X103,X104)
| ~ subactivity_occurrence(X102,X103)
| ~ leaf(X102,X104) ) ) ),
inference(miniscoping,[status(esa)],[f184]) ).
fof(f186,plain,
( ! [X102,X103] :
( ~ leaf_occ(X102,X103)
| ( occurrence_of(X103,sk0_14(X103,X102))
& subactivity_occurrence(X102,X103)
& leaf(X102,sk0_14(X103,X102)) ) )
& ! [X102,X103] :
( leaf_occ(X102,X103)
| ! [X104] :
( ~ occurrence_of(X103,X104)
| ~ subactivity_occurrence(X102,X103)
| ~ leaf(X102,X104) ) ) ),
inference(skolemization,[status(esa)],[f185]) ).
fof(f187,plain,
! [X0,X1] :
( ~ leaf_occ(X0,X1)
| occurrence_of(X1,sk0_14(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f186]) ).
fof(f189,plain,
! [X0,X1] :
( ~ leaf_occ(X0,X1)
| leaf(X0,sk0_14(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f186]) ).
fof(f191,plain,
! [X105] :
( ~ occurrence_of(X105,tptp0)
| ? [X106,X107,X108] :
( occurrence_of(X106,tptp3)
& root_occ(X106,X105)
& occurrence_of(X107,tptp4)
& next_subocc(X106,X107,tptp0)
& ( occurrence_of(X108,tptp1)
| occurrence_of(X108,tptp2) )
& next_subocc(X107,X108,tptp0)
& leaf_occ(X108,X105) ) ),
inference(pre_NNF_transformation,[status(esa)],[f36]) ).
fof(f192,plain,
! [X105] :
( ~ occurrence_of(X105,tptp0)
| ? [X108] :
( ? [X107] :
( ? [X106] :
( occurrence_of(X106,tptp3)
& root_occ(X106,X105)
& occurrence_of(X107,tptp4)
& next_subocc(X106,X107,tptp0) )
& ( occurrence_of(X108,tptp1)
| occurrence_of(X108,tptp2) )
& next_subocc(X107,X108,tptp0) )
& leaf_occ(X108,X105) ) ),
inference(miniscoping,[status(esa)],[f191]) ).
fof(f193,plain,
! [X105] :
( ~ occurrence_of(X105,tptp0)
| ( occurrence_of(sk0_17(X105),tptp3)
& root_occ(sk0_17(X105),X105)
& occurrence_of(sk0_16(X105),tptp4)
& next_subocc(sk0_17(X105),sk0_16(X105),tptp0)
& ( occurrence_of(sk0_15(X105),tptp1)
| occurrence_of(sk0_15(X105),tptp2) )
& next_subocc(sk0_16(X105),sk0_15(X105),tptp0)
& leaf_occ(sk0_15(X105),X105) ) ),
inference(skolemization,[status(esa)],[f192]) ).
fof(f200,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| leaf_occ(sk0_15(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f193]) ).
fof(f213,plain,
? [X109] :
( occurrence_of(X109,tptp0)
& ! [X110,X111] :
( ~ leaf_occ(X111,X109)
| ( occurrence_of(X111,tptp1)
& ? [X112] :
( occurrence_of(X112,tptp2)
& subactivity_occurrence(X112,X109)
& min_precedes(X110,X112,tptp0) ) )
| ( occurrence_of(X111,tptp2)
& ? [X113] :
( occurrence_of(X113,tptp1)
& subactivity_occurrence(X113,X109)
& min_precedes(X110,X113,tptp0) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f50]) ).
fof(f214,plain,
! [X109,X110,X111] :
( pd0_0(X111,X110,X109)
=> ( occurrence_of(X111,tptp1)
& ? [X112] :
( occurrence_of(X112,tptp2)
& subactivity_occurrence(X112,X109)
& min_precedes(X110,X112,tptp0) ) ) ),
introduced(predicate_definition,[f213]) ).
fof(f215,plain,
? [X109] :
( occurrence_of(X109,tptp0)
& ! [X110,X111] :
( ~ leaf_occ(X111,X109)
| pd0_0(X111,X110,X109)
| ( occurrence_of(X111,tptp2)
& ? [X113] :
( occurrence_of(X113,tptp1)
& subactivity_occurrence(X113,X109)
& min_precedes(X110,X113,tptp0) ) ) ) ),
inference(formula_renaming,[status(thm)],[f213,f214]) ).
fof(f216,plain,
( occurrence_of(sk0_18,tptp0)
& ! [X110,X111] :
( ~ leaf_occ(X111,sk0_18)
| pd0_0(X111,X110,sk0_18)
| ( occurrence_of(X111,tptp2)
& occurrence_of(sk0_19(X111,X110),tptp1)
& subactivity_occurrence(sk0_19(X111,X110),sk0_18)
& min_precedes(X110,sk0_19(X111,X110),tptp0) ) ) ),
inference(skolemization,[status(esa)],[f215]) ).
fof(f217,plain,
occurrence_of(sk0_18,tptp0),
inference(cnf_transformation,[status(esa)],[f216]) ).
fof(f221,plain,
! [X0,X1] :
( ~ leaf_occ(X0,sk0_18)
| pd0_0(X0,X1,sk0_18)
| min_precedes(X1,sk0_19(X0,X1),tptp0) ),
inference(cnf_transformation,[status(esa)],[f216]) ).
fof(f222,plain,
! [X109,X110,X111] :
( ~ pd0_0(X111,X110,X109)
| ( occurrence_of(X111,tptp1)
& ? [X112] :
( occurrence_of(X112,tptp2)
& subactivity_occurrence(X112,X109)
& min_precedes(X110,X112,tptp0) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f214]) ).
fof(f223,plain,
! [X109,X110,X111] :
( ~ pd0_0(X111,X110,X109)
| ( occurrence_of(X111,tptp1)
& occurrence_of(sk0_20(X111,X110,X109),tptp2)
& subactivity_occurrence(sk0_20(X111,X110,X109),X109)
& min_precedes(X110,sk0_20(X111,X110,X109),tptp0) ) ),
inference(skolemization,[status(esa)],[f222]) ).
fof(f227,plain,
! [X0,X1,X2] :
( ~ pd0_0(X0,X1,X2)
| min_precedes(X1,sk0_20(X0,X1,X2),tptp0) ),
inference(cnf_transformation,[status(esa)],[f223]) ).
fof(f229,plain,
! [X0] :
( ~ occurrence_of(sk0_18,X0)
| X0 = tptp0 ),
inference(resolution,[status(thm)],[f60,f217]) ).
fof(f327,plain,
leaf_occ(sk0_15(sk0_18),sk0_18),
inference(resolution,[status(thm)],[f200,f217]) ).
fof(f333,plain,
leaf(sk0_15(sk0_18),sk0_14(sk0_18,sk0_15(sk0_18))),
inference(resolution,[status(thm)],[f327,f189]) ).
fof(f334,plain,
occurrence_of(sk0_18,sk0_14(sk0_18,sk0_15(sk0_18))),
inference(resolution,[status(thm)],[f327,f187]) ).
fof(f380,plain,
sk0_14(sk0_18,sk0_15(sk0_18)) = tptp0,
inference(resolution,[status(thm)],[f334,f229]) ).
fof(f403,plain,
leaf(sk0_15(sk0_18),tptp0),
inference(forward_demodulation,[status(thm)],[f380,f333]) ).
fof(f404,plain,
! [X0] : ~ min_precedes(sk0_15(sk0_18),X0,tptp0),
inference(resolution,[status(thm)],[f403,f126]) ).
fof(f652,plain,
! [X0] :
( pd0_0(sk0_15(sk0_18),X0,sk0_18)
| min_precedes(X0,sk0_19(sk0_15(sk0_18),X0),tptp0) ),
inference(resolution,[status(thm)],[f221,f327]) ).
fof(f761,plain,
pd0_0(sk0_15(sk0_18),sk0_15(sk0_18),sk0_18),
inference(resolution,[status(thm)],[f652,f404]) ).
fof(f841,plain,
min_precedes(sk0_15(sk0_18),sk0_20(sk0_15(sk0_18),sk0_15(sk0_18),sk0_18),tptp0),
inference(resolution,[status(thm)],[f761,f227]) ).
fof(f842,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f841,f404]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : PRO011+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 00:06:04 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.20/0.36 % Drodi V3.6.0
% 0.20/0.37 % Refutation found
% 0.20/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.38 % Elapsed time: 0.030293 seconds
% 0.20/0.38 % CPU time: 0.098025 seconds
% 0.20/0.38 % Total memory used: 17.469 MB
% 0.20/0.38 % Net memory used: 17.425 MB
%------------------------------------------------------------------------------