TSTP Solution File: GEO083+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GEO083+1 : TPTP v8.1.2. Released v2.4.0.
% 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 20:17:03 EDT 2024
% Result : Theorem 19.43s 2.82s
% Output : CNFRefutation 19.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 50 ( 7 unt; 0 def)
% Number of atoms : 170 ( 18 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 186 ( 66 ~; 78 |; 34 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 130 ( 118 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [C,C1] :
( part_of(C1,C)
<=> ! [P] :
( incident_c(P,C1)
=> incident_c(P,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,C1,C2] :
( C = sum(C1,C2)
<=> ! [Q] :
( incident_c(Q,C)
<=> ( incident_c(Q,C1)
| incident_c(Q,C2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [C1,C2,C3,P] :
( ( part_of(C2,C3)
& meet(P,C1,C2)
& meet(P,C1,C3) )
=> part_of(sum(C1,C2),sum(C1,C3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [C1,C2,C3,P] :
( ( part_of(C2,C3)
& meet(P,C1,C2)
& meet(P,C1,C3) )
=> part_of(sum(C1,C2),sum(C1,C3)) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [C,C1] :
( part_of(C1,C)
<=> ! [P] :
( ~ incident_c(P,C1)
| incident_c(P,C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f20,plain,
! [C,C1] :
( ( ~ part_of(C1,C)
| ! [P] :
( ~ incident_c(P,C1)
| incident_c(P,C) ) )
& ( part_of(C1,C)
| ? [P] :
( incident_c(P,C1)
& ~ incident_c(P,C) ) ) ),
inference(NNF_transformation,[status(esa)],[f19]) ).
fof(f21,plain,
( ! [C,C1] :
( ~ part_of(C1,C)
| ! [P] :
( ~ incident_c(P,C1)
| incident_c(P,C) ) )
& ! [C,C1] :
( part_of(C1,C)
| ? [P] :
( incident_c(P,C1)
& ~ incident_c(P,C) ) ) ),
inference(miniscoping,[status(esa)],[f20]) ).
fof(f22,plain,
( ! [C,C1] :
( ~ part_of(C1,C)
| ! [P] :
( ~ incident_c(P,C1)
| incident_c(P,C) ) )
& ! [C,C1] :
( part_of(C1,C)
| ( incident_c(sk0_0(C1,C),C1)
& ~ incident_c(sk0_0(C1,C),C) ) ) ),
inference(skolemization,[status(esa)],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ~ part_of(X0,X1)
| ~ incident_c(X2,X0)
| incident_c(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( part_of(X0,X1)
| incident_c(sk0_0(X0,X1),X0) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( part_of(X0,X1)
| ~ incident_c(sk0_0(X0,X1),X1) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f26,plain,
! [C,C1,C2] :
( ( C != sum(C1,C2)
| ! [Q] :
( ( ~ incident_c(Q,C)
| incident_c(Q,C1)
| incident_c(Q,C2) )
& ( incident_c(Q,C)
| ( ~ incident_c(Q,C1)
& ~ incident_c(Q,C2) ) ) ) )
& ( C = sum(C1,C2)
| ? [Q] :
( ( ~ incident_c(Q,C)
| ( ~ incident_c(Q,C1)
& ~ incident_c(Q,C2) ) )
& ( incident_c(Q,C)
| incident_c(Q,C1)
| incident_c(Q,C2) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f2]) ).
fof(f27,plain,
( ! [C,C1,C2] :
( C != sum(C1,C2)
| ( ! [Q] :
( ~ incident_c(Q,C)
| incident_c(Q,C1)
| incident_c(Q,C2) )
& ! [Q] :
( incident_c(Q,C)
| ( ~ incident_c(Q,C1)
& ~ incident_c(Q,C2) ) ) ) )
& ! [C,C1,C2] :
( C = sum(C1,C2)
| ? [Q] :
( ( ~ incident_c(Q,C)
| ( ~ incident_c(Q,C1)
& ~ incident_c(Q,C2) ) )
& ( incident_c(Q,C)
| incident_c(Q,C1)
| incident_c(Q,C2) ) ) ) ),
inference(miniscoping,[status(esa)],[f26]) ).
fof(f28,plain,
( ! [C,C1,C2] :
( C != sum(C1,C2)
| ( ! [Q] :
( ~ incident_c(Q,C)
| incident_c(Q,C1)
| incident_c(Q,C2) )
& ! [Q] :
( incident_c(Q,C)
| ( ~ incident_c(Q,C1)
& ~ incident_c(Q,C2) ) ) ) )
& ! [C,C1,C2] :
( C = sum(C1,C2)
| ( ( ~ incident_c(sk0_1(C2,C1,C),C)
| ( ~ incident_c(sk0_1(C2,C1,C),C1)
& ~ incident_c(sk0_1(C2,C1,C),C2) ) )
& ( incident_c(sk0_1(C2,C1,C),C)
| incident_c(sk0_1(C2,C1,C),C1)
| incident_c(sk0_1(C2,C1,C),C2) ) ) ) ),
inference(skolemization,[status(esa)],[f27]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( X0 != sum(X1,X2)
| ~ incident_c(X3,X0)
| incident_c(X3,X1)
| incident_c(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( X0 != sum(X1,X2)
| incident_c(X3,X0)
| ~ incident_c(X3,X1) ),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( X0 != sum(X1,X2)
| incident_c(X3,X0)
| ~ incident_c(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f33,plain,
! [X0,X1,X2] :
( X0 = sum(X1,X2)
| ~ incident_c(sk0_1(X2,X1,X0),X0)
| ~ incident_c(sk0_1(X2,X1,X0),X2) ),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f34,plain,
! [X0,X1,X2] :
( X0 = sum(X1,X2)
| incident_c(sk0_1(X2,X1,X0),X0)
| incident_c(sk0_1(X2,X1,X0),X1)
| incident_c(sk0_1(X2,X1,X0),X2) ),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f104,plain,
? [C1,C2,C3,P] :
( part_of(C2,C3)
& meet(P,C1,C2)
& meet(P,C1,C3)
& ~ part_of(sum(C1,C2),sum(C1,C3)) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f105,plain,
? [C1,C2,C3] :
( ? [P] :
( part_of(C2,C3)
& meet(P,C1,C2)
& meet(P,C1,C3) )
& ~ part_of(sum(C1,C2),sum(C1,C3)) ),
inference(miniscoping,[status(esa)],[f104]) ).
fof(f106,plain,
( part_of(sk0_14,sk0_15)
& meet(sk0_16,sk0_13,sk0_14)
& meet(sk0_16,sk0_13,sk0_15)
& ~ part_of(sum(sk0_13,sk0_14),sum(sk0_13,sk0_15)) ),
inference(skolemization,[status(esa)],[f105]) ).
fof(f107,plain,
part_of(sk0_14,sk0_15),
inference(cnf_transformation,[status(esa)],[f106]) ).
fof(f110,plain,
~ part_of(sum(sk0_13,sk0_14),sum(sk0_13,sk0_15)),
inference(cnf_transformation,[status(esa)],[f106]) ).
fof(f111,plain,
! [X0,X1,X2] :
( ~ incident_c(X0,sum(X1,X2))
| incident_c(X0,X1)
| incident_c(X0,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f29]) ).
fof(f112,plain,
! [X0,X1,X2] :
( incident_c(X0,sum(X1,X2))
| ~ incident_c(X0,X1) ),
inference(destructive_equality_resolution,[status(esa)],[f30]) ).
fof(f113,plain,
! [X0,X1,X2] :
( incident_c(X0,sum(X1,X2))
| ~ incident_c(X0,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f31]) ).
fof(f161,plain,
! [X0,X1,X2] :
( part_of(sum(X0,X1),X2)
| incident_c(sk0_0(sum(X0,X1),X2),X0)
| incident_c(sk0_0(sum(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[f24,f111]) ).
fof(f164,plain,
! [X0,X1,X2] :
( part_of(X0,sum(X1,X2))
| ~ incident_c(sk0_0(X0,sum(X1,X2)),X2) ),
inference(resolution,[status(thm)],[f25,f113]) ).
fof(f165,plain,
! [X0,X1,X2] :
( part_of(X0,sum(X1,X2))
| ~ incident_c(sk0_0(X0,sum(X1,X2)),X1) ),
inference(resolution,[status(thm)],[f25,f112]) ).
fof(f166,plain,
! [X0,X1,X2] :
( part_of(X0,X1)
| ~ part_of(X2,X1)
| ~ incident_c(sk0_0(X0,X1),X2) ),
inference(resolution,[status(thm)],[f25,f23]) ).
fof(f243,plain,
! [X0] :
( part_of(X0,sk0_15)
| ~ incident_c(sk0_0(X0,sk0_15),sk0_14) ),
inference(resolution,[status(thm)],[f107,f166]) ).
fof(f285,plain,
! [X0,X1,X2,X3] :
( part_of(X0,sum(X1,X2))
| ~ part_of(X3,X2)
| ~ incident_c(sk0_0(X0,sum(X1,X2)),X3) ),
inference(resolution,[status(thm)],[f164,f23]) ).
fof(f342,plain,
! [X0] :
( X0 = sum(X0,X0)
| X0 = sum(X0,X0)
| ~ incident_c(sk0_1(X0,X0,X0),X0) ),
inference(resolution,[status(thm)],[f34,f33]) ).
fof(f343,plain,
! [X0] :
( X0 = sum(X0,X0)
| ~ incident_c(sk0_1(X0,X0,X0),X0) ),
inference(duplicate_literals_removal,[status(esa)],[f342]) ).
fof(f790,plain,
! [X0,X1,X2] :
( part_of(sum(X0,X1),sum(X0,X2))
| incident_c(sk0_0(sum(X0,X1),sum(X0,X2)),X1)
| part_of(sum(X0,X1),sum(X0,X2)) ),
inference(resolution,[status(thm)],[f161,f165]) ).
fof(f791,plain,
! [X0,X1,X2] :
( part_of(sum(X0,X1),sum(X0,X2))
| incident_c(sk0_0(sum(X0,X1),sum(X0,X2)),X1) ),
inference(duplicate_literals_removal,[status(esa)],[f790]) ).
fof(f796,plain,
( spl0_66
<=> part_of(sum(sk0_14,sk0_14),sk0_15) ),
introduced(split_symbol_definition) ).
fof(f797,plain,
( part_of(sum(sk0_14,sk0_14),sk0_15)
| ~ spl0_66 ),
inference(component_clause,[status(thm)],[f796]) ).
fof(f799,plain,
( part_of(sum(sk0_14,sk0_14),sk0_15)
| part_of(sum(sk0_14,sk0_14),sk0_15) ),
inference(resolution,[status(thm)],[f161,f243]) ).
fof(f800,plain,
spl0_66,
inference(split_clause,[status(thm)],[f799,f796]) ).
fof(f1711,plain,
! [X0] :
( X0 = sum(X0,X0)
| X0 = sum(X0,X0) ),
inference(resolution,[status(thm)],[f343,f34]) ).
fof(f1712,plain,
! [X0] : X0 = sum(X0,X0),
inference(duplicate_literals_removal,[status(esa)],[f1711]) ).
fof(f1837,plain,
( part_of(sk0_14,sk0_15)
| ~ spl0_66 ),
inference(forward_demodulation,[status(thm)],[f1712,f797]) ).
fof(f17289,plain,
! [X0,X1,X2] :
( part_of(sum(X0,X1),sum(X0,X2))
| part_of(sum(X0,X1),sum(X0,X2))
| ~ part_of(X1,X2) ),
inference(resolution,[status(thm)],[f791,f285]) ).
fof(f17290,plain,
! [X0,X1,X2] :
( part_of(sum(X0,X1),sum(X0,X2))
| ~ part_of(X1,X2) ),
inference(duplicate_literals_removal,[status(esa)],[f17289]) ).
fof(f20168,plain,
~ part_of(sk0_14,sk0_15),
inference(resolution,[status(thm)],[f17290,f110]) ).
fof(f20169,plain,
( $false
| ~ spl0_66 ),
inference(forward_subsumption_resolution,[status(thm)],[f20168,f1837]) ).
fof(f20170,plain,
~ spl0_66,
inference(contradiction_clause,[status(thm)],[f20169]) ).
fof(f20171,plain,
$false,
inference(sat_refutation,[status(thm)],[f800,f20170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GEO083+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.34 % Computer : n014.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Tue Apr 30 01:33:04 EDT 2024
% 0.11/0.34 % CPUTime :
% 0.11/0.35 % Drodi V3.6.0
% 19.43/2.82 % Refutation found
% 19.43/2.82 % SZS status Theorem for theBenchmark: Theorem is valid
% 19.43/2.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 19.43/2.87 % Elapsed time: 2.519470 seconds
% 19.43/2.87 % CPU time: 19.765221 seconds
% 19.43/2.87 % Total memory used: 148.130 MB
% 19.43/2.87 % Net memory used: 144.534 MB
%------------------------------------------------------------------------------